Free math worksheets

Which operation converts \(3.6\,\text{m}\) to centimeters: multiply by \(100\) or divide by \(100\)? Then give the converted measurement.

A bottle contains \(2500\,\text{mL}\). Which is an equivalent amount: \(0.25\,\text{L}\), \(2.5\,\text{L}\), or \(25\,\text{L}\)?

\(6\,\text{lb}\,12\,\text{oz}\) of candy is shared equally among \(18\) children. How many ounces does each child receive? Use \(1\,\text{lb} = 16\,\text{oz}\).

What fraction of the larger unit is the given measurement? Write each fraction in simplest form. a) \(250\,\text{m}\) of \(1\,\text{km}\) b) \(40\,\text{min}\) of \(1\,\text{hr}\) c) \(375\,\text{g}\) of \(1\,\text{kg}\) d) \(20\,\text{cm}\) of \(1\,\text{m}\) e) \(12\,\text{in}\) of \(1\,\text{yd}\)

Convert each measurement to the specified unit. a) \(450\,\text{mm}\) to centimeters b) \(15\,\text{s}\) to minutes c) \(800\,\text{mg}\) to grams d) \(250\,\text{mL}\) to liters

Convert each measurement to the specified larger unit. Write each result as a fraction in simplest form and as a decimal. a) \(750\,\text{mL}\) to liters b) \(12\,\text{min}\) to hours c) \(50\,\text{cm}\) to meters d) \(1250\,\text{g}\) to kilograms

Convert each value to the specified unit. Use a decimal when needed. a) \(45\,\text{min}\) to hours b) \(250\,\text{mL}\) to liters c) \(1.35\,\text{km}\) to meters

Divide and give each result in the requested units. a) \(11\,\text{m}\div4\): as a decimal in meters and in meters and centimeters b) \(3\,\text{kg}\div5\): as a decimal in kilograms and in grams c) \(9\,\text{L}\div2\): as a decimal in liters and in liters and milliliters

Convert each measurement to the indicated unit. Write each result as a fraction in simplest form. a) \(450\,\text{m}\) in kilometers b) \(12\,\text{min}\) in hours c) \(18\,\text{in}\) in yards d) \(800\,\text{mL}\) in liters

Match each everyday object with a reasonable volume. Use the relative sizes to justify your choices mentally. Objects: - a full cleaning bucket - a large grain silo - a carton of orange juice - a grain of rice - a USB flash drive Volumes: \(30\,\text{mm}^3\), \(8\,\text{cm}^3\), \(1000\,\text{cm}^3\), \(10\,\text{L}\), \(400\,\text{m}^3\)

Evaluate each expression. Give the answer in the unit shown in parentheses. a) \(1.2\,\text{L}+300\,\text{mL}+500\,\text{mL}\) (liters) b) \(20\,\text{L}-15\,\text{L}\) (milliliters)

Convert each measurement to the indicated unit. a) \(\frac{2}{5}\,\text{m}\) to centimeters b) \(\frac{3}{4}\,\text{L}\) to milliliters c) \(\frac{9}{10}\,\text{kg}\) to grams d) \(\frac{1}{8}\,\text{km}\) to meters

A sporting goods store measures the mass and diameter of several balls. Convert each mass from kilograms (\(\text{kg}\)) to grams (\(\text{g}\)) and each diameter from meters (\(\text{m}\)) to centimeters (\(\text{cm}\)). <table> <tr> <th>Ball</th> <th>Basketball</th> <th>Soccer ball</th> <th>Handball</th> <th>Tennis ball</th> </tr> <tr> <th>Mass</th> <td>\(0.625\,\text{kg}\)</td> <td>\(0.430\,\text{kg}\)</td> <td>\(0.375\,\text{kg}\)</td> <td>\(0.058\,\text{kg}\)</td> </tr> <tr> <th>Diameter</th> <td>\(0.24\,\text{m}\)</td> <td>\(0.22\,\text{m}\)</td> <td>\(0.19\,\text{m}\)</td> <td>\(0.07\,\text{m}\)</td> </tr> </table>

Convert each mass to grams (\(\text{g}\)): a) \(1.500\,\text{kg}\) b) \(0.725\,\text{kg}\) c) \(0.040\,\text{kg}\) d) \(3.005\,\text{kg}\)

Convert each amount to liters (\(\text{L}\)). Write each answer as a decimal number. \(5000\,\text{mL}\); \(800\,\text{mL}\); \(1500\,\text{mL}\); \(200\,\text{mL}\); \(600\,\text{mL}\)

Compare the capacities. Insert \(<\), \(>\), or \(=\). a) \(0.5\,\text{L}\ \_\_\_\ 500\,\text{mL}\) b) \(1200\,\text{mL}\ \_\_\_\ 1.5\,\text{L}\) c) \(1\,\text{L}\ 20\,\text{mL}\ \_\_\_\ 1.2\,\text{L}\) d) \(0.3\,\text{L}\ \_\_\_\ 30\,\text{mL}\) e) \(250\,\text{mL}\ \_\_\_\ 0.25\,\text{L}\)

Fill in each missing measurement. a) \(\frac{3}{4}\,\text{hr}=\_\_\_\,\text{min}\) b) \(130\,\text{min}=\_\_\_\,\text{hr}\ \_\_\_\,\text{min}\) c) \(1\,\text{hr}\ 25\,\text{min}=\_\_\_\,\text{min}\) d) \(0.5\,\text{L}=\_\_\_\,\text{mL}\) e) \(1.25\,\text{L}=\_\_\_\,\text{mL}\)

Write each mass as a decimal number of kilograms, \(\text{kg}\). Use three decimal places to show grams. a) \(3250\,\text{g}\) b) \(805\,\text{g}\) c) \(12{,}004\,\text{g}\)

Write each mixed-unit mass as a decimal number of kilograms. a) \(5\,\text{kg}\ 70\,\text{g}\) b) \(18\,\text{kg}\ 205\,\text{g}\) c) \(0\,\text{kg}\ 9\,\text{g}\)

Complete the table. <table> <tr> <td>Fraction form</td> <td>Mass in grams</td> <td>Decimal form in kilograms</td> </tr> <tr> <td>\(\frac{1}{2}\,\text{kg}\)</td> <td>\(500\,\text{g}\)</td> <td>\(0.500\,\text{kg}\)</td> </tr> <tr> <td>\(\frac{1}{4}\,\text{kg}\)</td> <td>...</td> <td>...</td> </tr> <tr> <td>\(\frac{3}{4}\,\text{kg}\)</td> <td>...</td> <td>...</td> </tr> </table>

Fill in each missing length unit. Use millimeters, centimeters, meters, or kilometers. a) \(13\,\text{m}=1300\,\square\) b) \(5\,\text{m}=500\,\square\) c) \(8000\,\text{m}=8\,\square\) d) \(4\,\square=40\,\text{mm}\)

Convert each measurement to the indicated unit. Write the missing numerical value. a) \(12\,\text{m}=\square\,\text{cm}\) b) \(900\,\text{cm}=\square\,\text{m}\) c) \(7\,\text{km}=\square\,\text{m}\) d) \(250\,\text{mm}=\square\,\text{cm}\)

Write \(<\), \(>\), or \(=\) in each blank. a) \(400\,\text{m}\ \square\ 4\,\text{km}\) b) \(300\,\text{cm}\ \square\ 3\,\text{m}\) c) \(25\,\text{cm}\ \square\ 250\,\text{mm}\) d) \(5\,\text{m}\ \square\ 550\,\text{cm}\)

Convert each length to the unit in parentheses. a) \(5200\,\text{mm}\) (centimeters) b) \(14\,\text{m}\ 5\,\text{cm}\) (centimeters) c) \(3200\,\text{cm}\) (meters) d) \(9\,\text{km}\ 75\,\text{m}\) (meters) e) \(63\,\text{cm}\) (millimeters)

Which measurements describe the same length? Find the three matching pairs. A: \(400\,\text{cm}\) B: \(40\,\text{m}\) C: \(40\,\text{cm}\) D: \(400\,\text{mm}\) E: \(4000\,\text{mm}\) F: \(4000\,\text{cm}\)

Julia says, “\(0.8\,\text{m}\) is shorter than \(75\,\text{cm}\) because \(0.8\) is less than \(75\).” Is Julia correct? Convert the measurements to the same unit and explain.

Two measuring cups contain water. The first contains \(0.4\,\text{L}\), and the second contains \(350\,\text{mL}\). Which cup contains more water, and by how many milliliters?

Four lengths are shown. A: \(4.6\,\text{m}\) B: \(540\,\text{cm}\) C: \(0.006\,\text{km}\) D: \(460\,\text{mm}\) Which two measurements have a combined length of exactly \(10\,\text{m}\)? Justify your choice by converting all four measurements to meters.

Fill in each missing number or unit so the equation is true. a) \(4.2\,\text{m}=4\,\text{m}\ \square\,\text{cm}\) b) \(520\,\text{mm}=52\,\square\) c) \(3\,\text{cm}\ 4\,\text{mm}=\square\,\text{mm}\) d) \(0.8\,\text{m}=\square\,\text{cm}\)

Fill in each missing value or unit. a) \(12.5\,\text{km}=12\,\text{km}\ \square\,\text{m}\) b) \(705\,\text{cm}=7\,\square\ 5\,\text{cm}\) c) \(2\,\text{m}\ 3\,\text{cm}=203\,\square\) d) \(1500\,\text{m}=1.5\,\square\)

Fill in each missing number or unit. a) \(8\,\text{cm}\ 9\,\text{mm}=\square\,\text{mm}\) b) \(1.03\,\text{m}=1\,\text{m}\ 3\,\square\) c) \(600\,\text{cm}=\square\,\text{m}\) d) \(4500\,\text{m}=\square\,\text{km}\)

Convert each length to the specified smaller unit. a) \(4.2\,\text{km}\) to meters b) \(17\,\text{m}\) to centimeters c) \(0.5\,\text{m}\) to centimeters d) \(240\,\text{cm}\) to millimeters

Write each length using the indicated mixed units. a) Write \(842\,\text{cm}\) in meters and centimeters. b) Write \(305\,\text{cm}\) in meters and centimeters. c) Write \(2007\,\text{mm}\) in meters and millimeters. d) Write \(95\,\text{mm}\) in centimeters and millimeters.

Pair the measurements that have the same weight. Which measurement has no partner? Explain by converting between pounds and ounces. \(7.5\,\text{lb}\); \(72\,\text{oz}\); \(5\,\text{lb}\); \(120\,\text{oz}\); \(80\,\text{oz}\)

Convert each length to the unit in parentheses. a) \(7.2\,\text{m}\) (centimeters) b) \(540\,\text{cm}\) (meters) c) \(20\,\text{cm}\ 8\,\text{mm}\) (millimeters) d) \(9000\,\text{mm}\) (centimeters)

For each pair, determine which length is longer and by how much. Give each difference in centimeters. a) \(2.8\,\text{m}\) and \(265\,\text{cm}\) b) \(0.004\,\text{km}\) and \(390\,\text{cm}\)

Write \(<\), \(>\), or \(=\) in each box. a) \(230\,\text{mm}\ \square\ 2.3\,\text{cm}\) b) \(1.5\,\text{m}\ \square\ 150\,\text{cm}\) c) \(47\,\text{cm}\ \square\ 407\,\text{mm}\) d) \(0.8\,\text{km}\ \square\ 800\,\text{m}\)

Order the lengths from least to greatest using \(<\). \(75\,\text{cm}\); \(0.8\,\text{m}\); \(720\,\text{mm}\); \(71\,\text{cm}\)

Convert \(4\,\text{kg}\ 20\,\text{g}\), \(420\,\text{g}\), \(4002\,\text{g}\), and \(0.42\,\text{kg}\) to grams. Then order the original measurements from least to greatest.

Convert \(5\,\text{m}\ 8\,\text{cm}\), \(580\,\text{cm}\), \(508\,\text{mm}\), and \(5.8\,\text{m}\) to centimeters. Then order the original measurements from greatest to least.

Convert \(2\,\text{L}\ 500\,\text{mL}\), \(2050\,\text{mL}\), \(2.5\,\text{L}\), and \(25\,\text{mL}\) to milliliters. Then order the original measurements from least to greatest.

Calculate each result and write it using mixed units of meters and centimeters. a) \(86\,\text{cm} + 45\,\text{cm}\) b) \(264\,\text{cm} - 0.84\,\text{m}\)

Convert each mass to the unit in parentheses. a) \(8\,\text{kg}\ 150\,\text{g}\) (grams) b) \(450\,\text{g}\) (kilograms) c) \(1.5\,\text{g}\) (milligrams) d) \(7200\,\text{mg}\) (grams)

Convert each length to the unit in parentheses. a) \(2.75\,\text{km}\) (meters) b) \(80\,\text{cm}\) (meters) c) \(4\,\text{m}\ 3\,\text{cm}\) (centimeters) d) \(5\,\text{cm}\) (millimeters)

Fill in each missing unit or numerical value. a) \(5600\,\text{g}=5.6\,\square\) b) \(12\,\text{cm}=\square\,\text{mm}\) c) \(0.25\,\text{km}=250\,\square\) d) \(35\,\text{g}=\square\,\text{mg}\)

Rewrite each decimal mass without a decimal, using mixed units when needed. a) \(5.4\,\text{kg}\) b) \(0.025\,\text{kg}\) c) \(10.705\,\text{kg}\) d) \(0.008\,\text{g}\)

Complete the table for each mass. <table> <tr> <td>Mass in grams</td> <td>\(7040\,\text{g}\)</td> <td></td> <td></td> <td>\(12{,}300\,\text{g}\)</td> </tr> <tr> <td>Mass in kilograms and grams</td> <td></td> <td>\(5\,\text{kg}\ 8\,\text{g}\)</td> <td></td> <td></td> </tr> <tr> <td>Decimal mass in kilograms</td> <td></td> <td></td> <td>\(0.015\,\text{kg}\)</td> <td></td> </tr> </table>

Write \(<\), \(>\), or \(=\) in each box. Convert to a common unit first. a) \(2\,\text{km}\ 50\,\text{m}\ \square\ 2.5\,\text{km}\) b) \(0.08\,\text{km}\ \square\ 80\,\text{m}\) c) \(1205\,\text{m}\ \square\ 1\,\text{km}\ 25\,\text{m}\) d) \(3.007\,\text{km}\ \square\ 3007\,\text{m}\)

Order the lengths from least to greatest. \(40.5\,\text{cm}\); \(4005\,\text{mm}\); \(4\,\text{m}\ 5\,\text{cm}\); \(0.004\,\text{km}\); \(420\,\text{cm}\); \(4.5\,\text{m}\)

Order the masses from least to greatest. \(850\,\text{g}\); \(0.805\,\text{kg}\); \(8\,\text{kg}\); \(8050\,\text{g}\); \(8.5\,\text{kg}\); \(85\,\text{g}\)

Order the capacities from least to greatest. \(1250\,\text{mL}\); \(1.2\,\text{L}\); \(0.125\,\text{L}\); \(1025\,\text{mL}\); \(1.205\,\text{L}\); \(12\,\text{L}\)

Convert each mass to the unit in parentheses. a) \(75\,\text{g}\) (kilograms) b) \(4000\,\text{g}\) (kilograms) c) \(850\,\text{g}\) (kilograms) d) \(1.2\,\text{g}\) (milligrams)

Write \(<\), \(>\), or \(=\) in each blank. a) \(0.3\,\text{kg}\ \square\ 30\,\text{g}\) b) \(\frac{1}{2}\,\text{kg}\ \square\ 500\,\text{g}\) c) \(1200\,\text{mg}\ \square\ 1.2\,\text{g}\) d) \(0.07\,\text{kg}\ \square\ 700\,\text{g}\)

A storage bin contains \(9\,\text{lb}\) of coffee beans. The beans are packed into \(8\)-ounce bags. How many full bags can be filled? Use \(1\,\text{lb} = 16\,\text{oz}\).

Convert each time measurement to the unit in parentheses. a) \(8\,\text{h}\) (minutes) b) \(360\,\text{s}\) (minutes) c) \(3\,\text{days}\) (hours) d) \(540\,\text{min}\) (hours)

Write each time interval entirely in the smaller unit shown. a) \(4\,\text{min}\ 12\,\text{s}\) b) \(2\,\text{h}\ 45\,\text{min}\) c) \(1\,\text{day}\ 10\,\text{h}\)

Write each mixed measurement entirely in the smaller unit. a) \(2\,\text{kg}\ 450\,\text{g}\) b) \(15\,\text{kg}\ 30\,\text{g}\) c) \(9\,\text{km}\ 75\,\text{m}\) d) \(4\,\text{m}\ 25\,\text{cm}\)

Write each amount entirely in cents. a) \(\$5.75\) b) \(\$12.05\) c) \(\$110.10\) d) \(\$2.04\)

An intercity train trip takes exactly \(2\,\text{h}\ 17\,\text{min}\). Write the entire travel time in minutes.

Write each time measurement using mixed units. a) \(450\,\text{s}\) b) \(190\,\text{min}\) c) \(2.5\,\text{h}\) d) \(62\,\text{h}\)

Which time measurements are equivalent? Match each letter to a number. A: \(130\,\text{s}\) B: \(2\,\text{h}\ 15\,\text{min}\) C: \(85\,\text{min}\) 1: \(135\,\text{min}\) 2: \(2\,\text{min}\ 10\,\text{s}\) 3: \(1\,\text{h}\ 25\,\text{min}\)

A computer needs \(3000\,\text{min}\) to complete a large update. Write this time in days, hours, and minutes.

Calculate: \(3\,\text{days}\ 18\,\text{h}\div15\)

Convert each measurement to the unit in parentheses. Use decimals when needed. a) \(45\,\text{mm}\) (centimeters); \(0.32\,\text{m}\) (centimeters); \(1\,\text{m}\ 5\,\text{cm}\) (centimeters) b) \(2700\,\text{g}\) (kilograms); \(4000\,\text{g}\) (kilograms); \(15\,\text{kg}\ 500\,\text{g}\) (kilograms)

Write \(<\), \(>\), or \(=\) in each blank. Convert one measurement to the other unit before comparing. a) \(2500\,\text{m}\ \square\ 2.5\,\text{km}\) b) \(75\,\text{min}\ \square\ 1.5\,\text{h}\) c) \(300\,\text{mg}\ \square\ 0.3\,\text{g}\) d) \(1\,\text{kg}\ 50\,\text{g}\ \square\ 1500\,\text{g}\)

Write each mixed measurement as a decimal in the larger unit. Example: \(3\,\text{m}\ 4\,\text{cm}=3.04\,\text{m}\). a) \(8\,\text{km}\ 20\,\text{m}\) b) \(5\,\text{kg}\ 7\,\text{g}\) c) \(12\,\text{m}\ 40\,\text{cm}\) d) \(3\,\text{L}\ 5\,\text{mL}\)

Fill in each missing number or unit. a) \(4\,\text{km}\ 12\,\text{m}=\square\,\text{m}\) b) \(7\,\text{kg}\ \square\,\text{g}=7005\,\text{g}\) c) \(2\,\text{m}\ 3\,\text{cm}\ 5\,\text{mm}=\square\,\text{mm}\) d) \(12\,\text{kg}\ 80\,\text{g}=12{,}080\,\square\)

Measurements can be written as decimals or with mixed units. Fill in each blank. a) \(5.4\,\text{m}=5\,\text{m}\ \square\,\text{cm}\) b) \(3.02\,\text{kg}=3\,\text{kg}\ \square\,\text{g}\) c) \(0.75\,\text{m}=\square\,\text{cm}\) d) \(8.1\,\text{cm}=8\,\text{cm}\ \square\,\text{mm}\)

Find each missing value. a) \(3\,\text{days}\ 4\,\text{h}=\square\,\text{h}\) b) \(2\,\text{h}\ 15\,\text{min}=\square\,\text{min}\) c) \(\square\,\text{h}\ 20\,\text{min}=200\,\text{min}\) d) \(1.5\,\text{h}=\square\,\text{min}\)

Write \(<\), \(>\), or \(=\) to make each statement true. a) \(2\,\text{km}\ 50\,\text{m}\ \square\ 2005\,\text{m}\) b) \(0.12\,\text{m}\ \square\ 12\,\text{cm}\) c) \(60\,\text{mm}\ \square\ 0.06\,\text{m}\)

Amira writes \(6.5\,\text{m} + 250\,\text{cm} = 256.5\,\text{m}\). Explain the error and find the correct result in meters.

Rewrite each measurement without a decimal, using mixed units when needed. a) \(12.050\,\text{km}\) b) \(4.07\,\text{m}\) c) \(0.625\,\text{kg}\) d) \(30.2\,\text{kg}\)

Rewrite each measurement without a decimal, using mixed units when needed. a) \(4.5\,\text{h}\) b) \(1.5\,\text{min}\) c) \(8.005\,\text{L}\) d) \(0.45\,\text{L}\)

Complete the missing equivalent forms. a) \(6.305\,\text{km}=\square\,\text{km}\ \square\,\text{m}=\square\,\text{m}\) b) \(15\,\text{kg}\ 400\,\text{g}=\square\,\text{kg}=\square\,\text{g}\) c) \(0.08\,\text{m}=\square\,\text{cm}\)

Write \(<\), \(>\), or \(=\) in each box. a) \(12\,\text{cm}\ 5\,\text{mm}\ \square\ 12.05\,\text{cm}\) b) \(3\,\text{km}\ 20\,\text{m}\ \square\ 3.2\,\text{km}\) c) \(450\,\text{m}\ \square\ 0.45\,\text{km}\)

Write \(<\), \(>\), or \(=\) in each box. a) \(4\,\text{kg}\ 50\,\text{g}\ \square\ 4.5\,\text{kg}\) b) \(0.8\,\text{kg}\ \square\ 80\,\text{g}\) c) \(2500\,\text{mg}\ \square\ 2.5\,\text{g}\)

Write \(<\), \(>\), or \(=\) in each box. a) \(1\,\text{h}\ 45\,\text{min}\ \square\ 100\,\text{min}\) b) \(3\,\text{min}\ 12\,\text{s}\ \square\ 192\,\text{s}\) c) \(2\,\text{days}\ 4\,\text{h}\ \square\ 50\,\text{h}\)

Write each length as a decimal in the unit in parentheses. a) \(6\,\text{m}\ 30\,\text{cm}\) (meters) b) \(25\,\text{cm}\) (meters) c) \(8\,\text{km}\ 75\,\text{m}\) (kilometers)

Write each mixed area measurement in the unit shown in parentheses. a) \(2\,\text{yd}^2\ 9\,\text{ft}^2\) \((\text{yd}^2)\) b) \(1\,\text{m}^2\ 20\,\text{cm}^2\) \((\text{cm}^2)\)

Convert each area measurement to the requested unit. a) \(12\,\text{m}^2\) to square centimeters b) \(0.5\,\text{m}^2\) to square centimeters c) \(7\,\text{yd}^2\) to square feet d) \(13.4\,\text{cm}^2\) to square millimeters

Compare each pair of area measurements. Insert \(<\), \(>\), or \(=\). a) \(5\,\text{m}^2\ \underline{\hspace{0.6cm}}\ 45{,}000\,\text{cm}^2\) b) \(0.2\,\text{yd}^2\ \underline{\hspace{0.6cm}}\ 1.8\,\text{ft}^2\) c) \(850\,\text{mm}^2\ \underline{\hspace{0.6cm}}\ 8.5\,\text{cm}^2\) d) \(1\,\text{ft}^2\ \underline{\hspace{0.6cm}}\ 150\,\text{in}^2\)

Convert each area measurement to the requested unit. a) \(1400\,\text{mm}^2\) to \(\text{cm}^2\) b) \(252\,\text{ft}^2\) to \(\text{yd}^2\) c) \(8000\,\text{cm}^2\) to \(\text{m}^2\) d) \(720\,\text{in}^2\) to \(\text{ft}^2\)

Convert each area measurement to the unit in parentheses. a) \(450\,\text{ft}^2\) \((\text{in}^2)\) b) \(6\,\text{yd}^2\) \((\text{ft}^2)\) c) \(288\,\text{ft}^2\) \((\text{yd}^2)\)

Write each mixed area measurement using the smaller of the two units. a) \(5\,\text{yd}^2\ 20\,\text{ft}^2\) b) \(12\,\text{ft}^2\ 7\,\text{in}^2\) c) \(4\,\text{m}^2\ 9\,\text{cm}^2\) d) \(1\,\text{m}^2\ 1500\,\text{cm}^2\)

Calculate each result and write it in the smaller unit used in the expression. a) \(7\,\text{yd}^2+15\,\text{ft}^2\) b) \(12\,\text{ft}^2-400\,\text{in}^2\) c) \(1\,\text{yd}^2+50\,\text{ft}^2\)

Convert each area measurement to square feet. a) \(7\,\text{yd}^2\ 12\,\text{ft}^2\) b) \(432\,\text{in}^2\) c) \(2\,\text{yd}^2\ 5\,\text{ft}^2\) d) \(10\,\text{yd}^2\) e) \(6480\,\text{in}^2\)

Complete each statement about area-unit conversion. a) To convert \(1800\,\text{mm}^2\) to square centimeters, divide the numerical value by _____. The result is _____ \(\text{cm}^2\). b) To convert \(0.45\,\text{m}^2\) to square centimeters, multiply the numerical value by _____. The result is _____ \(\text{cm}^2\).

A square cloth has an area of \(0.25\,\text{m}^2\). Find its area in square centimeters. Describe the conversion factor you use.

Which area is greatest? Convert all three measurements to square inches before comparing. A: \(5\,\text{ft}^2\ 4\,\text{in}^2\) B: \(540\,\text{in}^2\) C: \(5\,\text{ft}^2\ 40\,\text{in}^2\)

Convert each measurement to the unit in parentheses. a) \(34\,\text{m}\) (centimeters) b) \(8000\,\text{g}\) (kilograms) c) \(4000\,\text{g}\) (kilograms) d) \(120\,\text{min}\) (hours) e) \(70\,\text{cm}\) (meters)

Find each missing value. a) \(2.5\,\text{kg}=\square\,\text{g}\) b) \(3\,\text{h}\ 15\,\text{min}=\square\,\text{min}\) c) \(12\,\text{cm}\ 5\,\text{mm}=\square\,\text{mm}\) d) \(1.25\,\text{m}=\square\,\text{cm}\)

Convert each fractional measurement to the smaller unit. a) How many grams are in one-half kilogram? b) How many centimeters are in one-fifth meter? c) How many grams are in one-tenth kilogram?

Convert each fractional amount to the smaller unit. a) How many minutes are in \(\frac{1}{10}\) hour? b) How many milliliters are in \(\frac{3}{4}\) liter? c) How many grams are in \(\frac{2}{5}\) kilogram?

Convert each fractional measurement to the smaller unit. a) One-fifth liter in milliliters b) Two-fifths kilometer in meters c) One-eighth kilogram in grams

Complete the table for each money amount. <table> <thead><tr><th>Decimal dollars</th><th>Dollars and cents</th><th>Cents only</th></tr></thead> <tbody> <tr><td>\(\$15.24\)</td><td>...</td><td>...</td></tr> <tr><td>...</td><td>\(\$6\) and \(2\) cents</td><td>...</td></tr> <tr><td>...</td><td>...</td><td>\(90\) cents</td></tr> <tr><td>\(\$0.05\)</td><td>...</td><td>...</td></tr> </tbody> </table>

Fill in the blanks so each chain is correct. a) \(\$24.08=\$\square\) and \(\square\) cents \(=\square\) cents b) \(\$\square=\$3\) and \(70\) cents \(=\square\) cents c) \(\$\square=\$\square\) and \(\square\) cents \(=1005\) cents d) \(\$0.40=\$\square\) and \(\square\) cents \(=\square\) cents

How much time remains in a \(24\)-hour day after \(5\,\text{h}\ 18\,\text{min}\) have passed?

Evaluate each expression and give the result in the smaller unit. a) \(\frac{3}{10}\,\text{km}+450\,\text{m}\) b) \(1\,\text{h}-\frac{1}{12}\,\text{h}\) c) \(\frac{1}{4}\,\text{metric ton}-120\,\text{kg}\) d) \(\frac{7}{20}\,\text{L}+150\,\text{mL}\) For part c, use \(1\,\text{metric ton}=1000\,\text{kg}\).

Compare the values. Insert \(<\), \(>\), or \(=\). First evaluate each quotient and express both sides in the same unit. a) \(5\,\text{m}\div4\ \square\ 120\,\text{cm}\) b) \(1\,\text{kg}\div8\ \square\ 125\,\text{g}\) c) \(7\,\text{km}\div10\ \square\ 0.75\,\text{km}\)

Evaluate both expressions in square feet and compare the results. Which result is greater? Expression A: \(6\,\text{yd}^2\div8\) Expression B: \(70\,\text{ft}^2\div10\)

Compare each pair of measurements. State which measurement is greater and justify your answer by converting both measurements to the same unit. a) \(\frac{2}{5}\,\text{L}\) or \(450\,\text{mL}\) b) \(18\,\text{min}\) or \(\frac{1}{4}\,\text{hr}\) c) \(\frac{7}{20}\,\text{kg}\) or \(320\,\text{g}\)

Calculate each sum. Write each answer as a fraction in simplest form using the larger unit. a) \(25\,\text{cm} + \frac{1}{2}\,\text{m}\) b) \(150\,\text{g} + \frac{3}{4}\,\text{kg}\) c) \(10\,\text{min} + \frac{1}{6}\,\text{h}\)

Convert each measurement to the unit in parentheses. Then round to the nearest whole unit. a) \(675\,\text{m}\) (kilometers) b) \(1840\,\text{m}\) (kilometers) c) \(1456\,\text{g}\) (kilograms) d) \(1250\,\text{mL}\) (liters)

Three containers hold different amounts of water: Container A: \(2400\,\text{cm}^3\) Container B: \(2350\,\text{mL}\) Container C: \(2.6\,\text{dm}^3\) Use \(1000\,\text{cm}^3=1\,\text{L}\), \(1000\,\text{mL}=1\,\text{L}\), and \(1\,\text{dm}^3=1\,\text{L}\). Round each amount to the nearest whole liter. Which container has the greatest rounded volume?

Two packages are weighed. Package A weighs \(39\,\text{oz}\), and Package B weighs \(2.55\,\text{lb}\). a) What is each weight rounded to the nearest whole pound? b) Are the rounded weights different? Explain why this happens even though the actual weights are close.

Three friends compare their routes to school. Lucas walks \(\frac{3}{4}\) mile, Mia walks \(1200\) yards, and Ben walks \(\frac{4}{5}\) mile. Order the routes from shortest to longest.

Marisol needs \(\frac{3}{8}\) quart of cream for a soup recipe. The carton contains \(2\) cups of cream. How many fluid ounces of cream will remain after the recipe is made?

Find what fraction the combined area of \(100\,\text{yd}^2\) and \(140\,\text{yd}^2\) is of a total area of \(3600\,\text{ft}^2\). Write the fraction in simplest form.

Four packages have weights written in different forms. - Package A: \(40\,\text{oz}\) - Package B: \(20\,\text{lb}\) - Package C: \(2.05\,\text{lb}\) - Package D: \(2\,\text{lb}\ 0.8\,\text{oz}\) a) Convert every weight to pounds. b) Order the packages from lightest to heaviest.

Four students compare the weights of their lunch bags. - Alex: \(3.45\,\text{lb}\) - Mia: \(48.8\,\text{oz}\) - Jordan: \(3.6\,\text{lb}\) - Sam: \(3\frac{1}{2}\,\text{lb}\) Order the lunch bags from heaviest to lightest. Briefly explain why Mia’s bag is not the heaviest even though \(48.8\) is the largest numerical value shown.

A construction site receives these materials: - Sand: \(0.8\,\text{ton}\) - Gravel: \(1700\,\text{lb}\) - Cement: \(0.09\,\text{ton}\) - Water: \(240\,\text{lb}\) a) Find the total weight in tons. b) Which material has the second-greatest weight? Use \(1\,\text{ton} = 2000\,\text{lb}\).

A shelf can safely hold at most \(30\,\text{lb}\). Four packages on the shelf weigh \(7 \frac{1}{2}\,\text{lb}\), \(4 \frac{1}{4}\,\text{lb}\), \(9 \frac{3}{4}\,\text{lb}\), and \(3 \frac{1}{2}\,\text{lb}\). Can another package weighing \(72\,\text{oz}\) be added safely? Explain.

A beverage dispenser holds at most \(5 \frac{1}{4}\) gallons. It already contains \(1 \frac{1}{2}\) gallons of orange juice, \(\frac{3}{4}\) gallon of apple juice, \(1 \frac{1}{2}\) gallons of sparkling water, and \(\frac{3}{4}\) gallon of grape juice. Can \(13\) more cups of cherry juice be added without overflowing the dispenser? Explain.

A flatbed truck can carry at most \(12 \frac{1}{8}\) tons. It is already carrying loads of \(2 \frac{3}{8}\) tons, \(3 \frac{1}{2}\) tons, \(1 \frac{3}{4}\) tons, and \(2 \frac{1}{2}\) tons. A pallet weighing \(4200\,\text{lb}\) is ready to be added. Find the truck's remaining capacity and decide whether the pallet can be loaded safely.

For a simplified scale comparison, take a red blood cell diameter as \(0.008\,\text{mm}\) and a small blood vessel's inside diameter as \(0.032\,\text{mm}\). a) Convert both measurements to micrometers \((\mu\text{m})\). Use \(1\,\text{mm}=1000\,\mu\text{m}\). b) How many times as large is the blood vessel's diameter as the blood cell's diameter?

In a particle-size model, Particle A has diameter \(0.024\,\text{mm}\), Particle B has diameter \(0.006\,\text{mm}\), and Particle C has diameter \(0.3\,\mu\text{m}\). Use \(1\,\text{mm}=1000\,\mu\text{m}\). a) How many Particle B diameters placed end to end equal one Particle A diameter? b) How many Particle C diameters placed end to end equal one Particle B diameter?

A workshop receives a box containing \(400\) identical metal washers. The full box weighs \(1.58\,\text{kg}\), and the empty box weighs \(140\,\text{g}\). a) Find the weight of one washer in grams. b) How many grams do \(10\) washers weigh?

A room is \(12.5\,\text{ft}\) long. a) Find the room length in inches. b) A hallway runner is \(12\,\text{ft}\ 8\,\text{in}\) long. Will it fit lengthwise in the room? Justify your answer by comparing the lengths in the same unit.

A rectangular container has a volume of \(2.5\,\text{dm}^3\). a) Express this volume in liters, milliliters, and cubic centimeters. b) What do you notice when you compare the numerical values in liters and cubic decimeters, and in milliliters and cubic centimeters?

Express \(0.045\,\text{m}^3\) first in cubic decimeters and then in cubic centimeters.

Find the sum \(V=1.2\,\text{dm}^3+800\,\text{cm}^3\). Give \(V\) in both liters and cubic centimeters.

A water bottle has a capacity of \(750\,\text{mL}\). a) How many cubic centimeters of water fit in the bottle? b) Assume that \(1\,\text{cm}^3\) of water has a mass of exactly \(1\,\text{g}\). Find the mass of the water in a full bottle in kilograms.

Two containers are being compared. Container A holds \(2.05\,\text{L}\) of water. Container B holds \(1\,\text{L}+800\,\text{mL}\) of juice. a) Which container holds more liquid? b) Find the total amount of liquid in both containers in liters, written as a decimal. c) Write the total as a sum of whole liters and milliliters.

Convert each volume to the requested unit. a) \(4\frac{3}{4}\,\text{m}^3\) to \(\text{dm}^3\) b) \(0.2\,\text{dm}^3\) to \(\text{cm}^3\) c) \(1\frac{1}{2}\,\text{cm}^3\) to \(\text{mm}^3\) d) \(2\frac{1}{4}\,\text{L}\) to \(\text{mL}\)

A rectangular aquarium has a total capacity of \(120\,\text{L}\). a) Express this volume in cubic decimeters. b) The aquarium is currently \(\frac{3}{4}\) full. Find the volume of water in cubic centimeters.

Compare each pair of volumes. Write \(<\), \(>\), or \(=\). a) \(\frac{1}{4}\,\text{m}^3\quad\Box\quad250\,\text{L}\) b) \(3\frac{1}{5}\,\text{dm}^3\quad\Box\quad320\,\text{cm}^3\) c) \(0.8\,\text{L}\quad\Box\quad850\,\text{mL}\) d) \(\frac{1}{20}\,\text{cm}^3\quad\Box\quad50\,\text{mm}^3\)

Three containers hold water. Container A holds \(0.05\,\text{m}^3\), Container B holds \(48\,\text{L}\), and Container C holds \(52{,}000\,\text{cm}^3\). Order the containers from least to greatest amount of water. Justify your order by converting every volume to liters.

A large tank has a capacity of exactly \(1\,\text{m}^3\). It already contains \(650\,\text{dm}^3\) of water and \(120\,\text{L}\) of oil. How many cubic decimeters of space remain before the tank is full?

Write each volume as a fraction of the indicated larger unit. Write each fraction in simplest form. a) \(15\,\text{cm}^3\) in \(\text{dm}^3\) b) \(800\,\text{mL}\) in \(\text{L}\) c) \(125\,\text{dm}^3\) in \(\text{m}^3\) d) \(600\,\text{mm}^3\) in \(\text{cm}^3\) e) \(350\,\text{mL}\) in \(\text{L}\)

A science lab has \(1.35\,\text{dm}^3\) of liquid in a container. Another \(275\,\text{cm}^3\) is added. a) What is the total volume in cubic centimeters? b) What is the same total volume in milliliters? c) Explain why the numerical answers to a) and b) are the same.

A class is making fruit punch. They combine: - \(1\frac{1}{4}\,\text{L}\) of apple juice - \(0.8\,\text{L}\) of sparkling water - \(750\,\text{mL}\) of orange juice - \(\frac{1}{5}\,\text{L}\) of berry syrup - \(50\,\text{mL}\) of lemon juice Will all the punch fit in a bowl that holds \(3\,\text{L}\)? Find the total volume and explain your decision.

A relay course has six sections with these lengths: \(1.45\,\text{mi}\), \(\frac{3}{4}\,\text{mi}\), \(2.55\,\text{mi}\), \(0.25\,\text{mi}\), \(1\frac{1}{2}\,\text{mi}\), and \(880\,\text{yd}\). Find the total length. Group the values strategically and explain which values you combined.

Convert each measurement to the smaller unit. a) \(\frac{7}{12}\,\text{yd}\) to inches b) \(\frac{11}{16}\,\text{ft}^2\) to square inches c) \(\frac{17}{32}\,\text{gal}\) to fluid ounces d) \(\frac{5}{8}\,\text{lb}\) to ounces

Compare the measurements. Insert \(<\), \(>\), or \(=\). a) \(\frac{3}{8}\,\text{km}\ \square\ 370\,\text{m}\) b) \(\frac{4}{5}\,\text{L}\ \square\ 800\,\text{mL}\) c) \(\frac{7}{16}\,\text{ft}^2\ \square\ 64\,\text{in}^2\) d) \(\frac{13}{20}\,\text{kg}\ \square\ 640\,\text{g}\)

A case contains \(12\) identical juice pouches. The full case weighs \(2.7\,\text{kg}\), and the empty cardboard case weighs \(60\,\text{g}\). Find the weight of one juice pouch in grams.

Convert each area measurement to the requested unit. a) \(0.8\,\text{m}^2\) to square centimeters b) \(12{,}500\,\text{mm}^2\) to square centimeters c) \(5\,\text{yd}^2\) to square feet d) \(3400\,\text{cm}^2\) to square meters

Order the area measurements from least to greatest: \(4500\,\text{in}^2\), \(30\,\text{ft}^2\), \(31\,\text{ft}^2\), and \(4400\,\text{in}^2\).

Complete each equation with the missing number or unit. a) \(0.75\,\text{m}^2=7500\,\underline{\hspace{1cm}}\) b) \(252\,\text{ft}^2=\underline{\hspace{1cm}}\,\text{yd}^2\) c) \(12\,\text{cm}^2=1200\,\underline{\hspace{1cm}}\) d) \(\underline{\hspace{1cm}}\,\text{in}^2=5\,\text{ft}^2\)

A water dispenser at a recreation center starts with \(18.5\,\text{L}\) of water. During the morning, people fill \(60\) cups with \(250\,\text{mL}\) of water each. How many milliliters of water remain in the dispenser?

Two pitchers are in a kitchen. Pitcher A contains \(2500\,\text{mL}\) of water. Pitcher B contains \(2.45\,\text{L}\) and has a maximum capacity of \(2.6\,\text{L}\). Then \(125\,\text{mL}\) of water is poured from Pitcher A into Pitcher B. Will Pitcher B overflow? Justify your answer with a calculation.

A bakery orders flour in bags that each have a mass of \(25\,\text{kg}\). Use \(1\,\text{metric ton}=1000\,\text{kg}\). a) How many bags have a total mass of exactly \(1\) metric ton? b) What is the total mass of \(10\) bags in grams?

Darius attends school on \(180\) days each year. His one-way walk to school is \(950\,\text{m}\). How many kilometers does he walk altogether traveling to and from school during the year?

Two ropes are cut into equal-length pieces. Rope A is \(25.68\,\text{m}\) long and is cut into \(8\) equal pieces. Rope B is \(19.26\,\text{m}\) long and is cut into \(6\) equal pieces. Find the length of one piece from each rope in centimeters. Which rope makes longer pieces, or are the pieces equal in length?

A bakery uses exactly \(500\,\text{g}\) of butter for one sheet cake. A bulk box contains \(10\,\text{kg}\) of butter. a) How many sheet cakes can be made with one box? b) The bakery uses \(12\) boxes in one week. How many sheet cakes are made that week?

Nora records the time she spends on homework and studying each school day: <table> <tr><td>Math</td><td>\(25\,\text{minutes}\)</td></tr> <tr><td>Language arts</td><td>\(25\,\text{minutes}\)</td></tr> <tr><td>Science</td><td>\(15\,\text{minutes}\)</td></tr> <tr><td>Spanish</td><td>\(10\,\text{minutes}\)</td></tr> <tr><td>Independent reading</td><td>\(15\,\text{minutes}\)</td></tr> </table> a) Find the total study time per day in minutes. b) Find the total study time in a \(5\)-day school week. Give the answer in hours and minutes. c) A school year has \(40\) school weeks. Find the total study time for the school year in hours.

A school festival needs at least \(45\,\text{L}\) of apple juice. The school buys four \(10\)-liter containers that cost \(\$8\) each and three \(2000\,\text{mL}\) bottles that cost \(\$2\) each. Does the school have enough juice, and what is the total cost?

An elephant in a national park lives to be \(70\) years old. Determine whether the elephant has lived more than \(600{,}000\) hours by its 70th birthday. Assume every year has exactly \(365\) days.

A high-speed train travels \(2850\,\text{km}\) on its route. Priya claims that this distance is greater than \(250\) million centimeters. Is Priya correct? Show how you know.

A recycling facility processes \(3500\,\text{kg}\) of material each day. Does it process more than \(1250\) metric tons in \(365\) days? Use \(1\,\text{metric ton}=1000\,\text{kg}\). Show how you know.

Ethan takes exactly \(2000\) steps on a walk. His average step length is \(60\,\text{cm}\). Find the total distance first in centimeters, then convert it to meters and kilometers.

Nadia and Tom each walk exactly \(400\,\text{m}\). Nadia’s average step length is \(50\,\text{cm}\), and Tom’s average step length is \(80\,\text{cm}\). How many steps does each person take?

A hiking trail is \(3\,\text{km}\) long. Mrs. Smith estimates that she takes \(4000\) steps to complete the trail. a) If her estimate is exact, what is her average step length in centimeters? b) Her small dog travels the same distance using exactly twice as many steps. How many steps does the dog take, and what is the dog’s average step length?

Order the lengths from least to greatest using \(<\). First convert every measurement to centimeters. \(30\,\text{cm}\); \(250\,\text{mm}\); \(0.5\,\text{m}\); \(12\,\text{cm}\); \(0.002\,\text{km}\)

A stack of \(100\) sheets of printer paper is exactly \(1\,\text{cm}\) high. a) How thick is one sheet of paper in millimeters? b) How many sheets are in a stack that is \(20\,\text{cm}\) high? c) Elena claims, “A package of \(500\) sheets is \(25\,\text{cm}\) high.” Use a calculation to decide whether the claim is reasonable.

Fill in each missing number or unit so the equation is true. a) \(7\,\text{m}\ 4\,\text{cm}=\square\,\text{cm}\) b) \(85\,\text{mm}=8\,\text{cm}\ \square\,\text{mm}\) c) \(1200\,\text{m}=1\,\text{km}\ \square\,\text{m}\) d) \(4500\,\text{cm}=45\,\square\) e) \(3\,\text{cm}\ 2\,\text{mm}=\square\,\text{mm}\)

Complete the conversion chain. \(0.05\,\text{km}=\square\,\text{m}=\square\,\text{cm}=\square\,\text{mm}\)

Write each length without a decimal. For a), b), and d), use only meters and centimeters. For c), use only kilometers and meters. Omit a larger unit when its amount is zero. a) \(7.2\,\text{m}\) b) \(14.06\,\text{m}\) c) \(5.125\,\text{km}\) d) \(0.68\,\text{m}\)

Rewrite each length without a decimal using the indicated units. Omit any unit whose amount is zero. a) Write \(10.04\,\text{km}\) in kilometers and meters. b) Write \(2.5\,\text{cm}\) in centimeters and millimeters. c) Write \(4070\,\text{mm}\) in meters and centimeters. d) Write \(0.009\,\text{m}\) in millimeters.

Evaluate each expression. First convert every measurement to the smallest unit used in that part. a) \(12\,\text{m}\ 8\,\text{cm}+30\,\text{cm}\) b) \(2\,\text{km}\ 45\,\text{m}-120\,\text{m}\) c) \((40\,\text{cm}\ 6\,\text{mm})\times 5\)

Write \(<\), \(>\), or \(=\) in each box. a) \(6\,\text{m}\ 50\,\text{cm}\ \square\ 6.05\,\text{m}\) b) \(1200\,\text{mm}\ \square\ 120\,\text{cm}\) c) \(0.04\,\text{km}\ \square\ 400\,\text{m}\) d) \(9\,\text{cm}\ 2\,\text{mm}\ \square\ 9.2\,\text{cm}\)

A package currently weighs \(16\,\text{lb}\,7\,\text{oz}\). Two more items are added, and each weighs \(1\,\text{lb}\,14\,\text{oz}\). Is the package now heavier or lighter than \(20\,\text{lb}\)? Use \(1\,\text{lb} = 16\,\text{oz}\).

A large rain barrel contains \(155.75\,\text{L}\) of water. A storm adds \(45\,\text{L}\,350\,\text{mL}\). The barrel can hold \(200\,\text{L}\). Will the barrel overflow?

A rope is \(12.4\,\text{m}\) long. First, a \(3.85\,\text{m}\) piece is cut off. Then a piece measuring \(4\,\text{m}\,60\,\text{cm}\) is cut off. Is the remaining piece longer or shorter than \(4\,\text{m}\)?

Find the remaining length and write the result as a decimal number of meters: \(3.5\,\text{m} - 120\,\text{cm} - 450\,\text{mm}\).

Calculate and write the result as a decimal number of kilograms: \(1.25\,\text{kg} + 850\,\text{g} - 0.4\,\text{kg} - 325\,\text{g}\).

Evaluate each expression. Convert units as needed. Decide whether the result is a measurement or a unitless number. a) \(450\,\text{g}+1.2\,\text{kg}\) (grams) b) \(3\,\text{m}\times25\) (centimeters) c) \(72\,\text{cm}\div8\,\text{mm}\) d) \(2\,\text{L}-450\,\text{mL}\) (milliliters)

Evaluate the left side of each comparison, then write \(<\), \(>\), or \(=\). a) \(5\times200\,\text{mg}\ \square\ 1\,\text{g}\) b) \(1\,\text{km}-350\,\text{m}\ \square\ 700\,\text{m}\) c) \(48\,\text{h}\div2\ \square\ 1\,\text{day}\) d) \(3.5\,\text{L}+1500\,\text{mL}\ \square\ 5\,\text{L}\)

Convert all addends to grams, write the sum as a product, and calculate: \(250\,\text{g} + 250\,\text{g} + 250{,}000\,\text{mg} + 0.25\,\text{kg} + 250\,\text{g}\).

Write the sum as a product, calculate its value, and give the result in meters: \(45\,\text{cm} + 0.45\,\text{m} + 450\,\text{mm} + 45\,\text{cm}\).

Calculate efficiently and give the result in meters and centimeters: \(6\,\text{m}\,80\,\text{cm} + 14\,\text{m}\,36\,\text{cm} + 20\,\text{cm} + 65\,\text{cm}\).

Calculate each result and write it in mixed units of meters and centimeters. a) \(18\,\text{m}\,42\,\text{cm} - 5.9\,\text{m}\) b) \(2\,\text{m}\,5\,\text{cm} + 740\,\text{mm} + 30\,\text{cm}\)

Calculate each result and briefly describe what happens to the units. a) \(4.2\,\text{m} \div 7\) b) \(4.2\,\text{m} \div 30\,\text{cm}\) c) \(4.2\,\text{m} - 50\,\text{cm}\) What general rule can you state about dividing one measurement by another measurement of the same kind, as in part b)?

A ribbon is \(2.4\,\text{m}\) long. a) The ribbon is cut into \(12\) equal pieces. Find the length of each piece in centimeters and explain your method. b) How many \(15\,\text{cm}\) pieces can be cut from the entire ribbon? c) Give another everyday example in which dividing one length by another length gives a count.

A class hikes for four days. The distances are \(12\,\text{km}\,450\,\text{m}\), \(15\,\text{km}\,720\,\text{m}\), \(8\,\text{km}\,900\,\text{m}\), and \(11\,\text{km}\,130\,\text{m}\). How far does the class hike altogether? Give the result in kilometers and meters.

A courier records four driving segments during the morning. <table> <tr><th>Segment</th><th>Distance</th></tr> <tr><td>Warehouse to Stop A</td><td>\(8\,\text{mi}\,1200\,\text{ft}\)</td></tr> <tr><td>Stop A to Stop B</td><td>\(2600\,\text{ft}\)</td></tr> <tr><td>Stop B to Stop C</td><td>\(2\,\text{mi}\,375\,\text{ft}\)</td></tr> <tr><td>Stop C back to the warehouse</td><td>\(1800\,\text{ft}\)</td></tr> </table> Find the total distance driven. Give the result in miles and feet. Use \(1\,\text{mi} = 5280\,\text{ft}\).

A truck carries two heavy crates. The first weighs \(2\,\text{tons}\,900\,\text{lb}\), and the second weighs \(1750\,\text{lb}\). First estimate the total weight. Then find the exact total in pounds. Use \(1\,\text{ton} = 2000\,\text{lb}\).

A garden fence requires \(12\) rolls of wire. Each roll is \(15\,\text{ft}\,11\,\text{in}\) long. First estimate the total length. Then find the exact total in feet and inches.

A ribbon \(15\,\text{ft}\,6\,\text{in}\) long is cut into \(6\) equal pieces. First estimate the length of one piece. Then find the exact length.

Evaluate and write the result as a decimal number of kilograms: \(12.5\,\text{kg} - (4\,\text{kg}\,250\,\text{g} - 1\,\text{kg}\,75\,\text{g})\).

Evaluate and write the result as a decimal number of liters: \(10\,\text{L} - [3.4\,\text{L} + (1\,\text{L}\,250\,\text{mL} - 800\,\text{mL})]\).

Leo wants to hang a picture. The hook is \(7\,\text{ft}\,1\,\text{in}\) above the floor. Leo is \(5\,\text{ft}\,2\,\text{in}\) tall and can reach \(10\,\text{in}\) above the top of his head. He stands on a \(16\)-inch stool. Can Leo reach the hook?

Maya wants to touch a ceiling that is \(8\,\text{ft}\,2\,\text{in}\) high. She is \(4\,\text{ft}\,10\,\text{in}\) tall and can reach \(13\,\text{in}\) above the top of her head. Each ladder step raises her \(8\,\text{in}\). What is the lowest step Maya must stand on to reach the ceiling with her fingertips?

An apple hangs from a branch \(9\,\text{ft}\,4\,\text{in}\) above the ground. Tom is \(5\,\text{ft}\,1\,\text{in}\) tall, can reach \(14\,\text{in}\) above his head, and has a \(24\)-inch stool. Marie is \(5\,\text{ft}\,4\,\text{in}\) tall, can reach \(15\,\text{in}\) above her head, and has a \(36\)-inch step ladder. Who can reach the apple? Find each person’s maximum reach.

Estimate first, then evaluate exactly: \((15\,\text{m} - 700\,\text{cm}) \times 12 + 400\,\text{cm} \times 5\).

Estimate first, then evaluate exactly: \((2\,\text{km} + 400\,\text{m}) \div 8 + 70\,\text{m} \times 6\).

Estimate first, then evaluate exactly: \(25\,\text{cm} \times 4 + (1.8\,\text{m} - 60\,\text{cm}) \div 3\).

During a school fundraiser walk, Team A travels \(6.2\,\text{km}\). Team B travels \(450\,\text{m}\) farther than Team A. Team C travels half as far as Team A. Give all three distances in kilometers.

Three crates have different masses. Find the missing masses for Crates 2 and 3 in grams. <table> <tr><th>Crate</th><th>Mass</th></tr> <tr><td>Crate 1</td><td>\(3.6\,\text{kg}\)</td></tr> <tr><td>Crate 2</td><td>\(150\,\text{g}\) less than Crate 1</td></tr> <tr><td>Crate 3</td><td>Half the mass of Crate 1</td></tr> </table>

A bucket contains \(4.8\,\text{L}\) of rainwater. A watering can contains \(1500\,\text{mL}\) more water than the bucket. A small pitcher contains exactly one-third as much water as the bucket. How many liters of water are in the three containers altogether?

A hiking trail is \(15\,\text{km}\,600\,\text{m}\) long and is divided into equal sections of \(1300\,\text{m}\). a) Determine whether the trail has \(8\), \(10\), or \(12\) sections. b) A hiker’s average step length is \(65\,\text{cm}\). About how many steps are needed for one section?

Kofi converted each mass to mixed units. Check each result. Identify the incorrect results and write the correct conversion. a) \(4.5\,\text{kg}=4\,\text{kg}\ 5\,\text{g}\) b) \(0.025\,\text{kg}=25\,\text{g}\) c) \(7.08\,\text{g}=7\,\text{g}\ 80\,\text{mg}\) d) \(1.3\,\text{kg}=1\,\text{kg}\ 3\,\text{g}\)

Mei wrote three chains of equivalent masses, but each row contains exactly one error. Find and correct the incorrect measurement. a) \(4500\,\text{g}=4\,\text{kg}\ 500\,\text{g}=45\,\text{kg}\) b) \(3\,\text{kg}\ 20\,\text{g}=3020\,\text{g}=3.2\,\text{kg}\) c) \(6\,\text{kg}\ 4\,\text{g}=6.004\,\text{kg}=604\,\text{g}\)

Calculate and give each result in kilograms. Use \(1\,\text{metric ton}=1000\,\text{kg}\). a) \(14.8\,\text{kg}+350\,\text{g}\) b) \(2.05\,\text{metric tons}-80\,\text{kg}\) c) \(1.2\,\text{kg}+400\,\text{g}+0.85\,\text{kg}\)

Calculate and give each result in kilograms. Use \(1\,\text{metric ton}=1000\,\text{kg}\). a) \(12\frac{1}{2}\,\text{kg}-4.25\,\text{kg}-750\,\text{g}\) b) \(3\,\text{metric tons}-(1200\,\text{kg}+400\,\text{kg}\times2)\)

Calculate and give each final result in kilograms. Use \(1\,\text{metric ton}=1000\,\text{kg}\). a) \(5.4\,\text{kg}+(8.2\,\text{kg}-6500\,\text{g})\times5\) b) \(0.6\,\text{metric ton}-150\frac{1}{2}\,\text{kg}-4500\,\text{g}\)

Evaluate: \(12\,\text{kg}\,750\,\text{g} \div 250\,\text{g} + 8\,\text{g}\,40\,\text{mg} \div 20\,\text{mg} - 15\).

Evaluate: \(15\,\text{kg} - (3\,\text{kg}\,450\,\text{g} + 720\,\text{g} \times 5)\).

Convert each mass to the unit in parentheses. Pay attention to fractions and mixed units. a) \(\frac{3}{4}\,\text{kg}\) (grams) b) \(5\,\text{kg}\ 20\,\text{g}\) (kilograms) c) \(12\,\text{kg}\ 500\,\text{g}\) (kilograms) d) \(2\,\text{kg}\ \frac{1}{2}\,\text{g}\) (grams)

A charter bus is preparing for a class trip with \(48\) students and \(2\) teachers. Use an average person weight of \(120\,\text{lb}\). Each person may also bring a suitcase weighing up to \(30\,\text{lb}\) and a carry-on weighing \(10\,\text{lb}\). a) If everyone uses the full luggage allowance, what total weight do the people and luggage add to the bus? b) The unloaded bus weighs \(13\) tons. What is the fully loaded bus’s total weight in tons? Use \(1\,\text{ton} = 2000\,\text{lb}\). c) Ten people each have a suitcase that is \(4\,\text{lb}\) over the limit. By how many pounds does this increase the answer to part a)?

Evaluate and give the result in kilograms: \((1\,\text{kg}\,450\,\text{g} + 850\,\text{g} - 700\,\text{g}) \times 6\).

Evaluate: \(7.2\,\text{kg} - (2\frac{1}{4}\,\text{kg} + 1\,\text{kg}\,850\,\text{g} + 450\,\text{g})\).

Find the sum: \(4\,\text{kg}\,200\,\text{g} \div 60 + 12\,\text{kg} \div 80\).

A satellite needs exactly \(1\,\text{day}\ 5\,\text{h}\ 12\,\text{min}\) to complete a set of measurements. Find the total time in minutes.

Evaluate each expression. a) \(2\,\text{h}-\frac{1}{4}\,\text{h}-55\,\text{min}\) b) \(3\times(12\,\text{min}\ 45\,\text{s})\) c) \(5\,\text{kg}\div 125\,\text{g}\) d) \(3\,\text{km}\ 50\,\text{m}-1\,\text{km}\ 200\,\text{m}\)

A delivery van carries packages that each weigh \(5\,\text{lb}\,8\,\text{oz}\). a) What is the total weight of \(18\) packages? b) The van can carry at most \(1320\,\text{lb}\) of cargo. What is the greatest number of these packages it can carry?

Evaluate both sides and write \(<\), \(>\), or \(=\). Show your calculations. a) \(10\,\text{h}\div 15\ \square\ 45\,\text{min}\) b) \(0.5\,\text{km}\times 8\ \square\ 3\,\text{km}\ 900\,\text{m}\) c) \(4\,\text{kg}-1\,\text{kg}\ 200\,\text{g}\ \square\ 14\times 200\,\text{g}\)

An elephant at a zoo is exactly \(2000\) days old. How many years and days is that? Use \(365\) days for one year.

A record says that an olive tree was planted \(1150\) months ago. A gardener claims, “The tree is already more than \(95\) years old.” Is the gardener correct? Justify your answer with a calculation.

Find the value of the quotient: \(4\,\text{h}\ 30\,\text{min}\div18\,\text{min}\)

Find the sum: \(1\,\text{day}\ 14\,\text{h}\ 45\,\text{min}+19\,\text{h}\ 30\,\text{min}\)

Evaluate each expression. Convert units when needed. a) \(3.4\,\text{kg}+850\,\text{g}-1.02\,\text{kg}+470\,\text{g}\) b) \(12\,\text{m}\ 5\,\text{cm}-4.8\,\text{m}+72\,\text{cm}\) c) \((4.2\,\text{kg}+580\,\text{g})\times 15\)

Evaluate each expression. Write time answers in hours and minutes. a) \(4\,\text{h}\ 12\,\text{min}-155\,\text{min}+1\,\text{h}\ 48\,\text{min}\) b) \(18\,\text{km}\div25\,\text{m}\) c) \(144\,\text{kg}\div12-3600\,\text{g}\div12\)

Evaluate each expression and write the result as a decimal in the larger unit. a) \(2\,\text{h}\ 30\,\text{min}+45\,\text{min}-1.25\,\text{h}\) b) \(6.3\,\text{kg}-(2100\,\text{g}+850\,\text{g})\)

Evaluate each expression and write the result as a decimal. a) \((15\,\text{m}\,60\,\text{cm} + 4.4\,\text{m}) \div 5\) b) \(0.85\,\text{km} - 320\,\text{m} + 1.2\,\text{km}\)

Evaluate each expression. Write each final answer as a decimal. a) \(2.5\,\text{h} + (1\,\text{h}\ 45\,\text{min} + 45\,\text{min})\) b) \(4.8\,\text{kg} \div 8 + 325\,\text{g} \times 4\)

A wooden fence has \(4\) sections, each \(6\,\text{ft}\) long. The fence will be made from vertical boards that are each \(6\,\text{in}\) wide, placed directly next to one another with no gaps. How many boards are needed altogether?

Find the missing measurement \(\square\) that makes the equation true: \(8\,\text{kg}\,450\,\text{g} - \square + 1250\,\text{g} = 7\,\text{kg}\,100\,\text{g}\).

Find the missing length: \(3.4\,\text{km} - 850\,\text{m} + \square = 4\,\text{km}\,20\,\text{m}\).

Complete the missing table entries and write each mass as a decimal in kilograms. <table> <tr> <th>\(100\,\text{kg}\)</th> <th>\(10\,\text{kg}\)</th> <th>\(1\,\text{kg}\)</th> <th>\(100\,\text{g}\)</th> <th>\(10\,\text{g}\)</th> <th>\(1\,\text{g}\)</th> <th>Decimal in kilograms</th> </tr> <tr><td>4</td><td>0</td><td>7</td><td>2</td><td>0</td><td>0</td><td>\(?\,\text{kg}\)</td></tr> <tr><td></td><td>5</td><td>0</td><td>3</td><td>0</td><td>0</td><td>\(?\,\text{kg}\)</td></tr> <tr><td>0</td><td>0</td><td>0</td><td>8</td><td>1</td><td>5</td><td>\(?\,\text{kg}\)</td></tr> <tr><td>1</td><td>2</td><td>0</td><td>4</td><td>5</td><td>0</td><td>\(?\,\text{kg}\)</td></tr> </table>

Enter each length in a place-value table with columns for kilometers, hundreds of meters, tens of meters, meters, tenths of a meter, hundredths of a meter, and thousandths of a meter. Then write each length as a decimal in meters. a) \(2\,\text{km}\ 45\,\text{m}\ 3\,\text{cm}\) b) \(80\,\text{m}\ 70\,\text{cm}\ 5\,\text{mm}\) c) \(6\,\text{km}\ 90\,\text{cm}\)

Three packages are weighed. Package A weighs \(1\,\text{kg}\ 25\,\text{g}\). Package B weighs \(1.205\,\text{kg}\). Package C weighs \(1250\,\text{g}\). a) Enter each mass in a place-value table with columns for \(1\,\text{kg}\), \(100\,\text{g}\), \(10\,\text{g}\), and \(1\,\text{g}\). b) Write all three masses as decimals in kilograms. c) Which package is heaviest?

Evaluate both sides. Then write \(<\), \(>\), or \(=\). a) \(1\,\text{km}-450\,\text{m}\ \square\ 500\,\text{m}+50\,\text{m}\) b) \(0.38\,\text{m}+22\,\text{cm}\ \square\ 0.6\,\text{m}-5\,\text{cm}\)

Santiago wrote: \(32\,\text{kg} \div 800\,\text{g} = 40\,\text{g}\). Find the error, explain it briefly, and give the correct result.

Check the calculation for an error and correct it: \(4\times15\,\text{min}+2\,\text{h}=62\,\text{min}\)

Sarah's goal is to read for exactly \(7\) hours this week. Her reading times from Monday through Saturday are shown below. <table> <tr><th>Day</th><th>Reading Time</th></tr> <tr><td>Monday</td><td>\(45\,\text{min}\)</td></tr> <tr><td>Tuesday</td><td>\(1\,\text{h}\ 10\,\text{min}\)</td></tr> <tr><td>Wednesday</td><td>\(55\,\text{min}\)</td></tr> <tr><td>Thursday</td><td>\(1\,\text{h}\ 20\,\text{min}\)</td></tr> <tr><td>Friday</td><td>\(40\,\text{min}\)</td></tr> <tr><td>Saturday</td><td>\(1\,\text{h}\ 5\,\text{min}\)</td></tr> </table> How long must Sarah read on Sunday to reach her goal?

Ms. Wagner takes the bus between Oakville and Riverton for work. Morning trip: Oakville departs \(7{:}12\) a.m. – Riverton arrives \(7{:}58\) a.m. Return trip: Riverton departs \(4{:}35\) p.m. – Oakville arrives \(5{:}19\) p.m. a) Find the travel time for each trip. b) How much total time does Ms. Wagner spend on the bus during a \(5\)-day workweek? Give the answer in hours and minutes. c) How long is Ms. Wagner in Riverton on one workday?

Liam attends a full-day school. His schedule is: - Leaves home: \(7{:}35\) a.m. - School begins: \(8{:}10\) a.m. - School ends: \(3{:}45\) p.m. - Arrives home: \(4{:}25\) p.m. a) How long is Liam away from home each day? b) How much time does he spend traveling to and from school each day? c) Find his total time at school, including breaks, during a \(5\)-day school week.

An express train takes \(52\) minutes to travel from Riverton to Lakeview. A local train takes \(1\,\text{h}\ 14\,\text{min}\) for the same trip because it makes more stops. a) How many minutes faster is the express train on one trip? b) A commuter makes a round trip on \(5\) days each week. How much time would the commuter save in one week by switching from the local train to the express train? Give the answer in hours and minutes.

Evaluate the expression and write the result in meters and centimeters: \(15.6\,\text{m} \div 4 + 85\,\text{cm} \times 7\).

Evaluate and write the result using mixed units: \(2.5\,\text{kg} \times 9 - 14\,\text{kg}\,400\,\text{g} \div 6\).

Calculate and give the result in mixed time units: \(1\,\text{h}\ 45\,\text{min}+(3\,\text{h}\ 20\,\text{min})\div8\)

A coffee roaster packages coffee in \(1\)-pound bags and \(8\)-ounce bags. The roaster will package \(30\,\text{lb}\) of coffee and use the same number of each bag size. How many bags will be filled altogether?

Four students made area conversions. Decide whether each statement is correct. Correct every statement that is false. Use \(1\,\text{cm}^2=100\,\text{mm}^2\), \(1\,\text{m}^2=100\,\text{dm}^2\), \(1\,\text{yd}^2=9\,\text{ft}^2\), and \(1\) acre \(=43{,}560\,\text{ft}^2\). a) \(2.4\,\text{cm}^2=24\,\text{mm}^2\) b) \(7\,\text{m}^2=700\,\text{dm}^2\) c) \(6\,\text{yd}^2=18\,\text{ft}^2\) d) \(0.5\) acre \(=21{,}780\,\text{ft}^2\)

The diagrams show rectangles A and B. Diego says rectangle B must have the smaller area because the side-length numbers shown on B are smaller. Use \(1\,\text{dm}^2=100\,\text{cm}^2\). Is Diego correct? Find both areas in square centimeters and explain.

A child's bedroom has an area of \(12{,}960\,\text{in}^2\). 1. Convert the area to square feet and then to square yards. 2. Which of the three units—square inches, square feet, or square yards—is best for describing the room in a real-estate listing? Briefly explain.

A rectangular community sports field is \(330\,\text{ft}\) long and \(132\,\text{ft}\) wide. 1. Find its area in square feet. 2. Convert the area to square yards. 3. How many acres is the field? Is acres a reasonable unit for comparing this field with larger properties?

A large poster is estimated by covering it with square sticky notes. Each sticky note has an area of about \(9\,\text{in}^2\), and \(40\) notes cover the poster. Estimate the poster's area in square inches and then convert it to square feet.

Convert each mixed area measurement to the unit in parentheses. a) \(5\,\text{yd}^2\ 12\,\text{ft}^2\) \((\text{ft}^2)\) b) \(9\,\text{ft}^2\ 4\,\text{in}^2\) \((\text{in}^2)\) c) \(14\,\text{m}^2\ 50\,\text{cm}^2\) \((\text{cm}^2)\)

Ms. Alvarez says, “Our classroom has an area of \(650{,}000\,\text{cm}^2\).” Noah thinks the number is too large for one room. Convert the area to square meters. Is the measurement reasonable for a classroom? Explain.

Two students compare area measurements from homework. Mateo says, “The front of my smartphone has an area of \(12{,}500\,\text{mm}^2\).” Julia says, “My postcard has an area of \(1.5\,\text{m}^2\).” One student made a major error. Convert both measurements to square centimeters and decide who is incorrect.

Check each area conversion. Correct any conversion that is wrong. a) \(300\,\text{mm}^2=30\,\text{cm}^2\) b) \(15\,\text{yd}^2=1.5\,\text{ft}^2\) c) \(2000\,\text{cm}^2=0.2\,\text{m}^2\)

Convert each area measurement to both requested units. a) \(810\,\text{ft}^2\) to square yards and square inches b) \(15{,}000\,\text{cm}^2\) to square meters and square millimeters c) \(400\,\text{yd}^2\) to square feet and square inches d) \(20{,}736\,\text{in}^2\) to square feet and square yards

Order the area measurements from least to greatest. Convert all measurements to square inches to compare. \(3\,\text{yd}^2\), \(2800\,\text{in}^2\), \(31\,\text{ft}^2\), \(2\,\text{yd}^2\ 90\,\text{in}^2\)

A farmer owns three fields. The first is \(15\) acres, the second is \(217{,}800\,\text{ft}^2\), and the third is \(435{,}600\,\text{ft}^2\). Find the total area in acres.

What number belongs in each box? a) \(5\,\text{ft}^2-\square\,\text{in}^2=420\,\text{in}^2\) b) \(2\,\text{yd}^2+\square\,\text{ft}^2=26\,\text{ft}^2\)

Compare the values. Insert \(<\), \(>\), or \(=\). a) \(4\,\text{ft}^2+9\,\text{in}^2\ \underline{\hspace{0.6cm}}\ 490\,\text{in}^2\) b) \(10\,\text{yd}^2-10\,\text{ft}^2\ \underline{\hspace{0.6cm}}\ 80\,\text{ft}^2\)

Which area measurements are equal? Find the three matching pairs. A: \(2\,\text{yd}^2\ 4\,\text{ft}^2\) B: \(24\,\text{ft}^2\) C: \(3168\,\text{in}^2\) D: \(2\,\text{yd}^2\ 6\,\text{ft}^2\) E: \(240\,\text{ft}^2\) F: \(34{,}560\,\text{in}^2\)

Write each area measurement in mixed units. a) \(4005\,\text{in}^2\) as square feet and square inches b) \(10{,}200\,\text{in}^2\) as square feet and square inches c) \(807\,\text{ft}^2\) as square yards and square feet d) \(30{,}050\,\text{cm}^2\) as square meters and square centimeters

A property has an area of \(56{,}343\,\text{ft}^2\). a) Write the area in square yards and square feet. b) Write the area in acres, square yards, and square feet.

Find the missing area needed to reach each target. a) \(5\,\text{ft}^2+\underline{\hspace{1cm}}=1\,\text{yd}^2\) b) \(62\,\text{in}^2+\underline{\hspace{1cm}}=1\,\text{ft}^2\) c) \(450\,\text{cm}^2+\underline{\hspace{1cm}}=0.05\,\text{m}^2\) d) \(8.5\,\text{cm}^2+\underline{\hspace{1cm}}=0.01\,\text{m}^2\)

Calculate the quotient: \(2\,\text{yd}^2\ 42\,\text{ft}^2\div 3\,\text{ft}^2\).

Evaluate the expression step by step: \(5\,\text{yd}^2\ 2\,\text{ft}^2-(18\,\text{ft}^2\div 2+3\,\text{ft}^2)\times 2\).

Ms. Rivera is painting her garage floor. The total floor area is \(180\,\text{ft}^2\ 20\,\text{in}^2\). She has painted \(90\,\text{ft}^2\ 50\,\text{in}^2\). What area remains? Write the result in square feet and square inches.

A farmer has a field measuring \(4\) acres \(21{,}780\,\text{ft}^2\). The field will be divided equally into \(6\) paddocks. What is the area of each paddock in square feet?

A wall area of \(7\,\text{yd}^2\ 9\,\text{ft}^2\) will be completely covered with posters. Each poster covers exactly \(6\,\text{ft}^2\). Assume the posters can be arranged with no gaps or waste. How many posters are needed?

Convert each area measurement to the unit in parentheses, then round to the nearest whole unit. a) \(548\,\text{ft}^2\) \((\text{yd}^2)\) b) \(12{,}750\,\text{mm}^2\) \((\text{cm}^2)\) c) \(142.8\,\text{in}^2\) \((\text{ft}^2)\)

Solve by converting and rounding to the requested whole unit. a) A sports field has an area of \(7420\,\text{ft}^2\). Round the area to the nearest square yard. b) A nature preserve has an area of \(28{,}490\,\text{yd}^2\). Round the area to the nearest acre.

Complete the table. Convert each area to the target unit, then round to the nearest whole unit. <table> <tr> <th>Area</th> <th>Nearest square yard</th> <th>Nearest acre</th> </tr> <tr> <td>\(184{,}300\,\text{ft}^2\)</td> <td></td> <td></td> </tr> <tr> <td>\(75{,}550\,\text{ft}^2\)</td> <td></td> <td></td> </tr> </table>

Calculate each expression. When the result has an area unit, write it in the smallest area unit used in that expression. a) \(5\,\text{yd}^2+35\,\text{ft}^2\) b) \((2\,\text{yd}^2\ 5\,\text{ft}^2)\times4\) c) \(1\text{ acre}-40{,}000\,\text{ft}^2\) d) \(12\,\text{ft}^2\div48\,\text{in}^2\)

Calculate. a) \(12\,\text{m}\,40\,\text{cm} - 85\,\text{cm}\) b) \(7 \times 3\,\text{m}\,20\,\text{cm}\) c) \(2\,\text{km} - 750\,\text{m}\) d) \(1\,\text{m} \div 5\,\text{mm}\)

Calculate each expression. a) \(3\,\text{yd}^2\ 5\,\text{ft}^2-12\,\text{ft}^2\) b) \(1\,\text{acre}-1\,\text{ft}^2\) c) \(4\,\text{ft}^2\ 4\,\text{in}^2\div5\,\text{in}^2\) d) \(12\times(2\,\text{ft}^2\ 50\,\text{in}^2)\)

A farmer has \(4\) acres \(21{,}780\,\text{ft}^2\) of land. Corn is planted on \(1\) acre. The remaining land is divided into \(4\) equal vegetable plots. Find the area of one vegetable plot in square feet.

Determine whether each statement is true. Correct any false statement. a) “\(288\,\text{in}^2\) is equal to \(2\,\text{ft}^2\).” b) “To convert \(3\,\text{yd}^2\) to square inches, multiply by \(9\) and then by \(12\).”

Calculate the sum. Give your answer in square feet. \(4\,\text{yd}^2\ 12\,\text{ft}^2+88\,\text{ft}^2+2\,\text{yd}^2\ 5\,\text{ft}^2\)

Calculate each expression. Write each area answer in mixed units when possible. a) \((5\,\text{yd}^2\ 3\,\text{ft}^2)\times8\) b) \((24\,\text{ft}^2\ 48\,\text{in}^2)\div6\)

For each measurement, find how much more area is needed to make \(1\,\text{ft}^2\). Give each answer in square inches. a) \(75\,\text{in}^2\) b) \(0.5\,\text{ft}^2\) c) \(30\,\text{in}^2+0.25\,\text{ft}^2\)

Form three groups of three equivalent money amounts. \(\$3.20\); \(\$3\) and \(2\) cents; \(32\) cents; \(\$3\) and \(20\) cents; \(\$3.02\); \(320\) cents; \(\$0.32\); \(302\) cents; \(\$0\) and \(32\) cents

A runner starts at exactly \(10{:}45{:}15\) a.m. (hours:minutes:seconds) and crosses the finish line at \(11{:}02{:}40\) a.m. How long is the run? Give the answer in minutes and seconds.

Solve these time conversion and addition problems: a) How many hours and minutes are \(315\,\text{min}\)? b) Find \(1\,\text{h}\ 45\,\text{min}+230\,\text{min}\). Give the result in hours and minutes.

The diagram shows a square metal sheet with a centered square opening. Using the side lengths shown, find the area of the remaining metal in square feet.

The diagram shows a rectangular field. What is its area in acres? Use \(1\) acre \(=43{,}560\,\text{ft}^2\).

Evaluate the expression. Give the result in cubic decimeters. \(1.2\,\text{m}^3-450\,\text{dm}^3+12{,}000\,\text{cm}^3\)

What number makes the equation true? \(3500\,\text{cm}^3+\Box\,\text{dm}^3=0.02\,\text{m}^3\)

Fill in each missing value. a) \(4.5\,\text{L}=\dots\,\text{mL}\) b) \(250\,\text{cm}^3=\dots\,\text{dm}^3\) c) \(0.03\,\text{m}^3=\dots\,\text{L}\) d) \(12\,\text{dm}^3+5\,\text{cm}^3=\dots\,\text{cm}^3\)

Find the sum. Give the result in liters. \(0.4\,\text{m}^3+120\,\text{dm}^3+5000\,\text{cm}^3\)

Compare each pair of volumes. Write \(<\), \(>\), or \(=\) in the blank. a) \(450\,\text{mL}\quad\dots\quad0.45\,\text{dm}^3\) b) \(0.02\,\text{m}^3\quad\dots\quad2000\,\text{cm}^3\) c) \(1500\,\text{mm}^3\quad\dots\quad1.5\,\text{cm}^3\) d) \(12\,\text{L}\quad\dots\quad1200\,\text{cm}^3\)

Complete the table so that all three entries in each row represent the same volume. <table> <tr> <th>\(\text{m}^3\)</th> <th>\(\text{dm}^3\) (or \(\text{L}\))</th> <th>\(\text{cm}^3\) (or \(\text{mL}\))</th> </tr> <tr> <td>\(1.2\)</td> <td>a) \(\dots\)</td> <td>b) \(\dots\)</td> </tr> <tr> <td>c) \(\dots\)</td> <td>d) \(\dots\)</td> <td>\(3000\)</td> </tr> <tr> <td>e) \(\dots\)</td> <td>\(40\)</td> <td>f) \(\dots\)</td> </tr> </table>

Lucas says, “Since \(10\,\text{mm}=1\,\text{cm}\), it must be true that \(100\,\text{mm}^3=1\,\text{cm}^3\).” Explain Lucas's error and give the correct value of \(100\,\text{mm}^3\) in cubic centimeters.

Convert each measurement to the unit shown in parentheses. a) \(1.5\,\text{m}^3\) (\(\text{dm}^3\)) b) \(450\,\text{cm}^3\) (\(\text{dm}^3\)) c) \(0.02\,\text{dm}^3\) (\(\text{mm}^3\)) d) \(2\,\text{L}\ 5\,\text{mL}\) (\(\text{cm}^3\))

Determine which measurements represent equal volumes. Then arrange all the measurements in increasing order, beginning with the smallest. \(2.5\,\text{dm}^3\); \(0.025\,\text{m}^3\); \(2500\,\text{cm}^3\); \(25\,\text{L}\)

Two water tanks are being compared. Tank A has a volume of \(0.06\,\text{m}^3\). Tank B has a volume of \(55{,}000\,\text{cm}^3\). Which tank can hold more water? Find the difference in liters.

Fill in each missing number or unit so that the equation is true. a) \(3.5\,\text{m}^3=\dots\,\text{dm}^3\) b) \(7500\,\text{mL}=\dots\,\text{L}\) c) \(0.2\,\text{dm}^3=\dots\,\text{mm}^3\) d) \(450{,}000\,\text{cm}^3=0.45\,\dots\)

Evaluate the expression. Give the result in liters. \(1.5\,\text{m}^3-(400\,\text{dm}^3+250{,}000\,\text{cm}^3)\)

Fill in each missing number so that the equation is true. a) \(0.25\,\text{L}+\dots\,\text{cm}^3=1\,\text{dm}^3\) b) \(0.002\,\text{m}^3-1500\,\text{cm}^3=\dots\,\text{L}\)

A dump truck can carry at most \(12\,\text{m}^3\) of gravel. Three job sites ordered these amounts: Site A: \(11{,}500\,\text{dm}^3\) Site B: \(12{,}500{,}000\,\text{cm}^3\) Site C: \(11{,}000\,\text{L}\) For which sites is one truckload enough? Justify your answer by converting every amount to cubic meters.

Compare \(2500\,\text{mL}\) and \(0.03\,\text{m}^3\). Which volume is greater? Also find the difference in liters.

Evaluate each expression, paying attention to the units. For parts a) and b), give the result in the larger of the two units shown. a) \(1.5\,\text{dm}^3+800\,\text{cm}^3\) b) \(0.04\,\text{m}^3-15\,\text{dm}^3\) c) \(2.4\,\text{L}\div6\)

Find the missing value \(x\) in each equation. a) \(x+450\,\text{cm}^3=2\,\text{dm}^3\) b) \(0.5\,\text{m}^3-x=320\,\text{L}\) c) \(x\times5=1.5\,\text{L}\). Give \(x\) in milliliters.

Write each decimal volume as a sum using whole-number amounts of the listed units. a) \(4.007\,\text{m}^3\), using \(\text{m}^3\) and \(\text{dm}^3\) b) \(12.65\,\text{dm}^3\), using \(\text{dm}^3\) and \(\text{cm}^3\) c) \(2.304\,\text{m}^3\), using \(\text{m}^3\) and \(\text{dm}^3\) d) \(5.08\,\text{L}\), using \(\text{L}\) and \(\text{mL}\)

Write each sum as a decimal in the largest unit shown. a) \(7\,\text{m}^3+50\,\text{dm}^3\) b) \(2\,\text{dm}^3+4\,\text{cm}^3\) c) \(10\,\text{L}+5\,\text{mL}\) d) \(1\,\text{m}^3+125\,\text{dm}^3\)

Compare each pair. Write \(<\), \(>\), or \(=\). a) \(2.05\,\text{m}^3\quad\Box\quad2\,\text{m}^3+500\,\text{dm}^3\) b) \(3.4\,\text{dm}^3\quad\Box\quad3\,\text{dm}^3+40\,\text{cm}^3\) c) \(0.008\,\text{L}\quad\Box\quad80\,\text{mL}\) d) \(1\,\text{cm}^3+2\,\text{mm}^3\quad\Box\quad1.002\,\text{cm}^3\)

Jonas says, “My new school backpack can hold \(150{,}000\,\text{mL}\) of lemonade.” Decide whether this is realistic for a normal school backpack. First convert the volume to cubic centimeters and then to liters. Compare your result with a typical school backpack capacity of about \(20\) to \(30\) liters.

Solve each volume problem. a) Order the volumes from least to greatest: \(0.2\,\text{m}^3\), \(220\,\text{L}\), and \(21{,}000\,\text{cm}^3\). b) Evaluate \((4.8\,\text{L}-800\,\text{cm}^3)\div2\). c) Find the missing value in cubic decimeters: \(0.05\,\text{m}^3+\dots\,\text{dm}^3=100\,\text{L}\).

Consider two cubes. a) Find the volume of a small cube with an edge length of \(10\,\text{cm}\). b) How many of these small cubes fit inside a large cube with an edge length of \(1\,\text{m}\)? c) Use your result from part b) to state the conversion from \(1\,\text{m}^3\) to cubic centimeters.

Write \(<\), \(>\), or \(=\), or find the missing value so that each statement is true. a) \(0.2\,\text{m}^3\quad\Box\quad20{,}000\,\text{cm}^3\) b) \(4.5\,\text{L}-800\,\text{mL}=\Box\,\text{dm}^3\) c) \(\frac{3}{4}\,\text{m}^3+\Box\,\text{L}=1\,\text{m}^3\) d) \(12\times250\,\text{mL}\quad\Box\quad0.003\,\text{m}^3\)

A leaky faucet loses exactly one drop every second. How many weeks, days, hours, minutes, and seconds will pass before \(10{,}000{,}000\) drops have fallen? Use \(1\) week \(= 7\) days.

Roadside marker posts will be placed along both sides of a straight highway from mile marker \(7\) to mile marker \(12\). On each side, the posts are spaced every \(200\,\text{ft}\), with posts at both endpoints. How many posts are needed altogether? Use \(1\,\text{mi} = 5280\,\text{ft}\).

Evaluate the expression and write the result as a decimal number of meters: \(5\,\text{m}\,4\,\text{cm} - 4 \times (15\,\text{cm} + 22\,\text{mm})\).

Two boards have a total length of \(4.50\,\text{m}\). One board is \(70\,\text{cm}\) shorter than the other. Find the length of each board in meters.

A cargo plane can carry at most \(25\) metric tons of payload. Use \(1\,\text{metric ton}=1000\,\text{kg}\). For a relief flight, workers load \(840\) crates with a mass of \(25\,\text{kg}\) each. Twelve support staff members also fly, with a combined person-and-equipment mass of \(120\,\text{kg}\) each. a) Find the current payload mass in kilograms. b) How many metric tons of payload capacity remain? c) By how many kilograms would the remaining capacity decrease if improved packaging added \(500\,\text{g}\) to every crate?

Find the missing duration \(\square\) that makes the equation true: \(1\,\text{h}\ 25\,\text{min}+140\,\text{s}+\square=2\,\text{h}\)

Ms. Weber works exactly \(35\) hours each week. She takes a \(30\)-minute unpaid lunch break each day. Her times for Monday through Thursday are shown below. <table> <tr><th>Day</th><th>Start</th><th>End</th></tr> <tr><td>Monday</td><td>\(8{:}00\) a.m.</td><td>\(4{:}00\) p.m.</td></tr> <tr><td>Tuesday</td><td>\(8{:}30\) a.m.</td><td>\(3{:}30\) p.m.</td></tr> <tr><td>Wednesday</td><td>\(7{:}45\) a.m.</td><td>\(4{:}15\) p.m.</td></tr> <tr><td>Thursday</td><td>\(9{:}00\) a.m.</td><td>\(3{:}30\) p.m.</td></tr> </table> On Friday, Ms. Weber starts at \(8{:}00\) a.m. She also takes a \(30\)-minute unpaid lunch break. What time can she leave after completing exactly \(35\) work hours?

Two packages have a total mass of \(15.6\,\text{kg}\). The first package has a mass that is \(2\,\text{kg}\,400\,\text{g}\) greater than the second package. Find the mass of each package.

A city record lists a small park's area as \(0.04\,\text{km}^2\). A news article says, “The park covers only \(400\,\text{m}^2\).” Convert the official area to square meters and explain the article's error. How many times as large is the actual park as the reported area?

Evaluate the expression. Give the result in cubic centimeters. \(0.5\,\text{L}+450\,\text{mL}+250\,\text{cm}^3-0.001\,\text{m}^3\)

Find each value and give the result in the requested unit. a) \(0.8\,\text{m}^3+150\,\text{dm}^3=\dots\,\text{dm}^3\) b) \(4200\,\text{cm}^3-1.2\,\text{dm}^3=\dots\,\text{L}\) c) How many times does a volume of \(500\,\text{mm}^3\) fit into a volume of \(0.1\,\text{dm}^3\)?

Evaluate each expression. Give the answer to part a) in cubic decimeters and the answer to part b) in cubic centimeters. a) \(0.75\,\text{m}^3+250\,\text{dm}^3-400\,\text{L}\) b) \(1\frac{3}{4}\,\text{L}-850\,\text{cm}^3+0.1\,\text{dm}^3\)

Write \(<\), \(>\), or \(=\) in each box. Show your work. a) \(12.5\,\text{L}+500\,\text{mL}\quad\Box\quad0.014\,\text{m}^3\) b) \(2\frac{1}{5}\,\text{dm}^3-200\,\text{cm}^3\quad\Box\quad2000\,\text{mL}\)

Evaluate each expression. Give each final answer in liters. a) \(15\times(200\,\text{mL}+0.3\,\text{L})\) b) \((0.008\,\text{m}^3-3\,\text{dm}^3)\div4\)

Evaluate each expression and give the result in the requested unit. a) \(6\times750\,\text{mL}\) (liters) b) \(3.6\,\text{dm}^3\div9\) (cubic centimeters) c) \(2\frac{1}{2}\,\text{m}^3\div500\,\text{dm}^3\) d) \(1.2\,\text{L}-\frac{1}{4}\,\text{L}\) (milliliters)

Order these volumes from least to greatest: \(0.4\,\text{L}\); \(45\,\text{cm}^3\); \(4000\,\text{mm}^3\); \(0.05\,\text{dm}^3\); \(0.003\,\text{m}^3\)

Evaluate each expression. Convert to a common unit when needed and give each answer in the requested or most reasonable form. a) \(450\,\text{mL}+0.75\,\text{L}\) b) \(0.004\,\text{m}^3-1200\,\text{cm}^3\) c) \(1.2\,\text{dm}^3\times5\) (give the result in cubic centimeters) d) \(6\,\text{L}\div15\) e) \(2\,\text{m}^3\div400\,\text{L}\)

Evaluate each expression step by step. Give the final answer in the unit shown in parentheses. a) \(\left(\frac{1}{4}\,\text{m}^3+150\,\text{L}\right)\times2-0.3\,\text{m}^3\) (liters) b) \(0.08\,\text{dm}^3\div4+15\,\text{mL}\) (\(\text{cm}^3\)) c) \(\frac{2}{5}\,\text{L}\times10-3500\,\text{mL}\) (liters)