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Measure liquid volume and mass

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5402373
A classroom aquarium should contain \(8\,\text{L}\) of water. It currently contains \(3\,\text{L}\). How many more liters of water are needed?

Hints

- Compare the amount in the aquarium with the target amount. - Think about the operation that finds how much is still needed.

Solution

1. Subtract the current volume from the needed volume: \(8 - 3 = 5\).

Answer

The aquarium needs \(5\,\text{L}\) more water.
5402413
A pottery class divides \(63\,\text{g}\) of clay equally among \(7\) sample bags. What mass of clay goes in each bag?

Hints

- The bags must all contain the same mass. - Think about which multiplication fact is related to the needed division.

Solution

1. Divide the total mass into \(7\) equal groups: \(63 \div 7 = 9\).

Answer

Each bag gets \(9\,\text{g}\) of clay.
5402473
A lab has \(24\,\text{L}\) of rinse water. Each storage can holds \(6\,\text{L}\). How many storage cans can be filled completely?

Hints

- Decide whether the unknown is the size of each group or the number of groups. - Use a related multiplication fact to check that the equal containers account for all the water.

Solution

1. The unknown is the number of equal \(6\)-liter groups in \(24\) liters. 2. Divide: \(24 \div 6 = 4\). 3. Check: \(4 \times 6 = 24\).

Answer

The lab can fill \(4\) storage cans completely.
5402573
A display shelf is holding \(18\,\text{kg}\) of materials. Before the shelf is moved, the mass on it must be reduced to \(12\,\text{kg}\). How many kilograms of materials must be removed?

Hints

- Compare the current mass with the required final mass. - Think about whether the mass must increase or decrease.

Solution

1. The shelf must change from \(18\,\text{kg}\) to \(12\,\text{kg}\). 2. Subtract: \(18 - 12 = 6\).

Answer

\(6\,\text{kg}\) of materials must be removed.
5402773
A rain barrel starts with \(5\,\text{L}\) of water. A storm adds \(7\,\text{L}\). How much water is in the barrel after the storm?

Hints

- Decide whether the storm makes the volume increase or decrease. - Combine the starting volume and the added volume. - Keep liters as the unit in the answer.

Solution

1. The storm increases the amount of water, so add. 2. \(5 + 7 = 12\).

Answer

The barrel contains \(12\,\text{L}\) of water after the storm.
5402963
A \(12\)-liter jug currently contains \(8\,\text{L}\). How many more liters can the jug hold?

Hints

- Compare the jug’s full capacity with the amount already inside. - The question asks for the empty part of the capacity. - Subtract the current volume from the total capacity.

Solution

1. Subtract the amount in the jug from its capacity. 2. \(12 - 8 = 4\).

Answer

The jug can hold \(4\,\text{L}\) more.
5403023
Which is a reasonable estimate for the mass of a hardcover book: \(1\,\text{g}\), \(1\,\text{kg}\), or \(10\,\text{kg}\)? Explain your choice.

Hints

- Compare the choices with objects whose masses you know. - Eliminate estimates that would make the book extremely light or difficult to lift.

Solution

1. \(1\,\text{g}\) is far too light for a hardcover book. 2. \(10\,\text{kg}\) is much too heavy for one book. 3. \(1\,\text{kg}\) is a reasonable estimate.

Answer

\(1\,\text{kg}\) is a reasonable estimate for the mass of a hardcover book.
5403083
A small animal has a mass of \(7\,\text{kg}\), and its travel box has a mass of \(4\,\text{kg}\). What is their combined mass?

Hints

- Decide whether the two masses should be combined or compared. - Both measurements use kilograms. - Add the animal’s mass and the box’s mass.

Solution

1. The animal and box are carried together, so add their masses. 2. \(7 + 4 = 11\).

Answer

Their combined mass is \(11\,\text{kg}\).
5403114
A small water tank holds \(3\,\text{L}\). A larger tank holds \(4\) times as much water. How much water does the larger tank hold?

Hints

- Interpret “\(4\) times as much” as \(4\) equal groups. - Use the small tank’s capacity as the size of each group. - Keep liters as the unit in the answer.

Solution

1. Four times as much means \(4\) equal groups of \(3\) liters. 2. Multiply: \(4 \times 3 = 12\).

Answer

The larger tank holds \(12\,\text{L}\).
5403153
Six jars each contain \(4\,\text{g}\) of pigment. What is the total mass of the pigment?

Hints

- Identify the number of equal groups and the mass in each group. - Use multiplication to combine all the equal jar masses. - Keep grams as the unit in the answer.

Solution

1. The jars contain \(6\) equal groups of \(4\) grams. 2. Multiply: \(6 \times 4 = 24\).

Answer

The total mass is \(24\,\text{g}\).
5403203
One pail contains \(7\,\text{L}\) of water, and another contains \(5\,\text{L}\). How many more liters of water are in the first pail?

Hints

- The question asks for the difference between the two volumes. - Subtract the smaller amount from the larger amount. - Keep liters as the unit in the answer.

Solution

1. Compare the two volumes by subtraction. 2. \(7 - 5 = 2\).

Answer

The first pail contains \(2\,\text{L}\) more water.
5403473
Which is a reasonable estimate for the capacity of a reusable water bottle: \(1\,\text{L}\), \(10\,\text{L}\), or \(100\,\text{L}\)? Explain.

Hints

- Compare the choices with drink containers you have used. - Eliminate capacities that would be more suitable for large buckets or tanks.

Solution

1. \(10\,\text{L}\) and \(100\,\text{L}\) are far too large for a bottle a person carries. 2. \(1\,\text{L}\) is a reasonable estimate.

Answer

\(1\,\text{L}\) is the reasonable estimate.
5403503
Four work areas each need \(6\,\text{L}\) of water. How much water is needed altogether?

Hints

- Identify the number of equal groups and the amount needed by each group. - Use multiplication to combine the four equal water amounts. - Keep liters as the unit in the answer.

Solution

1. There are \(4\) equal groups of \(6\) liters. 2. Multiply: \(4 \times 6 = 24\).

Answer

The work areas need \(24\,\text{L}\) of water altogether.
5403553
A sports cooler contains \(18\,\text{L}\) of water. Coaches use \(7\,\text{L}\). How much water remains?

Hints

- Decide whether the amount in the cooler increases or decreases. - Subtract the amount used from the starting volume. - Keep liters as the unit in the answer.

Solution

1. The water used is removed from the starting volume. 2. Subtract: \(18 - 7 = 11\).

Answer

\(11\,\text{L}\) of water remains.
5403893
Twelve liters of water are shared equally among \(4\) watering cans. How many liters go into each can?

Hints

- The cans must receive equal amounts. - Find the size of one equal group when \(12\) liters is divided among \(4\) cans. - Check the quotient with a related multiplication fact.

Solution

1. The water is divided into \(4\) equal groups. 2. \(12 \div 4 = 3\).

Answer

Each watering can receives \(3\,\text{L}\).
5403933
A loaded cart has a mass of \(17\,\text{kg}\), and the empty cart has a mass of \(9\,\text{kg}\). What is the mass of the load?

Hints

- Identify the combined mass and the empty-cart mass. - Remove the cart’s mass from the loaded mass. - Keep kilograms as the unit in the answer.

Solution

1. The loaded mass includes the cart and its load. 2. Subtract the empty cart’s mass: \(17 - 9 = 8\).

Answer

The load has a mass of \(8\,\text{kg}\).
5404073
One container holds \(4\) liters of water, and another holds \(3\) liters. How many liters of water are in the two containers altogether?

Hints

- Identify the amount of water in each container. - Add the two measured amounts. - Label the answer in liters.

Solution

1. Add the two amounts: \(4 + 3 = 7\).

Answer

The two containers hold \(7\,\text{L}\) altogether.
5404183
A large water jug holds \(12\,\text{L}\). A smaller jug holds \(5\,\text{L}\) less. How much water does the smaller jug hold?

Hints

- “Less” means the smaller amount is below the larger amount. - Use the given difference to move from the larger volume to the smaller one.

Solution

1. Subtract the difference from the larger volume: \(12 - 5 = 7\).

Answer

The smaller jug holds \(7\,\text{L}\).
5548453
The dial scale below is marked in grams. The marks on the upper half are equally spaced. What mass does the pointer indicate?
Figure for problem 554845

Hints

- Compare the labeled \(0\,\text{g}\), \(500\,\text{g}\), and \(1000\,\text{g}\) marks. - Count the equal intervals between two labeled marks. - Identify which tick the pointer reaches.

Solution

1. From \(0\,\text{g}\) to \(500\,\text{g}\) there are two equal intervals, so each interval represents \(250\,\text{g}\). 2. The pointer is at the next tick after \(500\,\text{g}\). 3. Add one interval: \(500 + 250 = 750\,\text{g}\).

Answer

\(750\,\text{g}\)
5160043
A large pineapple weighs \(925\,\text{g}\). The peel and tough core weigh \(387\,\text{g}\) altogether. How many grams of fruit remain?

Hints

- Think about what remains after the peel and core are removed from the whole pineapple. - Which operation finds a difference or a remaining amount?

Solution

1. Subtract the weight of the peel and core from the total weight: \(925\,\text{g} - 387\,\text{g} = 538\,\text{g}\).

Answer

\(538\,\text{g}\) of fruit remain.
5166703
Match each object with a reasonable capacity. Objects: a teaspoon, a small yogurt cup, a mop bucket, a full bathtub Capacities: \(5\,\text{mL}\), \(150\,\text{mL}\), \(10\,\text{L}\), \(150\,\text{L}\)

Hints

- Order the objects from least capacity to greatest capacity. - Milliliters describe smaller capacities than liters. - Compare each object with a familiar water bottle or container.

Solution

1. A teaspoon holds about \(5\,\text{mL}\). 2. A small yogurt cup holds about \(150\,\text{mL}\). 3. A mop bucket holds about \(10\,\text{L}\). 4. A full bathtub holds about \(150\,\text{L}\).

Answer

Teaspoon: \(5\,\text{mL}\); small yogurt cup: \(150\,\text{mL}\); mop bucket: \(10\,\text{L}\); full bathtub: \(150\,\text{L}\)
5166803
A bottle holds \(600\,\text{mL}\) of juice. Four full cups fill the bottle exactly. How many milliliters does each cup hold?

Hints

- The four cups hold \(600\,\text{mL}\) altogether. - Divide the total volume into four equal parts. - Check by multiplying your answer by \(4\).

Solution

1. Four equal cupfuls have a total volume of \(600\,\text{mL}\). 2. Divide the total volume by \(4\): \(600\,\text{mL} \div 4 = 150\,\text{mL}\).

Answer

Each cup holds \(150\,\text{mL}\).
5217753
Give a reasonable estimate for each measurement. Include an appropriate metric unit. a) The mass of a chicken egg b) The amount of juice in a small juice box c) The mass of a packed elementary-school backpack d) The amount of water in a filled bathtub

Hints

- Compare each item with a familiar object or container. - Decide whether grams or kilograms are more suitable for each mass. - Decide whether milliliters or liters are more suitable for each liquid volume.

Solution

1. A chicken egg has a mass of about \(60\,\text{g}\). 2. A small juice box holds about \(250\,\text{mL}\). 3. A packed elementary-school backpack may have a mass of about \(4\,\text{kg}\). 4. A filled bathtub may contain about \(150\,\text{L}\) of water. Other nearby estimates with suitable units are also reasonable.

Answer

Sample estimates: a) About \(60\,\text{g}\) b) About \(250\,\text{mL}\) c) About \(4\,\text{kg}\) d) About \(150\,\text{L}\)
5402313
A nature center has \(125\,\text{g}\) of sunflower seeds and \(240\,\text{g}\) of pumpkin seeds. What is the total mass of the seeds?

Hints

- Decide which operation combines two masses into one total. - Check that both quantities use grams before combining them. - Use place value to add the hundreds, tens, and ones accurately.

Solution

1. The two masses are given in the same unit, so add them. 2. \(125 + 240 = 365\).

Answer

The total mass is \(365\,\text{g}\).
5402634
An art club has \(50\,\text{g}\) of modeling clay. Each sample packet must contain exactly \(8\,\text{g}\). How many full packets can the club make, and how many grams of clay will be left?

Hints

- Find how many complete equal packets can be made without using more clay than is available. - After accounting for the full packets, check whether any clay remains.

Solution

1. Find the greatest multiple of \(8\) that does not exceed \(50\): \(6 \times 8 = 48\). 2. The club can make \(6\) full packets. 3. Subtract the packed mass: \(50 - 48 = 2\).

Answer

The club can make \(6\) full packets, with \(2\,\text{g}\) of clay left.
5402673
A bicycle helmet has a mass of \(650\,\text{g}\). A set of knee pads has a mass of \(430\,\text{g}\). How many grams heavier is the helmet?

Hints

- The question asks for how much greater one mass is than the other. - Subtract the smaller mass from the larger mass.

Solution

1. Find the difference between the masses: \(650 - 430 = 220\).

Answer

The helmet is \(220\,\text{g}\) heavier.
5402733
A package is placed on a scale that is known to read \(200\,\text{g}\) too high. The scale shows \(850\,\text{g}\). What is the package’s actual mass?

Hints

- Decide whether the incorrect reading is greater or less than the actual mass. - Remove the amount by which the scale reads too high.

Solution

1. A reading that is too high includes an extra \(200\,\text{g}\). 2. Subtract the scale’s error: \(850 - 200 = 650\).

Answer

The package’s actual mass is \(650\,\text{g}\).
5403363
Six identical wax samples have a total mass of \(42\,\text{g}\). Which equation correctly finds the mass of one sample: \(42 \div 6\), \(6 \div 42\), \(42 - 6\), or \(42 + 6\)? Explain your choice and solve.

Hints

- Identify which number is the whole amount and which number tells how many equal parts there are. - Check whether the result could be multiplied by the number of samples to recover the total mass.

Solution

1. The total mass must be separated into \(6\) equal sample masses, so the whole is divided by the number of samples. 2. The correct equation is \(42 \div 6 = 7\).

Answer

The correct equation is \(42 \div 6\), and one sample has a mass of \(7\,\text{g}\).
5403413
A toolbox with its tools has a mass of \(9\,\text{kg}\). The tools alone have a mass of \(6\,\text{kg}\). Mina adds the numbers and says the empty toolbox has a mass of \(15\,\text{kg}\). Explain the error and find the empty toolbox's mass.

Hints

- Decide which amount is the whole and which amount is one part of that whole. - Check whether the missing part should be smaller than the combined mass.

Solution

1. The \(9\)-kilogram mass already includes the toolbox and the tools, so adding the tools again counts them twice. 2. Subtract the tools from the combined mass: \(9 - 6 = 3\).

Answer

Mina counted the tools twice. The empty toolbox has a mass of \(3\,\text{kg}\).
5403613
Boxes on a shelf have a total mass of \(14\,\text{kg}\), and the shelf can safely hold \(6\,\text{kg}\) more. A student says the shelf's mass limit is \(14 - 6 = 8\,\text{kg}\). Explain the error and find the correct limit.

Hints

- Decide whether the unused capacity is part of or separate from the final limit. - Check whether the limit should be greater than the mass already on the shelf.

Solution

1. The \(6\) kilograms describe additional capacity, so they must be combined with the current mass. 2. Add: \(14 + 6 = 20\).

Answer

The student subtracted an amount that can still be added. The shelf's mass limit is \(20\,\text{kg}\).
5403653
Each refill bottle holds \(2\,\text{L}\). Complete the total-volume entries in the table and describe the pattern. <table><thead><tr><th>Number of bottles</th><th>Total volume</th></tr></thead><tbody><tr><td>\(1\)</td><td>?</td></tr><tr><td>\(3\)</td><td>?</td></tr><tr><td>\(5\)</td><td>?</td></tr><tr><td>\(8\)</td><td>?</td></tr></tbody></table>

Hints

- Use the same amount for every bottle. - Look at how the total changes when the bottle count increases.

Solution

1. One bottle holds \(1 \times 2 = 2\) liters. 2. Three bottles hold \(3 \times 2 = 6\) liters. 3. Five bottles hold \(5 \times 2 = 10\) liters. 4. Eight bottles hold \(8 \times 2 = 16\) liters. 5. The total volume increases by \(2\) liters for each additional bottle.

Answer

\(1\) bottle: \(2\,\text{L}\) \(3\) bottles: \(6\,\text{L}\) \(5\) bottles: \(10\,\text{L}\) \(8\) bottles: \(16\,\text{L}\) The total increases by \(2\,\text{L}\) per bottle.
5403793
A student records the mass of one metal clip as \(5\,\text{kg}\). Explain why that unit is unreasonable and give a reasonable corrected measurement using the same number.

Hints

- Compare the object with familiar items measured in grams and kilograms. - Keep the numerical value fixed and decide which metric mass unit is sensible.

Solution

1. A mass of \(5\) kilograms is reasonable for a heavy bag or small piece of equipment, not for one metal clip. 2. Grams are an appropriate unit for a light object such as a clip.

Answer

The reasonable corrected measurement is \(5\,\text{g}\), not \(5\,\text{kg}\).
5404033
One bag of beads has a mass of \(480\,\text{g}\), and another has a mass of \(320\,\text{g}\). A student adds \(48 + 32 = 80\) and reports a total of \(80\,\text{g}\). Explain the place-value error and find the correct total mass.

Hints

- Check the value represented by each digit before adding. - Estimate the total to see whether an answer much smaller than either bag can be reasonable.

Solution

1. The student treated \(480\) and \(320\) as though they were \(48\) and \(32\), losing a factor of \(10\). 2. Add the actual masses: \(480 + 320 = 800\).

Answer

The student ignored the zero place values. The correct total mass is \(800\,\text{g}\).
5404273
Three mineral samples have a total mass of \(70\,\text{g}\). The first two samples have a combined mass of \(42\,\text{g}\). What is the mass of the third sample?

Hints

- Treat the first two samples as one known part. - Subtract that known part from the total mass. - Label the answer in grams.

Solution

1. Subtract the known combined mass from the total: \(70 - 42 = 28\).

Answer

The third sample has a mass of \(28\,\text{g}\).
5548463
The graduated container below is marked in milliliters. What volume of liquid is shown, and how many more milliliters are needed to reach \(1000\,\text{mL}\)?
Figure for problem 554846

Hints

- Read the labeled graduation that is level with the top of the shaded liquid. - Compare that reading with \(1000\,\text{mL}\). - Use subtraction to find the amount still needed.

Solution

1. The top of the liquid lines up with the \(750\,\text{mL}\) mark. 2. The target is \(1000\,\text{mL}\). 3. Subtract: \(1000 - 750 = 250\,\text{mL}\).

Answer

The container shows \(750\,\text{mL}\), and \(250\,\text{mL}\) more are needed to reach \(1000\,\text{mL}\).
5160053
Lucas wants to know which fruit gives him more to eat. A mango weighs \(453\,\text{g}\). Its pit and peel weigh \(165\,\text{g}\) altogether. An avocado weighs \(312\,\text{g}\). Its pit and peel weigh \(88\,\text{g}\) altogether. Which fruit has more edible fruit? How many more grams of edible fruit does it have?

Hints

- First find the edible amount for each fruit separately. - Compare the two results. - To find the difference, subtract the smaller result from the larger result.

Solution

1. Find the edible part of the mango: \(453\,\text{g} - 165\,\text{g} = 288\,\text{g}\). 2. Find the edible part of the avocado: \(312\,\text{g} - 88\,\text{g} = 224\,\text{g}\). 3. Compare the amounts: \(288\,\text{g} > 224\,\text{g}\), so the mango has more edible fruit. 4. Find the difference: \(288\,\text{g} - 224\,\text{g} = 64\,\text{g}\).

Answer

The mango has more edible fruit. It has \(64\,\text{g}\) more than the avocado.
5160063
A honeydew melon weighs \(870\,\text{g}\). After the rind and seeds are removed, \(615\,\text{g}\) of fruit remain. a) How much do the rind and seeds weigh? b) How much rind and seeds would there be altogether from two identical honeydew melons?

Hints

- For part a, find the difference between the whole melon and the edible fruit. - After you know the amount for one melon, how can you find the amount for two melons?

Solution

1. Find the weight of the rind and seeds from one melon: \(870\,\text{g} - 615\,\text{g} = 255\,\text{g}\). 2. Double that amount for two melons: \(255\,\text{g} + 255\,\text{g} = 510\,\text{g}\).

Answer

a) The rind and seeds weigh \(255\,\text{g}\). b) Two melons produce \(510\,\text{g}\) of rind and seeds altogether.
5403703
Three supply bags have masses of \(2\,\text{kg}\), \(5\,\text{kg}\), and \(8\,\text{kg}\). Put the bags in order from lightest to heaviest, find their total mass, and find the difference between the heaviest and lightest bags.

Hints

- Use the numerical masses to order the bags before calculating. - The total and the greatest-to-least difference answer different questions.

Solution

1. The masses in increasing order are \(2\), \(5\), and \(8\) kilograms. 2. Their total mass is \(2 + 5 + 8 = 15\) kilograms. 3. The difference between the heaviest and lightest bags is \(8 - 2 = 6\) kilograms.

Answer

Order: \(2\,\text{kg}\), \(5\,\text{kg}\), \(8\,\text{kg}\) Total mass: \(15\,\text{kg}\) Heaviest-lightest difference: \(6\,\text{kg}\)
5404223
A filled bucket has a mass of \(13\,\text{kg}\), and the empty bucket has a mass of \(1\,\text{kg}\). A student subtracts correctly but reports that the sand has a volume of \(12\,\text{L}\). Explain the unit error and state the correct measurement.

Hints

- Track both the measurement attribute and the unit used for the two given quantities. - A correct numerical calculation can still be reported with the wrong kind of unit.

Solution

1. The sand's mass is \(13 - 1 = 12\,\text{kg}\). 2. The subtraction compares masses measured in kilograms, so the result is also a mass measured in kilograms. 3. Liters measure volume, not mass, so \(12\,\text{L}\) does not describe the quantity found by the subtraction.

Answer

The sand has a mass of \(12\,\text{kg}\), not a volume of \(12\,\text{L}\).
5548473
Two dial scales have equally spaced marks, but the two scales use different gram intervals. Read both pointers. Which mass is greater, and by how many grams?
Figure for problem 554847

Hints

- Determine the value of one equal interval on each dial separately. - Read each pointer only after finding that dial's interval value. - Subtract the smaller mass reading from the larger one.

Solution

1. On scale a), \(0\) to \(400\) grams spans two equal intervals, so each interval is \(200\) grams. The pointer is at \(600\) grams. 2. On scale b), \(0\) to \(500\) grams spans two equal intervals, so each interval is \(250\) grams. The pointer is at \(750\) grams. 3. Compare the readings: \(750 - 600 = 150\) grams.

Answer

Scale b) shows the greater mass, by \(150\,\text{g}\).
5548483
Two graduated containers show the volume of water before and after more water was added. The marks are equally spaced. Read both volumes and determine how many milliliters were added.
Figure for problem 554848

Hints

- Use the labeled \(0\), \(500\), and \(1000\) mL marks to find the value of one equal interval. - Read the liquid surface in each container before comparing the volumes. - Subtract the earlier reading from the later reading.

Solution

1. From \(0\) to \(500\) milliliters there are two equal intervals, so each interval represents \(250\) milliliters. 2. Container a) is at the first tick above \(0\), so it shows \(250\) milliliters. 3. Container b) is at the first tick above \(500\), so it shows \(750\) milliliters. 4. Subtract: \(750 - 250 = 500\) milliliters were added.

Answer

Container a) shows \(250\,\text{mL}\), container b) shows \(750\,\text{mL}\), and \(500\,\text{mL}\) were added.

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