Free math worksheets

- Use a multiplication fact that has the same total as each division fact. - Your multiplication check must make the number being divided. - Write the multiplication check after each division answer.

1. Since \(7 \times 9 = 63\), \(63 \div 9 = 7\). 2. Since \(8 \times 4 = 32\), \(32 \div 4 = 8\). 3. Since \(9 \times 9 = 81\), \(81 \div 9 = 9\).

a) \(63 \div 9 = 7\); check: \(7 \times 9 = 63\) b) \(32 \div 4 = 8\); check: \(8 \times 4 = 32\) c) \(81 \div 9 = 9\); check: \(9 \times 9 = 81\)

- Think of a multiplication fact that uses the same two numbers. - Write the related multiplication fact to check each answer. - Your multiplication check should make the starting total.

1. \(32 \div 4 = 8\) because \(8 \times 4 = 32\). 2. \(42 \div 7 = 6\) because \(6 \times 7 = 42\). 3. \(45 \div 5 = 9\) because \(9 \times 5 = 45\). 4. \(56 \div 8 = 7\) because \(7 \times 8 = 56\).

a) \(32 \div 4 = 8\); check: \(8 \times 4 = 32\) b) \(42 \div 7 = 6\); check: \(6 \times 7 = 42\) c) \(45 \div 5 = 9\); check: \(9 \times 5 = 45\) d) \(56 \div 8 = 7\); check: \(7 \times 8 = 56\)

- What multiplication fact is related to each division equation? - When the first number is missing, multiply the other two numbers. - Check each completed equation with multiplication.

1. Since \(4\times8=32\), \(32\div8=4\). 2. Since \(6\times8=48\), the missing number in \(48\div\square=6\) is \(8\). 3. Since \(3\times8=24\), the missing number in \(\square\div8=3\) is \(24\). 4. Since \(10\times8=80\), the missing number in \(\square\div8=10\) is \(80\).

\(32 \div 8 = 4\) \(48 \div 8 = 6\) \(24 \div 8 = 3\) \(80 \div 8 = 10\)

- Read the number of rows and the number of dots in each row from the array. - The multiplication equation should describe the whole array. - Use the same three numbers to write the related division equations.

1. The array has \(4\) rows with \(8\) dots in each row, for \(32\) dots altogether. 2. The multiplication equation is \(4 \times 8 = 32\). 3. The related division equations are \(32 \div 4 = 8\) and \(32 \div 8 = 4\).

a) \(4\) rows and \(8\) dots in each row b) \(4 \times 8 = 32\) c) \(32 \div 4 = 8\) and \(32 \div 8 = 4\)

- Use the image to find how many equal sections there are. - Think of the total as being shared equally among those sections. - Use the same three numbers in both the multiplication and division equations.

1. The image shows \(3\) equal sections. 2. Dividing \(54\) tracks among \(3\) equal sections gives \(54 \div 3 = 18\) tracks per section. 3. The matching multiplication equation is \(3 \times 18 = 54\).

a) \(3\) sections b) \(18\) tracks in each section c) \(3 \times 18 = 54\) and \(54 \div 3 = 18\)

- Read the comics value first. - Think about what quantity would be one-half of the comics value. - Find the category whose bar has that value.

1. Comics were read \(20\) times. 2. Half of \(20\) is \(10\). 3. The mysteries bar shows \(10\), so mysteries were read half as often as comics.

Mysteries were read half as often as comics.

- Count the rows and the dots in one row. - Use the array to write a multiplication equation for the whole. - For each division equation, start with the whole and divide by one of the two factors to find the other.

1. The array has \(3\) rows with \(4\) dots in each row, so \(3 \times 4 = 12\). 2. Dividing the total by the number of rows gives the number in each row: \(12 \div 3 = 4\). 3. Dividing the total by the number in each row gives the number of rows: \(12 \div 4 = 3\).

\(3 \times 4 = 12\) \(12 \div 3 = 4\) \(12 \div 4 = 3\)

- Use the same three numbers in a related multiplication equation. - In the multiplication check, the product should be the number that was divided. - Use the multiplication equation to justify the missing number, not just to check it afterward.

1. a) Since \(7 \times 6=42\), the completed division equation is \(42 \div 6=7\). 2. b) Since \(9 \times 7=63\), the completed division equation is \(63 \div 7=9\). 3. c) Since \(4 \times 8=32\), the completed division equation is \(32 \div 8=4\). 4. d) Since \(9 \times 9=81\), the completed division equation is \(81 \div 9=9\). 5. In every part, the multiplication equation rebuilds the number being divided from the number you divide by and answer.

a) \(42 \div 6=7\); \(7 \times 6=42\) b) \(63 \div 7=9\); \(9 \times 7=63\) c) \(32 \div 8=4\); \(4 \times 8=32\) d) \(81 \div 9=9\); \(9 \times 9=81\)

- What number makes \(18\div\square=2\) true? - Use that same number in every row. - For a row with a missing starting number, use multiplication to work backward.

1. Since \(18 \div 9 = 2\), the number you divide by is \(9\). 2. Complete the second row: \(54 \div 9 = 6\). 3. Work backward in the third row: \(9 \times 9 = 81\), so \(81 \div 9 = 9\). 4. Any correct division fact with number you divide by \(9\) works in the last row, such as \(90 \div 9 = 10\).

The rule is divide by \(9\). The missing entries are \(6\) and \(81\). One possible final row is \(90\) and \(10\), because \(90 \div 9 = 10\).

- How can you find a missing factor when the product and one factor are known? - Use multiplication to work backward from a known product. - Complete the headers before filling the remaining products.

1. Since \(16 \div 2 = 8\), the first missing factor in the top row is \(8\). 2. Since \(20 \div 2 = 10\), the last missing factor in the top row is \(10\). 3. Since \(21 \div 7 = 3\), the missing factor in the first column is \(3\). 4. Complete the products: \(2 \times 7 = 14\), \(3 \times 8 = 24\), and \(3 \times 10 = 30\).

The completed table is: <table> <tr><td>\(\times\)</td><td>\(8\)</td><td>\(7\)</td><td>\(10\)</td></tr> <tr><td>\(2\)</td><td>\(16\)</td><td>\(14\)</td><td>\(20\)</td></tr> <tr><td>\(3\)</td><td>\(24\)</td><td>\(21\)</td><td>\(30\)</td></tr> </table>

- If you know a product and one number below it, divide to find the other number. - Start where a product and one number below it are both known. - Write the division equation before moving to the next missing brick.

1. The left bottom brick satisfies \(\square \times 4=8\), so \(8 \div 4=2\). 2. The missing right brick in the second row satisfies \(8 \times \square=64\), so \(64 \div 8=8\). 3. The right bottom brick satisfies \(4 \times \square=8\), so \(8 \div 4=2\). 4. The completed bottom row is \(2,4,2\), and the missing second-row value is \(8\).

Left bottom: \(8 \div 4=2\) Second-row right: \(64 \div 8=8\) Right bottom: \(8 \div 4=2\) Bottom row: \(2,4,2\) Second row: \(8,8\) Top: \(64\)

- Count the rows and the dots in each row of the array. - In part b), you know the total number of dots and the number of equal rows. - For part c), use the number of rows and the number of dots in each row. - Compare the three numbers in your division and multiplication equations.

1. The array has \(6\) rows with \(6\) dots in each row, so \(6 \times 6 = 36\). 2. The same \(36\) dots are arranged into \(4\) equal rows. \(36 \div 4 = 9\), so each row has \(9\) dots. 3. The multiplication check is \(4 \times 9 = 36\). 4. The division equation and multiplication equation use the same three numbers. Multiplication checks or undoes the division.

a) \(6 \times 6 = 36\) b) \(36 \div 4 = 9\) c) \(4 \times 9 = 36\) d) They use the same three numbers. Multiplication checks the division.

- Read the number represented by each bar. - Look for two quantities where the larger is a whole-number multiple of the smaller. - State the comparison in words after you identify the matching pair.

1. The graph shows \(18\) oak trees and \(9\) beech trees. 2. Since \(18=2 \times 9\), the number of oak trees is twice the number of beech trees.

There are twice as many oak trees as beech trees because \(18=2 \times 9\).

- Read the value represented by each bar. - Look for a pair in which the larger value is three groups of the smaller value. - State the relationship using the two bar names.

1. Bar B has a value of \(24\), and Bar A has a value of \(8\). 2. Since \(24=3 \times 8\), Bar B represents three times the quantity represented by Bar A.

Bar B represents three times the quantity represented by Bar A.

- Read each category’s value from the bar lengths and scale. - Look for a pair in which the larger value is two equal groups of the smaller value. - Use two different pairs for the two comparisons.

1. Apple has \(12\) votes, and pear has \(6\) votes. Since \(12=2 \times 6\), apple has twice as many votes as pear. 2. Pear has \(6\) votes, and melon has \(3\) votes. Since \(6=2 \times 3\), pear has twice as many votes as melon.

1) Apple has twice as many votes as pear. 2) Pear has twice as many votes as melon.