Free math worksheets

- Ask what number multiplied by \(6\) gives \(42\). - Use a familiar \(6\)s multiplication fact. - Check by multiplying your factor by \(6\).

1. Think of the multiplication fact that makes \(42\) with a factor of \(6\). 2. Since \(7 \times 6 = 42\), the missing factor is \(7\).

\(7\)

- In every part, the blank is one factor rather than the product. - Use a related division fact when the product and one factor are known. - Check each result by multiplying the two factors.

1. Since \(6 \times 7=42\), the missing factor in part a is \(6\). 2. Since \(9 \times 8=72\), the missing factor in part b is \(8\). 3. Since \(4 \times 6=24\), the missing factor in part c is \(4\). 4. Since \(9 \times 3=27\), the missing factor in part d is \(9\).

a) \(6\) b) \(8\) c) \(4\) d) \(9\)

- Think of the total as equal groups of \(\$4\). - Use a multiplication fact with an unknown factor. - Check that the contributions add to \(\$24\).

1. Let \(n\) be the number of sponsors. The equal contributions give \(4 \times n = 24\). 2. Since \(4 \times 6 = 24\), \(n = 6\).

\(6\) sponsors are needed.

- Find Ben's number first. - Use division to undo multiplication by \(3\). - Then add \(4\).

1. Find Ben’s number: \(30 \div 3 = 10\). 2. Mia’s number is \(10 + 4 = 14\).

Mia is thinking of \(14\).

- Think of the missing factor as the number that makes \(8\times\square=320\). - Use division by the known factor to find the missing factor. - Check your quotient by multiplying it by \(8\).

1. Divide the product by the known factor: \(320\div8=40\). 2. Check: \(8\times40=320\).

The other factor is \(40\).

- Use a multiplication fact with \(6\) and \(48\). - What number times \(6\) equals \(48\)? - Put that number in the division equation and check it.

1. Ask what number multiplied by \(6\) gives \(48\). 2. \(6\times8=48\), so the missing number is \(8\). 3. The complete equation is \(48\div8=6\).

\(48\div8=6\)

- One factor is the number of rows, and the product is the total number of tiles. - The unknown factor describes the equal size of each row. - Use the related division fact to find \(n\).

1. The unknown factor tells how many tiles are in each row. 2. Since \(28 \div 4=7\), \(n=7\). 3. Thus, the array has \(7\) tiles in each row.

\(n=7\). It represents the number of tiles in each row.

- “Four times \(n\)” is \(4\times n\). - Find \(50-10\). - What number multiplied by \(4\) gives that result?

1. The equation is \(4 \times n=50-10\). 2. \(50-10=40\), so \(4 \times n=40\). 3. Since \(4 \times 10=40\), \(n=10\).

a) \(4 \times n=50-10\) b) \(n=10\)

- Repeated subtraction to \(0\) can be represented by equal groups. - In each part, the number of subtractions is one factor and \(n\) is the other factor. - Use division to find the missing number from the starting total.

1. In part a, the repeated amount is the missing number in \(4 \times n=36\). Since \(36 \div 4=9\), \(n=9\). 2. In part b, the repeated amount is the missing number in \(7 \times n=63\). Since \(63 \div 7=9\), \(n=9\).

a) \(n=9\) b) \(n=9\)

- 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: \(64\)

- Use division to find a missing factor when the product and the other factor are known. - Check by multiplying from the bottom upward.

1. The bottom-left factor must satisfy \(\square \times 2=8\), so it is \(8 \div 2=4\). 2. The right factor in the second row must satisfy \(8 \times \square=48\), so it is \(48 \div 8=6\). 3. The bottom-right factor must satisfy \(2 \times \square=6\), so it is \(6 \div 2=3\).

Bottom row: \(4\), \(2\), \(3\) Second row: \(8\), \(6\) Top: \(48\)

- Use division to find a missing factor when the product is known. - Start with a small triangle in which two of the three values are known. - Check that every multiplication from bottom to top is correct.

1. The left brick in the second row must satisfy \(\square \times 10=80\), so it is \(8\). 2. The middle bottom value must satisfy \(4 \times \square=8\), so it is \(2\). 3. The right bottom value must satisfy \(2 \times \square=10\), so it is \(5\).

Bottom row: \(4\), \(2\), \(5\) Second row: \(8\), \(10\) Top: \(80\)

- Use the same total, \(42\), in both equations. - For Array A, ask: \(6\) times what number equals \(42\)? - For Array B, ask: \(7\) times what number equals \(42\)? Then compare the two missing numbers.

1. The first array has \(6\) rows and \(42\) dots, so \(6\times n=42\). Since \(6\times7=42\), \(n=7\). 2. The second array has \(7\) rows and \(42\) dots, so \(7\times n=42\). Since \(7\times6=42\), \(n=6\).

a) \(7\) tiles in each row b) \(6\) tiles in each row c) Array A: \(6\times n=42\), so \(n=7\). Array B: \(7\times n=42\), so \(n=6\). The values of \(n\) are \(7\) and \(6\).

- Start with the smallest allowed whole-number factor greater than \(6\). - Test the products in increasing factor order. - Once a product is greater than \(45\), think about what happens with still larger factors.

1. The allowed whole-number factors begin with \(7, 8, 9,\) and \(10\). 2. \(6 \times 7 = 42\), which is less than \(45\). 3. The next factor gives \(6 \times 8 = 48\), which is greater than \(45\). Any larger allowed factor gives an even larger product. 4. Therefore, the greatest possible missing factor is \(7\), and the product is \(42\).

The greatest possible missing factor is \(7\), and the product is \(42\). The next choice, \(8\), gives \(6\times8=48\), which is not less than \(45\).