Aimathic
Login | English | Deutsch

Free math worksheets

Build your own math worksheets from 30,000+ problems for grades 3 to 12, from fractions to AP Calculus. Every problem comes with step-by-step solutions.

Division fact fluency

Click problems to add them to your worksheet.

5184333
Find each answer. \(27 \div 9\); \(54 \div 9\); \(81 \div 9\); \(18 \div 9\); \(45 \div 9\) \(72 \div 9\); \(63 \div 9\); \(36 \div 9\); \(9 \div 9\); \(90 \div 9\)

Hints

- Think of the related multiplication fact. - Recall the \(9\)s multiplication facts. - Ask how many groups of \(9\) make each starting number.

Solution

1. The first row gives \(27 \div 9 = 3\), \(54 \div 9 = 6\), \(81 \div 9 = 9\), \(18 \div 9 = 2\), and \(45 \div 9 = 5\). 2. The second row gives \(72 \div 9 = 8\), \(63 \div 9 = 7\), \(36 \div 9 = 4\), \(9 \div 9 = 1\), and \(90 \div 9 = 10\).

Answer

\(3; 6; 9; 2; 5; 8; 7; 4; 1; 10\)
5205893
Find \(42\div7\). Write the complete equation.

Hints

- Think of the 7s multiplication facts. - What number times \(7\) equals \(42\)?

Solution

1. \(7\times6=42\). 2. So \(42\div7=6\).

Answer

\(42\div7=6\)
5503563
Find each answer. a) \(24 \div 6\) b) \(35 \div 5\) c) \(54 \div 9\) d) \(72 \div 8\)

Hints

- Think of the multiplication fact related to each division fact. - Ask what number makes the related multiplication fact true. - Check each answer with multiplication.

Solution

1. \(24 \div 6 = 4\). 2. \(35 \div 5 = 7\). 3. \(54 \div 9 = 6\). 4. \(72 \div 8 = 9\).

Answer

a) \(4\) b) \(7\) c) \(6\) d) \(9\)
5179344
The list is \(14,16,24,30,32,42,48,54,56,64,72,80\). Which numbers are multiples of \(8\)? Explain how you know.

Hints

- Think about the products you get by multiplying \(8\) by whole numbers. - Check each candidate against the sequence of multiples of \(8\). - Make sure every selected number can be written as \(8\) times a whole number.

Solution

1. A multiple of \(8\) can be written as \(8\times n\) for a whole number \(n\). 2. From the list, \(16=8\times2\), \(24=8\times3\), \(32=8\times4\), \(48=8\times6\), \(56=8\times7\), \(64=8\times8\), \(72=8\times9\), and \(80=8\times10\). 3. Therefore, those eight numbers are the multiples of \(8\) in the list.

Answer

\(16,24,32,48,56,64,72,80\)
5183303
Find the missing numbers. Use the 8s multiplication facts. \(32 \div 8 = \square\) \(48 \div \square = 6\) \(\square \div 8 = 3\) \(\square \div 8 = 10\)

Hints

- 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.

Solution

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 \(80\).

Answer

\(32 \div 8 = 4\) \(48 \div 8 = 6\) \(24 \div 8 = 3\) \(80 \div 8 = 10\)
5185153
Check each equation. Two are incorrect. Find them and write the corrected equations. a) \(42\,\text{lb} \div 6 = 7\,\text{lb}\) b) \(54\,\text{ft} \div 9 = 7\,\text{ft}\) c) \(32\,\text{cups} \div 4 = 8\,\text{cups}\) d) \(48\,\text{in.} \div 8 = 6\,\text{in.}\) e) \(\$63 \div 7 = \$8\)

Hints

- Use multiplication to check each division equation. - For each one, ask what number multiplied by the number you divide by makes the starting amount. - Exactly two equations need to be corrected.

Solution

1. Part a is correct because \(42 \div 6 = 7\). 2. Part b is incorrect because \(54 \div 9 = 6\). The correction is \(54\,\text{ft} \div 9 = 6\,\text{ft}\). 3. Part c is correct because \(32 \div 4 = 8\). 4. Part d is correct because \(48 \div 8 = 6\). 5. Part e is incorrect because \(63 \div 7 = 9\). The correction is \(\$63 \div 7 = \$9\).

Answer

b) \(54\,\text{ft} \div 9 = 6\,\text{ft}\) e) \(\$63 \div 7 = \$9\)
5185163
Work out each division expression. Which letters have the same answer, even though the units are different? A) \(56\,\text{oz}\div7\) B) \(72\,\text{min}\div9\) C) \(24\,\text{cups}\div3\) D) \(\$45\div5\) E) \(64\,\text{ft}\div8\)

Hints

- Find each expression separately. - Write the number answer next to each letter. - Compare the five number answers after you finish.

Solution

1. A gives \(56 \div 7 = 8\). 2. B gives \(72 \div 9 = 8\). 3. C gives \(24 \div 3 = 8\). 4. D gives \(45 \div 5 = 9\). 5. E gives \(64 \div 8 = 8\). 6. A, B, C, and E all have the answer \(8\).

Answer

A, B, C, and E; each equals \(8\).
5185353
Work out each pair mentally. Write \(<\), \(>\), or \(=\). a) \(32\div4\;\square\;18\div2\) b) \(45\div5\;\square\;54\div6\) c) \(21\div3\;\square\;28\div7\) d) \(40\div8\;\square\;30\div5\) e) \(72\div9\;\square\;64\div8\)

Hints

- Find the answer to each division fact. - Compare the two answers in each pair. - Use a multiplication fact to check any answer you are unsure about.

Solution

1. \(32 \div 4 = 8\) and \(18 \div 2 = 9\), so \(8 < 9\). 2. \(45 \div 5 = 9\) and \(54 \div 6 = 9\), so \(9 = 9\). 3. \(21 \div 3 = 7\) and \(28 \div 7 = 4\), so \(7 > 4\). 4. \(40 \div 8 = 5\) and \(30 \div 5 = 6\), so \(5 < 6\). 5. \(72 \div 9 = 8\) and \(64 \div 8 = 8\), so \(8 = 8\).

Answer

a) \(<\) b) \(=\) c) \(>\) d) \(<\) e) \(=\)
5211153
Find the missing number in each division equation. a) \(72\div8=\square\) b) \(\square\div4=8\) c) \(45\div\square=9\)

Hints

- Use multiplication facts to work backward when the missing number comes first. - Check each completed division equation. - The same multiplication and division facts use the same three numbers.

Solution

1. \(72\div8=9\). 2. \(32\div4=8\), so the missing number is \(32\). 3. \(45\div5=9\), so the missing number is \(5\).

Answer

a) \(9\) b) \(32\) c) \(5\)
5373643
Look at the array. Write a division equation that finds how many dots are in each row. Then write a multiplication equation to check your answer.
Figure for problem 537364

Hints

- Count the rows and the dots in one row. - Use the whole number of dots as the first number in your division equation. - Multiply the number of rows by the number in each row to check.

Solution

1. The array has \(32\) dots arranged in \(8\) rows, with \(4\) dots in each row. 2. The division equation is \(32\div8=4\). 3. The multiplication check is \(8\times4=32\).

Answer

\(32\div8=4\); check: \(8\times4=32\)
5503473
Find each answer. a) \(56 \div 7\) b) \(72 \div 9\) c) \(45 \div 5\) Choose one answer and verify it with a multiplication equation.

Hints

- For each division fact, think of a related multiplication fact with one missing number. - Keep the starting total as the product in your multiplication check. - Check one answer by multiplying the two smaller numbers.

Solution

1. \(56 \div 7 = 8\). 2. \(72 \div 9 = 8\). 3. \(45 \div 5 = 9\). 4. One possible check is \(7 \times 8 = 56\), which verifies part a).

Answer

a) \(8\) b) \(8\) c) \(9\) One possible check: \(7 \times 8 = 56\).
5503573
Find the missing starting number in each division fact. a) \(\square\div6=7\) b) \(\square\div8=5\) c) \(\square\div9=4\) d) \(\square\div3=8\)

Hints

- Work backward with multiplication. - Multiply the number after \(\div\) by the answer. - Check the completed division fact.

Solution

1. \(6 \times 7 = 42\), so \(42 \div 6 = 7\). 2. \(8 \times 5 = 40\), so \(40 \div 8 = 5\). 3. \(9 \times 4 = 36\), so \(36 \div 9 = 4\). 4. \(3 \times 8 = 24\), so \(24 \div 3 = 8\).

Answer

a) \(42\) b) \(40\) c) \(36\) d) \(24\)
5503583
Sort the four division facts into two groups: those with answer \(6\) and those with answer \(8\). \(42\div7\), \(54\div9\), \(48\div6\), \(64\div8\)

Hints

- Use related multiplication facts instead of guessing. - Look for facts that make \(6\) or \(8\) as the division answer. - Check every division fact before placing it in a group.

Solution

1. \(42 \div 7 = 6\) and \(54 \div 9 = 6\). 2. \(48 \div 6 = 8\) and \(64 \div 8 = 8\).

Answer

Answer \(6\): \(42\div7\), \(54\div9\) Answer \(8\): \(48\div6\), \(64\div8\)
5503593
Without a calculator, decide which is greater: \(63\div7\) or \(64\div8\). Explain using multiplication facts.

Hints

- Turn each answer into a multiplication question. - Which multiplication facts make \(63\) and \(64\)? - Compare the two whole-number answers after finding them.

Solution

1. Since \(7 \times 9 = 63\), \(63 \div 7 = 9\). 2. Since \(8 \times 8 = 64\), \(64 \div 8 = 8\). 3. Therefore, \(63 \div 7\) is greater by \(1\).

Answer

\(63 \div 7\) is greater. The answers are \(9\) and \(8\).
5503613
Write three division facts with answer \(5\): one that divides by \(4\), one that divides by \(7\), and one that divides by \(9\). Then check each fact with multiplication.

Hints

- Keep the answer fixed at \(5\). - Use multiplication to find the starting number for each division fact. - Check each completed division equation with multiplication.

Solution

1. For a fact that divides by \(4\), use \(4\times5=20\), so \(20\div4=5\). 2. For a fact that divides by \(7\), use \(7\times5=35\), so \(35\div7=5\). 3. For a fact that divides by \(9\), use \(9\times5=45\), so \(45\div9=5\).

Answer

\(20 \div 4 = 5\) \(35 \div 7 = 5\) \(45 \div 9 = 5\)
5158163
What number is each input divided by? Complete the table. Then add your own example in the last row. <table> <tr><th colspan="2">\(\div \square\)</th></tr> <tr><td>\(18\)</td><td>\(2\)</td></tr> <tr><td>\(54\)</td><td></td></tr> <tr><td></td><td>\(9\)</td></tr> <tr><td></td><td></td></tr> </table>

Hints

- 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.

Solution

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 \(90 \div 9 = 10\).

Answer

The rule is divide by \(9\). The missing entries are \(6\) and \(81\). One possible final row is \(90\) and \(10\), because \(90 \div 9 = 10\).
5207853
Find the amount being subtracted each time. Use \(n\) for the unknown amount. a) Starting at \(36\), subtract the same amount \(4\) times to reach \(0\). What is \(n\)? b) Starting at \(63\), subtract the same amount \(7\) times to reach \(0\). What is \(n\)?

Hints

- 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.

Solution

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 \(63 \div 7=9\), \(n=9\).

Answer

a) \(n=9\) b) \(n=9\)
5503603
Ari checked four division facts: \(72 \div 8 = 9\) \(54 \div 6 = 9\) \(49 \div 7 = 6\) \(40 \div 5 = 8\) Exactly one check is wrong. Find it, correct it, and verify the correction with multiplication.

Hints

- Check each division answer with multiplication. - Work through all four facts one at a time. - Exactly one equation needs to change.

Solution

1. The incorrect equation is \(49 \div 7 = 6\). 2. Since \(7 \times 7 = 49\), the correct equation is \(49 \div 7 = 7\). 3. The other three equations are correct.

Answer

The wrong fact is \(49 \div 7 = 6\). It should be \(49 \div 7 = 7\), because \(7 \times 7 = 49\).

All problems may be used, copied and printed free of charge for school and tutoring, including paid tutoring. Commercial adaptations as well as publication or redistribution on the internet are not permitted.

Building free math worksheets