Practice Division as Inverse in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

Understanding division as the reverse of multiplication: if a×b=ca \times b = c, then c÷b=ac \div b = a. This inverse relationship lets you undo multiplication to find missing factors.

If 3×4=123 \times 4 = 12, then 12÷4=312 \div 4 = 3. Division reverses the multiplication.

Showing a random 20 of 50 problems.

Example 1

easy
If 8×2=168 \times 2 = 16, what is 16÷816 \div 8?

Example 2

hard
If 3×n=2×243 \times n = 2 \times 24, find nn using division as inverse.

Example 3

easy
What is 20÷520 \div 5?

Example 4

easy
What number times 66 equals 4848?

Example 5

medium
Does dividing 1010 by 12\frac{1}{2} give a number bigger or smaller than 1010? Compute it.

Example 6

medium
A number times 9 equals 81. Use division as the inverse to find the unknown number.

Example 7

easy
If 3×4=123 \times 4 = 12, what is 12÷412 \div 4?

Example 8

medium
A bookshelf holds 144144 books in stacks of 1212. How many stacks?

Example 9

hard
If the area of a rectangle is 147147 and the length is 33 times the width, find both side lengths.

Example 10

medium
Solve: _÷9=7\_ \div 9 = 7.

Example 11

easy
If 5×6=305 \times 6 = 30, what is 30÷630 \div 6?

Example 12

hard
A bag of 144144 candies is shared so each kid gets 1212. The same total is later shared among twice as many kids. How many does each get?

Example 13

easy
If _×3=27\_ \times 3 = 27, what number fills the blank?

Example 14

medium
If 6×m=786 \times m = 78, what is mm?

Example 15

hard
A number is multiplied by 55, then 33 is added, giving 4848. What was the original number?

Example 16

easy
If 11×6=6611 \times 6 = 66, what is 66÷1166 \div 11?

Example 17

easy
Fill in the blank: _×9=72\_ \times 9 = 72.

Example 18

medium
If 54÷9=654 \div 9 = 6, write the two multiplication facts that confirm it.

Example 19

easy
Fill the blank: _×7=28\_ \times 7 = 28.

Example 20

medium
Solve for the missing factor: _×5=45\_ \times 5 = 45.
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