Practice Cancellation in Math

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

Quick Recap

Cancellation is the process of removing a common factor from the numerator and denominator of a fraction, or from both sides of an equation, to simplify. It works because dividing both parts by the same nonzero number leaves an equivalent but simpler form.

68=34\frac{6}{8} = \frac{3}{4} because we can cancel the common factor 2 from top and bottom.

Showing a random 20 of 50 problems.

Example 1

medium
Simplify 1421+13\frac{14}{21}+\frac{1}{3} by reducing first.

Example 2

challenge
Simplify x2โˆ’9x+3\frac{x^2-9}{x+3} for xโ‰ โˆ’3x\ne -3.

Example 3

easy
Simplify 1015\frac{10}{15}.

Example 4

challenge
Simplify x3โˆ’1xโˆ’1\frac{x^3-1}{x-1} for xโ‰ 1x\ne 1.

Example 5

easy
Simplify 2(xโˆ’1)4\frac{2(x-1)}{4}.

Example 6

easy
Simplify 1624\frac{16}{24}.

Example 7

medium
Simplify x(x+1)x\frac{x(x+1)}{x} for xโ‰ 0x\ne 0.

Example 8

medium
Simplify 12ab18b\frac{12ab}{18b} for bโ‰ 0b\ne 0.

Example 9

medium
Simplify 6x+93\frac{6x+9}{3}.

Example 10

medium
Simplify 23ร—94\frac{2}{3}\times\frac{9}{4} by cancelling before multiplying.

Example 11

medium
Solve 4x=204x = 20 using cancellation.

Example 12

challenge
Why is cancelling the 2 in 2+x2\frac{2+x}{2} to get xx wrong? Give the correct simplification.

Example 13

easy
Simplify 05\frac{0}{5}.

Example 14

medium
Simplify 1545\frac{15}{45} in one step.

Example 15

easy
Simplify 812\frac{8}{12}.

Example 16

medium
Reduce 3660\frac{36}{60}.

Example 17

easy
Simplify 5a5\frac{5a}{5}.

Example 18

easy
Simplify 3ร—53ร—7\dfrac{3 \times 5}{3 \times 7}.

Example 19

easy
Simplify 99\frac{9}{9}.

Example 20

medium
Simplify 49ร—278\frac{4}{9}\times\frac{27}{8} by cancelling before multiplying.