Practice Operations with Rational Numbers in Math

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

Worksheet PDF Free Answer-key PDF Family

Quick Recap

Extending addition, subtraction, multiplication, and division to the full set of rational numbers—including fractions, decimals, mixed numbers, and their negative counterparts.

Once you can handle integers and fractions separately, combine the skills: apply the sign rules you know from integers to fractions and decimals. −23+14-\frac{2}{3} + \frac{1}{4} uses common denominators AND sign rules at the same time.

Showing a random 20 of 50 problems.

Example 1

easy
Compute 27×0\dfrac{2}{7} \times 0.

Example 2

medium
Calculate 78÷34\frac{7}{8} \div \frac{3}{4}.

Example 3

easy
Convert 74\dfrac{7}{4} to a mixed number.

Example 4

medium
Compute 212×252\frac{1}{2} \times \frac{2}{5}.

Example 5

easy
Compute 23×35\frac{2}{3} \times \frac{3}{5}.

Example 6

medium
Compute 23÷4\frac{2}{3} \div 4.

Example 7

challenge
Compute 12+1312−13\dfrac{ \frac{1}{2} + \frac{1}{3} }{ \frac{1}{2} - \frac{1}{3} }.

Example 8

hard
A bank account starts at 00, deposits $45.75\$45.75, and then has a withdrawal of $60.20\$60.20. What is the balance?

Example 9

challenge
If x=−23x = -\dfrac{2}{3} and y=34y = \dfrac{3}{4}, compute x2−2xy+y2x^2 - 2xy + y^2.

Example 10

hard
Compute (−34)+56×310\left(-\dfrac{3}{4}\right) + \dfrac{5}{6} \times \dfrac{3}{10}.

Example 11

medium
Compute −1.2÷0.3-1.2 \div 0.3.

Example 12

medium
Compute −23+14-\frac{2}{3} + \frac{1}{4}.

Example 13

easy
Compute 35+15\dfrac{3}{5} + \dfrac{1}{5}.

Example 14

medium
Compute 314−1233\dfrac{1}{4} - 1\dfrac{2}{3}.

Example 15

medium
Compute (−2)3(-2)^3.

Example 16

medium
Compute −3−(−7)-3 - (-7).

Example 17

medium
Compute (−25)2\left(-\dfrac{2}{5}\right)^2.

Example 18

medium
Calculate 56×310\frac{5}{6} \times \frac{3}{10} and simplify.

Example 19

medium
Compute −23÷(−12)-\frac{2}{3} \div \left(-\frac{1}{2}\right).

Example 20

easy
Compute −3+7-3 + 7.
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