MathsFreePrintable

Algebraic Fractions Operations

A free maths worksheet ready for your classroom. Open in Kuraplan to grab the print-ready PDF, customize it for your students, or generate a fresh version in seconds.

Download now

Name:Date:

Algebraic Fractions Operations

Show your working. Give each answer in its simplest form, and state any values of a variable that must be excluded.

Add and subtract

Combine like terms when the denominators match. Otherwise, first find a common denominator.

1.Simplify \(\frac{5p}{12}+\frac{p}{12}\).

2.Simplify \(\frac{11q}{15}-\frac{2q}{15}\).

3.Simplify \(\frac{3r}{4}+\frac{5r}{8}\).

4.Which first step is appropriate for simplifying \(\frac{7u}{10}-\frac{u}{4}\)?

Subtract the numerators and keep the denominator 10.
Rewrite both fractions with denominator 20.
Multiply the numerators and denominators.
Take the reciprocal of the second fraction.

5.Simplify \(\frac{5s}{6}-\frac{s}{9}\).

Multiply and divide

Multiply numerators and denominators, or change division into multiplication by the reciprocal. Simplify where possible.

6.Simplify \(\frac{3v}{7}\times\frac{14}{15}\).

7.Simplify \(\frac{8w}{9}\div\frac{4}{3}\).

8.A pump moves water at \(\frac{5x}{6}\) litres per minute. How much water does it move in \(\frac{3}{5}\) of a minute? Give your answer in litres.

9.Simplify \(\frac{7a}{12}\times\frac{18}{14a}\), stating any excluded value of \(a\).

10.Simplify \(\frac{2b}{5}\div\frac{6b}{25}\), stating any excluded value of \(b\).

Match each expression to its simplified result

Write the letter of the matching result beside each expression.

11.Explain why \(\frac{2x}{3}+\frac{x}{5}\) needs a common denominator, while \(\frac{2x}{3}\times\frac{x}{5}\) does not. Include the simplified result of each expression.