Simplifying algebraic fractions

Cancel common factors to simplify algebraic fractions; add and subtract algebraic fractions with numeric denominators; multiply and divide algebraic fractions.

Worked examples

Simplifying a single algebraic fraction

Straightforward

Problem

Simplify

\dfrac{10x^2}{4x}

Adding algebraic fractions with different denominators

Moderate

Problem

Simplify

\dfrac{x}{4} + \dfrac{x}{6}

Dividing algebraic fractions

Challenging

Problem

Simplify

\dfrac{9x^2}{4} \div \dfrac{3x}{8}

Practise

Open Math

Simplifying algebraic fractions

Algebra · MA4-ALG-C-01

Name:

Date:

Q1Straightforward

Which of the following is the simplified form of

\dfrac{6x}{9}

A. $\dfrac{x}{3}$
B. $\dfrac{2x}{3}$
C. $\dfrac{6}{9}$
D. $\dfrac{2}{3}$

Q2Straightforward

Which of the following is the simplified form of

\dfrac{4x^2}{8x}

A. $\dfrac{x^2}{2}$
B. $\dfrac{x}{2}$
C. $\dfrac{x}{8}$
D. $\dfrac{4x}{8}$

Q3Straightforward

Which of the following is the simplified form of

\dfrac{15m}{10}

A. $\dfrac{5m}{4}$
B. $\dfrac{3m}{2}$
C. $\dfrac{m}{2}$
D. $\dfrac{3m}{5}$

Q4Straightforward

Simplify

\dfrac{12y}{4y}

. Enter the numeric value.

Q5Moderate

Which of the following is the simplified form of

\dfrac{x}{3} + \dfrac{x}{4}

A. $\dfrac{7x}{12}$
B. $\dfrac{2x}{7}$
C. $\dfrac{x}{7}$
D. $\dfrac{2x}{12}$

Q6Moderate

Which of the following is the simplified form of

\dfrac{x}{2} + \dfrac{x}{5}

A. $\dfrac{7x}{10}$
B. $\dfrac{2x}{7}$
C. $\dfrac{x}{10}$
D. $\dfrac{3x}{7}$

Q7Moderate

Which of the following is the simplified form of

\dfrac{3x}{4} - \dfrac{x}{8}

A. $\dfrac{5x}{8}$
B. $\dfrac{x}{4}$
C. $\dfrac{x}{2}$
D. $\dfrac{2x}{4}$

Q8Moderate

Which of the following is the simplified form of

\dfrac{2x}{3} - \dfrac{x}{6}

A. $\dfrac{x}{2}$
B. $\dfrac{x}{3}$
C. $\dfrac{3x}{9}$
D. $\dfrac{x}{6}$

Q9Challenging

Simplify

\dfrac{3x}{4} \times \dfrac{8}{x}

. Enter the numeric value.

Q10Challenging

Simplify

\dfrac{2x}{5} \div \dfrac{x}{10}

. Enter the numeric value.

Q11Challenging

Which of the following is the simplified form of

\dfrac{6x^2}{5} \times \dfrac{10}{3x}

A. $2x$
B. $4x$
C. $\dfrac{4x^2}{3}$
D. $\dfrac{x}{4}$

Q12Challenging

Which of the following is the simplified form of

\dfrac{4x}{9} \div \dfrac{2x^2}{3}

A. $\dfrac{2}{3x}$
B. $\dfrac{8x^3}{27}$
C. $\dfrac{2x}{3}$
D. $\dfrac{3x}{2}$

Worked solutions and answers at openmath.au/year-8/algebraic-techniques/simplifying-algebraic-fractions