Sec 3 · G1 (N(T))

Multiplying and dividing algebraic fractions

Practise multiplying and dividing algebraic fractions with step-by-step help. Free account.

1. Multiplying and dividing

Cancel	How	Example
numbers	divide the top and the bottom by their HCF	$\dfrac{6}{36} = \dfrac{1}{6}$
letters	cross out a letter on top with the same letter underneath	$\dfrac{a \times a}{a} = a$

Write the letters out, then cross out pairs

\displaystyle \dfrac{a^{2}b}{ab^{3}}

e.g.

\displaystyle \dfrac{a^{2}b}{ab^{3}}

\displaystyle = \dfrac{a \times a \times b}{a \times b \times b \times b}

\displaystyle = \dfrac{a}{b^{2}}

Multiply: tops together, bottoms together, then cancel

\displaystyle \dfrac{3a}{4b} \times \dfrac{2b}{9}

e.g.

\displaystyle \dfrac{3a}{4b} \times \dfrac{2b}{9}

\displaystyle = \dfrac{6ab}{36b}

\displaystyle = \dfrac{a}{6}

Divide: flip the second fraction and multiply

\displaystyle \dfrac{5x}{6} \div \dfrac{10x^{2}}{3y}

e.g.

\displaystyle \dfrac{5x}{6} \div \dfrac{10x^{2}}{3y}

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

\displaystyle = \dfrac{15xy}{60x^{2}}

\displaystyle = \dfrac{y}{4x}

📖 Worked example

Simplify $\dfrac{11}{6x} \times \dfrac{4xy}{9}$ , giving your answer in its simplest form.

Step 1 of 3

Multiply the tops together and the bottoms together (write the letters out in full)

\dfrac{11}{6x} \times \dfrac{4xy}{9} = \dfrac{44 \times x \times y}{54 \times x}

📖 Worked example

Simplify $\dfrac{5}{11m} \div \dfrac{12n}{11m^2}$ , giving your answer in its simplest form.

Step 1 of 4

Change the division into a multiplication

\dfrac{5}{11m} \div \dfrac{12n}{11m^2} = \dfrac{5}{11m} \times \dfrac{11m^2}{12n}

Practise multiplying and dividing algebraic fractions with step-by-step help

Endless questions from basic to exam level. Get one wrong and see where it went wrong. Free account.

1. Multiplying and dividing

Cancel	How	Example
numbers	divide the top and the bottom by their HCF	$\dfrac{6}{36} = \dfrac{1}{6}$
letters	cross out a letter on top with the same letter underneath	$\dfrac{a \times a}{a} = a$

Write the letters out, then cross out pairs

\displaystyle \dfrac{a^{2}b}{ab^{3}}

e.g.

\displaystyle \dfrac{a^{2}b}{ab^{3}}

\displaystyle = \dfrac{a \times a \times b}{a \times b \times b \times b}

\displaystyle = \dfrac{a}{b^{2}}

Multiply: tops together, bottoms together, then cancel

\displaystyle \dfrac{3a}{4b} \times \dfrac{2b}{9}

e.g.

\displaystyle \dfrac{3a}{4b} \times \dfrac{2b}{9}

\displaystyle = \dfrac{6ab}{36b}

\displaystyle = \dfrac{a}{6}

Divide: flip the second fraction and multiply

\displaystyle \dfrac{5x}{6} \div \dfrac{10x^{2}}{3y}

e.g.

\displaystyle \dfrac{5x}{6} \div \dfrac{10x^{2}}{3y}

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

\displaystyle = \dfrac{15xy}{60x^{2}}

\displaystyle = \dfrac{y}{4x}

📖 Worked example

Simplify $\dfrac{11}{6x} \times \dfrac{4xy}{9}$ , giving your answer in its simplest form.

Step 1 of 3

Multiply the tops together and the bottoms together (write the letters out in full)

\dfrac{11}{6x} \times \dfrac{4xy}{9} = \dfrac{44 \times x \times y}{54 \times x}

📖 Worked example

Simplify $\dfrac{5}{11m} \div \dfrac{12n}{11m^2}$ , giving your answer in its simplest form.

Step 1 of 4

Change the division into a multiplication

\dfrac{5}{11m} \div \dfrac{12n}{11m^2} = \dfrac{5}{11m} \times \dfrac{11m^2}{12n}

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