Study notes

Fractions

Multiplying fractions and mixed numbers, fraction of a set, and fraction word problems.

Learn it step by step

Multiplying a fraction by a whole number

Multiply the numerator by the whole number and keep the denominator: $\frac{2}{5} \times 10 = \frac{20}{5} = 4$ . "Of" in a word problem usually signals multiplication.

taken

rest

\frac{2}{5}

of a set means 2 equal parts out of 5.

Multiplying two proper fractions

Multiply straight across: numerator times numerator, denominator times denominator. $\frac{2}{3} \times \frac{3}{4} = \frac{6}{12} = \frac{1}{2}$ , always simplify the final answer.

Multiplying with a mixed number

Change the mixed number to an improper fraction first, then multiply straight across: $1 \frac{1}{2} = \frac{3}{2}$ , so $1 \frac{1}{2} \times \frac{2}{3} = \frac{3}{2} \times \frac{2}{3} = \frac{6}{6} = 1$ .

Fraction of a set finds part of a group of objects

To find $\frac{3}{4}$ of 20 marbles, divide 20 into 4 equal parts ( $20 \div 4 = 5$ ) then take 3 of those parts: $3 \times 5 = 15$ .

\frac{3}{4}

of a group is the same idea as

75

out of

100

Worked examples

Work out

\frac{3}{4} \times 12

Multiply the numerator by 12: $3 \times 12 = 36$ .
Divide by the denominator: $36 \div 4 = 9$ .
$\frac{3}{4} \times 12 = 9$ .

Work out

\frac{2}{5} \times \frac{5}{6}

Multiply straight across: $\frac{2 \times 5}{5 \times 6} = \frac{10}{30}$ .
Simplify: $\frac{10}{30} = \frac{1}{3}$ .

Work out

2 \frac{1}{3} \times \frac{3}{7}

Change to an improper fraction: $2 \frac{1}{3} = \frac{7}{3}$ .
Multiply: $\frac{7}{3} \times \frac{3}{7} = \frac{21}{21}$ .
Simplify: $\frac{21}{21} = 1$ .

There are 36 pupils in a class.

\frac{2}{9}

of them wear glasses. How many pupils wear glasses?

Divide 36 into 9 equal parts: $36 \div 9 = 4$ .
Take 2 of those parts: $2 \times 4 = 8$ .
8 pupils wear glasses.

Mind map

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