Study notes

Fractions

The four operations with fractions and mixed numbers, and solving fraction word problems.

Learn it step by step

Equivalent fractions have the same value

Multiplying (or dividing) the numerator and denominator by the same number gives an equivalent fraction: $\frac{2}{3} = \frac{4}{6} = \frac{6}{9}$ . Use this to compare or combine fractions with different denominators.

\frac{2}{3}

shaded is the same as

\frac{4}{6}

shaded, about 67 out of 100.

Add or subtract unlike fractions with a common denominator

To work out $\frac{1}{2} + \frac{1}{3}$ , rewrite both with denominator 6: $\frac{3}{6} + \frac{2}{6} = \frac{5}{6}$ . Always simplify the final answer if you can.

Multiply a fraction by a fraction

Multiply straight across: numerator times numerator, denominator times denominator. $\frac{2}{3} \times \frac{3}{4} = \frac{6}{12} = \frac{1}{2}$ . "Of" in a word problem usually means multiply.

Divide a fraction by flipping and multiplying

Dividing by a fraction means multiplying by its reciprocal (flip it upside down). $\frac{2}{3} \div \frac{1}{2} = \frac{2}{3} \times \frac{2}{1} = \frac{4}{3} = 1 \frac{1}{3}$ .

Fraction of a remainder problem

Many PSLE-style problems use a fraction of what is left. If $\frac{1}{4}$ of a ribbon is cut off, $\frac{3}{4}$ remains; a further fraction taken "of the remainder" applies to that $\frac{3}{4}$ , not the original whole.

cut

left

The ribbon splits into 4 equal parts: 1 part cut, 3 parts remain.

Worked examples

Work out

\frac{3}{4} + \frac{1}{6}

Common denominator of 4 and 6 is 12.
$\frac{3}{4} = \frac{9}{12}$ and $\frac{1}{6} = \frac{2}{12}$ .
$\frac{9}{12} + \frac{2}{12} = \frac{11}{12}$ .

Work out

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

Change to an improper fraction: $1 \frac{1}{2} = \frac{3}{2}$ .
Multiply: $\frac{3}{2} \times \frac{2}{3} = \frac{6}{6}$ .
Simplify: $\frac{6}{6} = 1$ .

Work out

\frac{5}{6} \div \frac{5}{9}

Flip the second fraction: $\frac{9}{5}$ .
Multiply: $\frac{5}{6} \times \frac{9}{5} = \frac{45}{30}$ .
Simplify: $\frac{45}{30} = 1 \frac{1}{2}$ .

Jun has 60 sweets. He eats

\frac{1}{3}

of them, then gives

\frac{1}{2}

of what is left to his sister. How many are left?

He eats $\frac{1}{3}$ of 60 = 20, leaving 40.
He gives away $\frac{1}{2}$ of 40 = 20.
Sweets left: $40 - 20 = 20$ .

Mind map

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