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Fractions

Equivalent fractions, simplest form, comparing fractions, adding and subtracting like fractions, and finding a fraction of a quantity.

Learn it step by step

Equivalent fractions show the same amount in different ways

Multiplying (or dividing) the numerator and denominator by the same number gives an equivalent fraction: $\frac{1}{2} = \frac{2}{4} = \frac{3}{6}$ . They all shade the same amount of a whole.

1/2

\frac{1}{2}

and

\frac{2}{4}

cover exactly the same amount of the whole.

Simplest form uses the smallest possible numbers

A fraction is in simplest form when the numerator and denominator have no common factor other than 1. $\frac{4}{8}$ simplifies to $\frac{1}{2}$ by dividing both numbers by 4.

Compare like fractions by their numerators

Like fractions share the same denominator, so the one with the bigger numerator is bigger: $\frac{5}{8} > \frac{3}{8}$ . Simple unlike fractions can often be compared by first finding an equivalent fraction with a matching denominator.

Add or subtract like fractions by keeping the denominator

Only add or subtract the numerators; the denominator stays the same: $\frac{2}{7} + \frac{3}{7} = \frac{5}{7}$ . The answer in P3 will never be more than one whole.

A fraction of a quantity means dividing into equal groups

$\frac{1}{3}$ of 9 apples means splitting 9 apples into 3 equal groups and taking 1 group: $9 \div 3 = 3$ apples. For $\frac{2}{3}$ of 9, find one group first, then take 2 groups.

1 part

9 apples split into 3 equal parts of 3 apples each;

\frac{1}{3}

of 9 is 3.

Look and learn

Write an equivalent fraction for

\frac{3}{5}

with denominator 10.

Multiply the numerator and denominator by 2.
$\frac{3 \times 2}{5 \times 2} = \frac{6}{10}$ .

Write

\frac{6}{9}

in simplest form.

Both 6 and 9 can be divided by 3.
$\frac{6 \div 3}{9 \div 3} = \frac{2}{3}$ .

Work out

\frac{4}{9} + \frac{3}{9}

Same denominator, so add the numerators: $4 + 3 = 7$ .
Answer: $\frac{7}{9}$ .

Find

\frac{2}{5}

of 20 sweets.

Find 1 part: $20 \div 5 = 4$ .
Take 2 parts: $4 \times 2 = 8$ .
$\frac{2}{5}$ of 20 is 8 sweets.

Mind map

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