Year 7AC9M7N04

Equivalent Fractions and Simplifying

Find equivalent representations of rational numbers and represent rational numbers on a number line.

Two fractions can look completely different and still be the same amount. Once you can move between those forms, every other fraction skill gets easier.

Method

Multiply or divide both parts by the same number

\frac{a}{b} = \frac{a \times k}{b \times k}

The value does not change. Only the way it is written changes.

Adding to the top and bottom does not work

\frac{1}{2} \neq \frac{1+1}{2+1}

You must multiply or divide. Adding changes the amount.

Simplest form means no common factor left

\frac{12}{18} = \frac{2}{3}

Divide by the highest common factor to get there in one step.

Simplify before you calculate

Smaller numbers mean fewer mistakes. Do it first, every time.

Improper fractions and mixed numerals are the same value

\frac{11}{4} = 2\frac{3}{4}

Divide top by bottom for the whole part; the remainder stays over the same bottom.

Worked example

e.g.

\text{Write } \frac{18}{24} \text{ in its simplest form.}

Find a number that divides into both the top and the bottom. $6 \text{ divides into } 18 \text{ and } 24$
Use the highest common factor so you finish in one step. $HCF(18, 24) = 6$
Divide the top by it. $18 \div 6 = 3$
Divide the bottom by the same number. $24 \div 6 = 4$
Write the answer. $\frac{18}{24} = \frac{3}{4}$
Check nothing divides into both any more. $3 \text{ and } 4 \text{ share no factor} \quad\checkmark$

Practice

Simplify each one fully.

\frac{10}{15}

Answer

\frac{2}{3}

\frac{24}{36}

Answer

\frac{2}{3}

\frac{45}{60}

Answer

\frac{3}{4}

\text{Fill the gap: } \frac{3}{5} = \frac{?}{20}

Answer

12

\text{Fill the gap: } \frac{7}{8} = \frac{35}{?}

Answer

40

\text{Is } \frac{6}{9} = \frac{8}{12}?

Answer

\text{Yes — both simplify to } \frac{2}{3}

\text{Write } \frac{17}{5} \text{ as a mixed numeral.}

Answer

3\frac{2}{5}

\text{Write } 2\frac{3}{4} \text{ as an improper fraction.}

Answer

\frac{11}{4}