Ordering rational numbers on number lines | Year 7

01 / LEARN

The idea, step by step

Compare the same-sized parts

If fractions have the same denominator, the greater numerator gives the greater amount. Otherwise, rename them with a common denominator or use an exact decimal form.

Numerator size alone cannot decide the order. Three quarters is greater than five eighths because a quarter is twice the size of an eighth.

Positions on a number line

Values increase to the right. Label the ends, count equal intervals, and find their size before placing a point. Trailing zeros help compare decimal place values without changing the values.

For example, 0.4 and 0.40 name exactly the same point. A fraction also names one point; its numerator and denominator are not separate positions.

A common trap

A decimal with more decimal digits is always larger.

Instead: Compare place values. For instance, 0.9 is greater than 0.85, even though 0.85 has more decimal digits.

02 / WORKED EXAMPLES

See the thinking

Example 1

Find common parts

Compare $\frac{3}{4}$ and $\frac{5}{8}$ .

$\frac{3}{4} = \frac{6}{8}$ .
Six eighths is greater than five eighths.

\frac{3}{4} > \frac{5}{8}

Example 2

Mix different forms

Order $0.6$ , $\frac{5}{8}$ and $0.58$ from smallest to largest.

$\frac{5}{8} = 0.625$ .
Compare 0.580, 0.600 and 0.625.

0.58 < 0.6 < \frac{5}{8}

Check your understanding

Which is further right: $\frac{2}{5}$ or $0.45$ ?

Show answer

$0.45$

$\frac{2}{5} = 0.40$ , which is smaller than 0.45.

03 / WORKSHEET

Your turn

6 questions · 14 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Compare $\frac{5}{6}$ and $\frac{3}{4}$ using equal parts.
2 marks
Order 0.7, 0.67 and 0.705 from smallest to largest.
2 marks
On a number line from 0 to 1, give the left-to-right order of $\frac{1}{4}$ , $\frac{3}{4}$ , $\frac{1}{2}$ .
2 marks
Find a fraction strictly between $\frac{1}{3}$ and $\frac{1}{2}$ .
2 marks
Which is closer to 1: $\frac{7}{8}$ or 0.8?
3 marks
Order race times $12.4$ s, $12 \frac{3}{8}$ s and $12.45$ s from fastest to slowest.
3 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Compare $\frac{5}{6}$ and $\frac{3}{4}$ using equal parts.
2 marks
$\frac{5}{6} = \frac{10}{12}$ and $\frac{3}{4} = \frac{9}{12}$ .
$\frac{5}{6} > \frac{3}{4}$
Order 0.7, 0.67 and 0.705 from smallest to largest.
2 marks
Compare 0.670, 0.700 and 0.705.
0.67, 0.7, 0.705
On a number line from 0 to 1, give the left-to-right order of $\frac{1}{4}$ , $\frac{3}{4}$ , $\frac{1}{2}$ .
2 marks
Divide the unit into four equal parts; these occupy the first, second and third marks.
$\frac{1}{4}, \frac{1}{2}, \frac{3}{4}$
Find a fraction strictly between $\frac{1}{3}$ and $\frac{1}{2}$ .
2 marks
$\frac{1}{3} = \frac{4}{12}$ and $\frac{1}{2} = \frac{6}{12}$ .
For example, $\frac{5}{12}$ .
Which is closer to 1: $\frac{7}{8}$ or 0.8?
3 marks
The distances are $\frac{1}{8} = 0.125$ and $0.2$ .
0.125 is smaller.
$\frac{7}{8}$
Order race times $12.4$ s, $12 \frac{3}{8}$ s and $12.45$ s from fastest to slowest.
3 marks
$\frac{3}{8} = 0.375$ .
A shorter time is faster; compare 12.375, 12.400 and 12.450.
$12 \frac{3}{8}$ s, $12.4$ s, $12.45$ s

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Curriculum reference & lesson scope

Australian Curriculum v9 / SA Curriculum Mathematics

Equivalent fractions and mixed numbers; ordering rational numbers on number lines; adding/subtracting fractions; multiplying/dividing fractions; four operations with decimals; converting between fractions and decimals; multi-step problems and checking estimates.

Official curriculum source ↗

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