Fractions, decimals and the number line

Many ways to write the same number

Three quarters of a pizza can be written as 3/4 = 6/8 = 75/100 = 0.75 = 75%. They're all the same amount — equivalent representations.

Equivalent fractions

• Multiply or divide the top (numerator) and bottom (denominator) by the same number: 3/4 = (3 × 2)/(4 × 2) = 6/8
• To simplify, divide both by their highest common factor: 18/24 → divide by 6 → 3/4

Mixed numbers and improper fractions

2 1/3 means 2 and 1/3. As an improper fraction: 2 wholes = 6 thirds, plus 1 third = 7/3. Going back: 17/4 = 17 ÷ 4 = 4 remainder 1 = 4 1/4.

Fractions to decimals and back

• A fraction is a division: 3/8 = 3 ÷ 8 = 0.375
• Some never end: 1/3 = 0.333… (the 3 repeats forever)
• Decimal to fraction: read the place value. 0.6 = 6/10 = 3/5; 0.45 = 45/100 = 9/20

Negative fractions and decimals on the number line

To compare, change them to the same form (decimals are easiest). −3/4 = −0.75 is left of −1/2 = −0.5, so −3/4 is smaller.

Worked example: ordering

1. Order 0.7, 2/3, 3/4, 0.65 from smallest to largest.
2. Change to decimals: 0.7, 0.666…, 0.75, 0.65
3. Order: 0.65, 2/3, 0.7, 3/4

Your turn

Use a pencil and paper. The answers are at the bottom of the page — try first!

1. Simplify 15/20.
2. Write 2 3/5 as an improper fraction.
3. Write 17/4 as a mixed number.
4. Write 7/8 as a decimal.
5. Write 0.6 as a fraction in simplest form.
6. Which is greater: −2/5 or −1/2?

Answers

1. 3/4 (divide both by 5)
2. 13/5
3. 4 1/4
4. 0.875
5. 3/5
6. −2/5, because −0.4 is to the right of −0.5

For parents and teachers — this lesson covers the Victorian Curriculum Mathematics Version 2.0, Level 7:

• VC2M7N03: find equivalent representations of rational numbers and represent positive and negative rational numbers and mixed numbers on a number line