Fractions, decimals & percentages
Comparing & ordering
You can change improper fractions into mixed numbers, and put fractions, decimals and percentages in order by writing them the same way first.
Two useful skills
• Improper fraction → mixed number: divide the numerator by the denominator. The whole-number answer is the whole part, and the remainder is the new numerator. • To compare values, change them all into the same form (for example, decimals) first.
Worked examples
Improper fraction to mixed number
- Change 13/4 to a mixed number.
- 13 ÷ 4 = 3 remainder 1.
- So there are 3 wholes and 1/4 left over.
Answer: 13/4 = 3 1/4
Ordering different forms
- Compare 0.2, 70% and 0.34.
- Write them all as decimals: 0.2, 0.7, 0.34.
- In order: 0.2, 0.34, 0.7.
Answer: Largest is 70%; smallest is 0.2.
Where you see this in real life
- Ordering prices or scores from smallest to largest.
- Comparing 30% off with 1/4 off to see which is the better deal.
- Reading a measuring jug marked with fractions and decimals.
Key words
- Improper fraction
- A fraction where the numerator is greater than or equal to the denominator, e.g. 5/3.
- Mixed number
- A whole number and a proper fraction combined, e.g. 1 3/4.
- Proper fraction
- A fraction smaller than a whole, where the numerator is smaller than the denominator.