Fractions and Decimals: Year 4 Study Guide
Fractions and decimals are two ways of writing parts of a whole.
Year 4 students recognise that a fraction names equal parts of a whole or collection. They use unit fractions such as 1/2, 1/4 and 1/5 as building blocks: 3/4 is three of the 1/4 pieces. They find equivalent fractions using diagrams, fraction walls and number lines.
They also meet decimals for the first time in a formal way. Tenths and hundredths link to fractions with denominators 10 and 100, and to Australian money, where 5 cents is $0.05.
Equivalent fractions on a fraction wall
A fraction wall lines up equal-sized strips divided into different numbers of parts. It shows that 1/2 = 2/4 = 4/8 and that 1/3 = 2/6. Multiplying or dividing the numerator and denominator by the same number gives an equivalent fraction.
| Fraction | Equivalent | Equivalent |
|---|---|---|
| 1/2 | 2/4 | 5/10 |
| 1/5 | 2/10 | 20/100 |
| 3/4 | 6/8 | 75/100 |
Adding and subtracting fractions
When the denominators are the same, add or subtract the numerators. 2/7 + 3/7 = 5/7. 7/8 − 2/8 = 5/8. If the answer is more than one whole, it can be written as a mixed number: 3/4 + 3/4 = 6/4 = 1 2/4 = 1 1/2.
Decimals, tenths and hundredths
A decimal fraction is a part of a whole written with a point. 0.3 means three tenths (3/10). 0.25 means twenty-five hundredths (25/100) or one quarter. Money is a handy model: $1.50 is one dollar and fifty cents, and 50 cents is 50/100 of a dollar. A decimal can be placed on a number line between two whole numbers.
0.7.
Seven tenths.
7/10.
Seven steps along from 0 to 1.
Worked examples and common mistakes
Example: Is 2/3 equivalent to 6/9? Multiply the top and bottom by 3: yes. Example: 0.4 = 4/10 = 2/5. Common mistakes: adding denominators (1/5 + 2/5 is 3/5, not 3/10), thinking 0.5 is larger than 0.50, and thinking that a larger denominator means a larger fraction. Use fraction strips to compare.
Check your understanding: model answers
1. For example, 6/10. 2. 6/9 (or 2/3). 3. 6/10 (or 3/5).
✨ Key Takeaways
- Equivalent fractions name the same amount.
- Add fractions with the same denominator by adding numerators.
- Tenths and hundredths are decimals.
- Money is a model for decimals.
💬 Questions for Discussion & Reflection
- Write a fraction equivalent to 3/5.
- Work out 4/9 + 2/9.
- Write 0.6 as a fraction.
Print a fractions equivalence chart →