Equivalent Fractions, Comparing and Adding Fractions: Grade 4 Study Guide
A fraction can be written in many ways. Equivalent fractions name the same amount.
A fraction names equal parts of a whole. The denominator says how many equal parts make the whole, and the numerator says how many parts are counted. In Grade 4, children explain why two fractions are equivalent, compare fractions with different numerators and denominators, and add and subtract fractions that share a denominator.
Number lines, strip diagrams and fraction circles show why the rules work. Memorizing 'multiply top and bottom' is easier when children have seen that cutting each part into smaller pieces keeps the amount the same.
Equivalent fractions
Multiplying the numerator and denominator by the same number gives an equivalent fraction. 1/2 = 2/4 = 3/6 = 4/8. Dividing both by the same number also works: 6/8 = 3/4. The fractions look different but sit at the same point on the number line.
| Fraction | × 2 | × 3 | × 4 |
|---|---|---|---|
| 1/2 | 2/4 | 3/6 | 4/8 |
| 2/3 | 4/6 | 6/9 | 8/12 |
| 3/4 | 6/8 | 9/12 | 12/16 |
Comparing fractions
Compare using a common denominator, a common numerator or a benchmark such as 1/2. To compare 3/4 and 5/8, rewrite 3/4 as 6/8. Since 6/8 > 5/8, then 3/4 > 5/8. Compare with 1/2: 3/8 is less than 1/2 because 4/8 would equal 1/2. Only compare fractions of the same whole.
Are they the same?
Find an equivalent fraction.
The larger numerator is larger.
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Adding and subtracting like fractions
When denominators match, add or subtract the numerators and keep the denominator. 3/8 + 2/8 = 5/8. 7/10 − 3/10 = 4/10. A mixed number such as 2 1/4 can be broken into 2 + 1/4, and 9/4 can be rewritten as 2 1/4 because 8/4 = 2.
Worked examples and common mistakes
Example: 3 × 2/5 = 2/5 + 2/5 + 2/5 = 6/5 = 1 1/5. Example: Is 4/6 equivalent to 2/3? Divide top and bottom by 2: yes. Common mistakes: adding the denominators (3/8 + 2/8 is not 5/16), thinking a bigger denominator means a bigger fraction, and comparing fractions of different wholes. Draw two identical bars and shade to check.
Check your understanding: model answers
1. For example, 4/10 (or 6/15). 2. 2/3 = 4/6, and 5/6 > 4/6, so 5/6 is greater. 3. 7/9.
✨ Key Takeaways
- Equivalent fractions name the same amount.
- Multiply or divide the top and bottom by the same number.
- Compare using a common denominator or benchmark 1/2.
- Add like fractions by adding the numerators only.
💬 Questions for Discussion & Reflection
- Write a fraction equivalent to 2/5.
- Which is greater: 5/6 or 2/3?
- Find 4/9 + 3/9.
Print a fractions equivalence chart →