Grades 3–5
Fractions
A fraction is a part of a whole that has been split into equal parts. Most fraction rules make sense once you picture the parts.
What a fraction means
In 34 the bottom number, the denominator, says the whole is cut into 4 equal parts. The top number, the numerator, says 3 of them are taken.
The bigger the denominator, the smaller each part: 18 is less than 14, because cutting the same whole into 8 makes smaller pieces than cutting it into 4.
Worked examples
Equivalent fractions
The same amount shaded three ways: 12 = 24 = 48. Multiply the top and bottom by the same number.
Same denominator
The parts are the same size, so add the numerators and keep the denominator.
27 + 37 = 57
Different denominators
Change the quarters into eighths first, then add.
34 + 18 = 68 + 18 = 78
A fraction of an amount
Divide by the denominator to find one part, then multiply by the numerator.
35 of 20 = 20 ÷ 5 × 3 = 12
Strategies that help
Simplify
Divide the top and bottom by a number that goes into both: 68 = 34.
Compare with a common denominator
23 or 34? As twelfths they are 812 and 912, so 34 is bigger.
Mixed numbers
74 is four quarters and three more: 1 34.
Unit fractions
Every fraction is a count of unit fractions: 34 is three lots of 14.
Equivalent fractions
Each row names one amount in different ways.
| Fraction | Equal to |
|---|---|
| 1/2 | 2/4, 3/6, 4/8, 5/10 |
| 1/3 | 2/6, 3/9, 4/12 |
| 2/3 | 4/6, 6/9, 8/12 |
| 1/4 | 2/8, 3/12, 5/20 |
| 3/4 | 6/8, 9/12, 12/16 |
Practice questions
Work each one on paper first, then open the answer to check it.
- A pizza is cut into 8 equal slices and 3 are eaten. What fraction is left?
Answer
58 - 15 + 25
Answer
35 - 56 − 16
Answer
46, which simplifies to 23 - Fill the gap: 23 = ?12
Answer
812 - Simplify 912
Answer
34 - Which is larger, 35 or 23?
Answer
23: as fifteenths they are 915 and 1015. - 12 + 14
Answer
34 - 34 of 28
Answer
21 - Write 114 as a mixed number.
Answer
2 34 - 23 × 9
Answer
6
Common questions
- Why don't you add the denominators?
- Because the denominator names the size of the parts, not how many there are. A quarter and a quarter make two quarters, 2/4, not 2/8: eighths are smaller pieces.
- What is a unit fraction?
- A fraction with 1 on top, such as 1/3 or 1/10. Every other fraction is a number of them: 3/4 is three lots of 1/4.