Of 1/2 and 1/3, the bigger is 1/□

2. Both have numerator 1: the smaller the denominator, the bigger each part, so 1/2 is bigger.

Which fraction is the smallest? A. 2/9 B. 2/10 C. 2/7 D. 2/6 Choose the right answer

B. 2/10. All have numerator 2: the bigger the denominator, the smaller each part, and the smaller the fraction.

6/11 < □/11 < 8/11. What number goes in □?

7. Same denominator, so the numerator is between 6 and 8: 7.

中文

First fractions · Usually met around P3

Comparing fractions

Same bottom: compare tops. Same top: the bigger bottom is smaller.

How to do it

Method

Same bottom: compare tops. Same top: the bigger bottom is smaller

58 > 38; 13 > 15

Another way

Draw strips

A third of a strip is longer than a fifth

In full

Same denominator: the parts are the same size, so the bigger numerator (more parts) is the bigger fraction: 58 > 38. Same numerator: the same number of parts is taken, but a bigger denominator cuts the whole into more, smaller parts, so that fraction is smaller: 13 > 15, 25 > 29. Or draw two strips the same length and compare how much of each is shaded.

Worked examples

Have a go first, then open each one for the answer and the working.

Example 1
Of 12 and 13, the bigger is 1/□
Show the answer and working
Answer: 2
Both have numerator 1: the smaller the denominator, the bigger each part, so 12 is bigger.
Example 2
Which fraction is the smallest?
- A. 29
- B. 210
- C. 27
- D. 26
Choose the right answer
Show the answer and working
Answer: B. 210
All have numerator 2: the bigger the denominator, the smaller each part, and the smaller the fraction.
Example 3
611 < □/11 < 811. What number goes in □?
Show the answer and working
Answer: 7
Same denominator, so the numerator is between 6 and 8: 7.

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