☰ Year plan · Mathematics

Comparing and equivalent fractions

Week 18 · Comparing and equivalent fractions · 3 lessons
3

Benchmarks: zero, one half or one?

Discover Mathematics P4: Term 2, Unit 9, Lessons 8–12
GoalUse the benchmarks 0, 1/2 and 1 to compare and estimate fractions.
New words
benchmark · an easy number to compare with: 0, 1/2 or 1close to · only a little more or less thanhalf of the denominator · the numerator needed to make exactly one half
Explanation

Benchmarks are easy fractions to compare with: 0, 1/2 and 1. To place a fraction, compare its numerator with half of its denominator. For 5/10, half of 10 is 5, so 5/10 = 1/2 exactly. For 1/8, the numerator 1 is much less than 4 (half of 8), so 1/8 is close to 0. For 7/8, the numerator 7 is much more than 4 and almost the whole 8, so 7/8 is close to 1. For 5/6, half of 6 is 3 and 5 is more than 3, so 5/6 is more than a half and close to 1. To compare 5/10 and 5/6 we can use the benchmark: 5/10 = 1/2 and 5/6 > 1/2, so 5/6 > 5/10. This agrees with the same-numerator rule.

01/211/84/87/8
Worked examples
01/211/84/87/8
Where do 1/8, 4/8 and 7/8 go? 1/8 is close to 0. 4/8 is exactly 1/2 because 4 is half of 8. 7/8 is close to 1.
Which is greater, 4/10 or 7/8? Half of 10 is 5, so 4/10 is less than 1/2. Half of 8 is 4, so 7/8 is more than 1/2. Therefore 7/8 > 4/10.
Compare 5/10 and 5/6. 5/10 = 1/2. Half of 6 is 3 and 5 > 3, so 5/6 > 1/2. Therefore 5/6 > 5/10.
Class activity

Benchmark sort. A grown-up writes 10 fractions on cards. The child sorts them into three piles: close to 0, close to 1/2 and close to 1. Check one card by drawing a number line.

Practice
1
Is 1/10 close to 0, 1/2 or 1? And 9/10?
2
Is 6/12 less than, equal to or greater than 1/2?
3
Use the benchmark 1/2 to compare 3/10 and 5/6.
4
Omar has done 3/8 of his homework and Mina has done 5/8. Who has done more than half?
5
Karim says 5/8 > 5/6 because 8 > 6. What is wrong? Which fraction is greater?