☰ Year plan · Mathematics

Fractions of sets and on number lines

Week 20 · Fractions of sets and on number lines · 3 lessons
2

Which fraction is more?

Discover Mathematics P3: Term 2, Lessons 71–80
GoalCompare two fractions with the same bottom number by looking at how many parts are taken.
New words
compare · to say which is more, which is less or if they are equalgreater than (>) · more thanless than (<) · not as much as
Explanation

To compare fractions with the same bottom number, look at the top numbers. The parts are the same size, so the fraction with more parts is greater. Compare 3/4 and 1/4: both are fourths, and 3 parts are more than 1 part, so 3/4 > 1/4. We can also write 1/4 < 3/4. A picture helps: shade the same bar in both fractions and see which one has more shaded. The wholes must be the same size. A fraction of a small cake is not comparable with a fraction of a big cake. If the top numbers are the same too, the fractions are equal.

Worked examples
Compare 3/4 and 1/4. Both bars have 4 equal parts. The top bar has 3 shaded and the bottom bar has 1 shaded, so 3/4 > 1/4.
Compare 5/6 and 2/6. Both are sixths. 5 parts are more than 2 parts, so 5/6 > 2/6 and 2/6 < 5/6.
Mina eats 3/8 of a pizza and Omar eats 5/8 of an identical pizza. Eighths are the same size, and 5 is more than 3, so Omar ate more.
Class activity

Which is more? Draw two bars of the same length on squared paper. Divide both into 6 equal parts. Shade some parts in the first bar and a different number in the second. Write the two fractions and compare them using more than or less than. Make three pairs.

Practice
1
Which is more, 3/4 or 1/4?
2
Write > or < in the circle: 2/6 ... 5/6.
3
The two bars have the same length. Which bar has the greater shaded part, and how do you know?
4
Put in order from least to greatest: 5/8, 1/8, 7/8, 3/8.
5
Salma drinks 2/4 of a bottle of water and Farida drinks 3/4 of an identical bottle. Who drinks less?