الأسبوع 21 · مقارنة الكسور ومراجعة الحلول · 3 دروس
1
Comparing fractions on number lines
Discover Mathematics P3: Term 2, Lessons 81–90
GoalCompare and order fractions by finding them on a number line.
New words
further right · closer to 1 on a number line, so a greater numberorder · to put in a line from the least to the greatestunit fraction · a fraction with 1 on top
Explanation
A number line helps us compare fractions. On a line from 0 to 1, the fractions farther to the right are greater, and the fractions closer to 0 are smaller. When the bottom numbers are the same, the one with the bigger top number is farther right, so 5/6 > 2/6. We can also compare unit fractions, which have 1 on top. If a whole is cut into more equal parts, each part is smaller. So 1/2 > 1/4 > 1/8. Half of a cake is bigger than a fourth of the same cake. To put fractions in order, find each one on the line and read them from left to right.
Worked examples
Point
Fraction
Place
A
2/6
nearer 0
B
5/6
nearer 1
On the number line, point A is at 2/6 and point B is at 5/6. B is farther to the right, so 5/6 > 2/6.
Compare 1/2 and 1/4 of the same bar. Halves are bigger than fourths, because a bar cut into 2 parts has bigger parts than the same bar cut into 4 parts. So 1/2 > 1/4.
Order 3/8, 7/8, 1/8 and 5/8 from least to greatest. Find them on the line and read from left to right: 1/8, 3/8, 5/8, 7/8.
Class activity
Number line race. Draw a number line from 0 to 1 and cut it into 6 equal spaces. Write 5 fractions with sixths on small cards, mix them up, and put them in the right places. Then order the cards from the least to the greatest.
Practice
1
Which is greater, 2/6 or 4/6? Use the number line.
4/6 is farther to the right, so 4/6 > 2/6.
2
Which is greater, 1/3 or 1/6?
Thirds are bigger than sixths, so 1/3 > 1/6.
3
Put in order from least to greatest: 4/8, 2/8, 6/8.
2/8, 4/8, 6/8.
4
Write > or <: 1/4 ... 1/2.
1/4 < 1/2.
5
Marina says 1/8 is greater than 1/4 because 8 is greater than 4. Is she right?
No. A whole cut into 8 parts has smaller parts than the same whole cut into 4 parts, so 1/8 < 1/4.
