42
Comparing fractions
Textbook: Part 2, lesson 42, pp. 24–27
GoalEqual fractions; comparing fractions with the same denominator and on the number ray; finding a number from its known part.
New words
equal fractions · teng kasrlarcomparing · taqqoslashnumber ray · sonlar nurifinding the whole · butunni topish
Explanation
Two fractions may be different writings of the same number: 1/2 and 2/4 are equal fractions, because half a loaf and two quarters are the same. Of two fractions with the same denominator, the one with the larger numerator is larger: 5/7 > 3/7. On the number ray, the fraction lying further left is smaller and the one further right is larger. If a/b of a number equals m, then to find the number itself we divide m by a and multiply by b. For example, if 2/3 of a number is 14, then 14 : 2 = 7 is one share and the whole is 7 · 3 = 21.
Worked examples
Compare 3/8 and 5/8: the denominators are the same, 3 < 5, so 3/8 < 5/8. On the number ray the point 3/8 lies to the left of 5/8.
3/5 of a book is 90 pages. One share is 90 : 3 = 30 pages, the whole book is 30 · 5 = 150 pages.
Class activity
“Fraction wall”: fold paper strips into 2, 4 and 8 equal parts. Place the strips side by side and find which fractions are equal (for example 1/2 = 4/8).
Practice
1
Which is larger: 6/11 or 9/11? Why?
9/11, because the denominators are equal and its numerator is larger.
2
4/7 of a number is 28. Find the number.
49
3
On the number ray, which of the points 2/9 and 7/9 lies to the right?
7/9
4
A runner ran 5/6 of a race, which is 25 km. How long is the race (km)?
30