Page 190 - Math Smart - 7

Example 4

Which of the fractions, ^ and |, is the smallest? Which is the greatest?

Solution
Write the fractions as like fractions.
1 2 2 X 10 X 5 100
3 " 3 X 10 X 5 ~ 150
The LCM of 3, 10
7 7x3x5 105
10 " 10 X 3 X 5 ~ 150 and 5 is 150.
3 3 X 3 X 10 90
5 " 5 X 3 X 10 ~ 150

We compare, ]iand:^.

has the smallest numerator.
So, I is the smallest fraction.

has the greatest numerator.

So, is the greatest fraction.

When comparing unlike fractions:
• convert all the fractions to like fractions and
• then compare their numerators.

Example 5

Arrange the fractions, |, f :j^, in increasing order.

Solution
Write the fractions as like fractions.
^
and
We see that |, | 3x3 _9 5x4 20 7_
1
7X2
can be expressed with 8x3 24 6X4 24 12 12 X 2 14
24
denominators of 24. Use
Weget^,^,g and
their equivalent fractions. 24 n
Compare their numerators.
9<14<19<20

So ^< 19 20 14
24 ^ 24 ^ 24 ^ 24 •
So, the fractions arranged in increasing order are:

3 19 5
8' 12' 24' 6

UNIT 8 I Fractions