How_To_Be_Good_At_Math

50 NUMBERS •^ COMPARING NON-UNIT FRACTIONS

Now we have two fractions we can easily

compare. We know that if^10 ⁄ 15 is larger than

(^9) ⁄ 15 , then the same is true about their equivalent
fractions. So, we can say that^2 ⁄ 3 >^3 ⁄ 5.
Which of these fractions is larger? If we
change them into fractions with the same
denominators, we can compare the numerators.
One way to give the fractions the same
denominator is to multiply each fraction by
the other’s denominator. First, let’s multiply the
numerator and denominator of^2 ⁄ 3 by 5,
because 5 is the denominator of^3 ⁄ 5.
Next, we change^3 ⁄ 5 into an equivalent
fraction with a denominator of 15 by
multiplying the numerator and denominator by
3, because 3 is the denominator of^2 ⁄ 3.
Using a number line
to compare fractions
You can also use a number line to
compare fractions, just as with whole
numbers. This number line shows
fractions from 0-1, split into quarters
at the top and fifths at the bottom.
so
Let’s compare^3 ⁄ 4 and^4 ⁄ 5. It’s easy
to see by looking along the line
that^4 ⁄ 5 is larger than^3 ⁄ 4.
You can make a number
line like this to compare
any fractions.
0
0
1
1
(^1) ⁄ 4 2 ⁄ 4 3 ⁄ 4
(^1) ⁄ 5 2 ⁄ 5 3 ⁄ 5 4 ⁄ 5
Multiply by 5,
the denominator
of^3 ⁄ 5
(^4) ⁄ 5 is larger than (^3) ⁄ 4
Multiply by 3,
the denominator
of^2 ⁄ 3
This symbol means
“greater than”
2
3
3
? 5
2
3
3

5

Comparing

non-unit fractions

To compare non-unit fractions, we often have to rewrite them so

they have the same denominator. Remember, a non-unit fraction

has a numerator greater than 1.

10

15

9

> 15

2

3

10

15

× 5

× 5

3

5

9

15

× 3

× 3

=

=

050_051_Comparing_Non_Unit_Fractions.indd 50 29/02/2016 14:09