Page 79 - Mathematics Coursebook

7.3 Comparing fractions

7.3 Comparing fractions

!ere are several di%erent ways that you can compare two fractions. One way is to use diagrams

like these.
1

In the #rst rectangle is shaded.
3
1
In the second rectangle is shaded.
4
1
1
1
1
You can see that is smaller than , so you write < . Remember that < means ‘is smaller
4
4
3
3
1
1
1
1
Or you can say that is bigger than , so you write > . or less than’ and > means ‘is greater
3 4 3 4 or more than’.
Another way to compare two fractions is to use your calculator.
1
1
Take the fraction . To change into a decimal, work out 1 ÷ 3. ! e answer is 0.33...
3 3
0.33... is called a recurring decimal. ! e three dots at the You can also write 0.33... as 0.3. The dot
˙
end show that the number goes on for ever. above the 3 shows that the number is
1
So = 0.33... recurring.
3
1
Now do the same to 1 . To change into a decimal, work out 1 ÷ 4. !e answer is 0.25. So 1 = 0.25.

4
4
4
1
1
You can now compare the decimal numbers. 0.25 is smaller than 0.33... so you can write < .
4
3
Worked example 7.3
a i Write the fractions 3 and 7 in the correct positions on this
4
number line. 8 0 1
ii Which is the larger fraction?
b Use your calculator to work out which is the smaller fraction out of 3 and 2 .
5 3
a i The black lines show the eighths and the red lines show the
quarters.
0 3 7 1
4 8
7 7 3
ii is the larger. is closer to 1 than , so is the bigger of the two.
8 8 4
3
b = 3 ÷ 5 = 0.6 Divide the numerator by the denominator.
5
2 = 2 ÷ 3 = 0.66... Write down the fi rst two decimal places then ... to show
3
the decimal carries on.
3
is the smaller.
5

78 7 Fractions