Download Ratios involving fractions

STRAND: Measurement
TOPIC:
Ratio & rates
Ratios involving fractions
To express two fractions as a ratio in simplest form, follow the steps below:
1. convert mixed number(s) into improper fraction(s)
2. change both fractions to the equivalent fractions with the same denominator
3. omit denominators and write numerators as a ratio
4. simplify the ratio by dividing both numbers by the highest common factor.
WORKED Example
Express each of the following as a ratio in its simplest form.
2 11
2
3
4
1
- -----a ----b 2 --5- : 1 --5c 1 --7- : 1 --313 : 13
Solution
2
11
a Both ------ and ------ are proper fractions with the same denominator, so omit the denominators and write the
13
13
numerators as a ratio.
The ratio is 2 : 11
2
3 12 8
b 2 --- : 1 --- = ------ : --(Change mixed numbers into improper fractions.)
5
5
5 5
Since denominators are the same, write the numerators as a ratio and simplify.
The ratio is 12 : 8
or
3:2
(Divide both numbers by 4 — the HCF of 12 and 8.)
4
1 11 4
c 1 --- : 1 --- = ------ : --(Change the mixed numbers into improper fractions.)
7
3
7 3
33 28
= ------ : -----(Change both fractions to the lowest common denominator.)
21 21
Since the denominators are the same, write the numerators as a ratio.
The ratio is 33 : 28
Try these
Express each of the following as a ratio in its simplest form.
2 3
1 --- : --5 5
1 1
2 1 --- : --2 2
2
5
3 4 --- : 2 --9
9
3
7
4 2 ------ : 3 -----11
11
3
1
5 6 --- : 2 --4
3
3
3
6 1 --- : 2 --7
5
2
2
7 5 --- : 7 --3
9
5
4
8 2 --- : 3 --9
9
5
3
9 1 ------ : 6 --12
8
3
1
10 7 --- : 11 --4
9
2
1
11 3 ------ : 4 --11
3
5
7
12 9 --- : 2 -----6
15
15
3
13 1 ------ : 1 --16
8
3
1
14 1 ------ : -----17 51
2
1
15 3 --- : 4 --7
8
1
1
16 12 --- : 1 -----3
13
 John Wiley & Sons Australia, Ltd 2001