Page 136 - Start Up Mathematics_6

1 1 2 × 4 1 8 1 8 + 1 9
2 = 2 + = + = + = =
4 4 4 4 4 4 4 4

We can convert a mixed fraction into an improper fraction as follows:
Numerator (Whole part × Denominator) + Numerator
Whole part Denominator = Denominator
q p × r + q 1 2 × 4 + 1 9
i.e., p = For example, 2 = =
r r 4 4 4

1 3 4 7 9
Example 11: Locate the points , , , , on a number line.
5 5 5 5 5

Solution:
0 1 3 4 1 7 9 2
5 5 5 5 5
Example 12: Express the following as mixed fractions:

17 23 23 35
(a) (b) (c) (d)
4 5 7 9

17 1 4 23 3 4
Solution: (a) = 4 4 17 (b) = 4 5 23
4 4 –16 5 5 –20

1 3

3 3
23 2 35 8
(c) = 3 7 23 (d) = 3 9 35
7 7 –21 9 9 –27
2 8

Example 13: Express the following as improper fractions:
2 6
(a) 6 (b) 12
5 7
2 6 × 5 + 2 32 6 12 × 7 + 6 90
Solution: (a) 6 = = (b) 12 = =
5 5 5 7 7 7

EXERCISE 7.1

1. What fraction of an hour is 25 minutes?

2. What fraction of a week is 3 days?
3. A painter is required to make 21 portraits for a business tycoon. He has already made 14
of them. What fraction of the total portraits has he made so far?
4. Write natural numbers from 1 to 50. What fraction of them are prime numbers?

5. Locate the following points on a number line.
1 3 5 6 1 2 5 7
(a) , , , (b) , , ,
6 6 6 6 10 10 10 10

128