Page 38 - Start Up Mathematics_7

Value of the Product
• The product of two proper fractions is always smaller than each of the fractions.
3 1 3 3 1
For example, × = , which is smaller than each of the proper fractions, and .
2
4
4
2
8
• The product of two improper fractions is always greater than each of the fractions.
3 4 3 4
For example, × = 2, which is greater than each of the improper fractions, and .
2 3 2 3
1 3 1 4
Example 16: Find: (a) of (b) of
3 5 7 9
1 3 1 3 3 1 1 4 1 4 4
Solution: (a) of = × = = (b) of = × =
3 5 3 5 15 5 7 9 7 9 63
Example 17: Multiply and reduce each of the following to the lowest terms. In case the result
obtained is improper, convert it into mixed fractions.
2 5 11 4 3 1
(a) × (b) × (c) × 5
5 9 2 10 5 4
2 5 2
Solution: (a) × =
5 9 9

11 4 44 1
(b) × = = 2
2 10 20 5
3 1 3 21 63 3
(c) × 5 = × = = 3
5 4 5 4 20 20
4
2
2
6
2
2
1
Example 18: Which is greater: (a) of or of (b) of or of 3
7 3 5 6 2 7 3 7
2 2 2 2 4 4 2 4 2 8 4
Solution: (a) of = × = ; of = × = =
7 3 7 3 21 5 6 5 6 30 15
 Numerators of both the fractions are same.
∴ Fraction with smaller denominator would be greater.
4 4 4 2 2 2
i.e., > ⇒ of > of
15 21 5 6 7 3
1 6 1 6 6 3 2 3 2 3 6 2
(b) of = × = = ; of = × = =
2 7 2 7 14 7 3 7 5 7 21 7
 Denominators of both the fractions are same.
∴ Fraction with greater numerator would be greater.
3 2 1 6 2 3
i.e., > ⇒ of > of
7 7 2 7 5 7
1
Example 19: Dipika reads a book for 1 hours every day. She reads the entire book in 6 days.
4
How many hours in all were required by her to read the book?
Solution: Number of hours Dipika spent every day = 1 1
4
 She reads the entire book in 6 days,
1
∴ Total number of hours required to read the book = 6 × 1 4
5 30 15 1
= 6 × = = = 7 hours
4 4 2 2

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