Page 201 - Ganit Kaushal

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Ex: Find equivalent fractions for the fractions and such that the fractional units are the same.
6 9 (NCERT)
Sol. LCM of denominators (6, 9) = 2 × 3 × 3 = 18.
So, we multiply the numerators and denominators of both the fractions by suitable numbers, 2 6, 9
so that the denominator of both fractions becomes 18. 3 3, 9
×
13 13 3 39 1 12 2 3 1, 3
×
We can do it as: = = and = = 1, 1
6 63 18 9 9 × 2 18
×
39 2 13 1 1
∴ and are the fractions equivalent to and respectively with the same unit fraction .
18 18 6 9 18
Solved Examples
Ex 1. Express the following as mixed fractions:
20 11 17
(a) (b) (c)
3 5 7

20 6 11 2
Sol. (a) , 3 20 (b) , 5 11
3 –18 5 –10
2 1
[ Here, quotient = 6 and remainder = 2] [ Here, quotient = 2 and remainder = 1]

20 2 11 1
So, = 6 So, = 2
3 3 5 5
2
17 7 17
(c) , [ Here, quotient = 2 and remainder = 3]
7 –14
3
17 3
So, = 2
7 7
Ex 2. Express the following mixed fractions as improper fractions:

(a) 7 3 (b) 5 6 (c) 2 5 (d) 10 3
4 7 6 5
Sol. We convert a mixed fraction into an improper fraction by using the formula given in section 7.3.
×
)
)
+
3 ( 7 × 4 + 3 28 3 31 6 ( 57 + 6 35 + 6 41
(a) 7 = = = (b) 5 = = =
4 4 4 4 7 7 7 7
(An improper fraction) (An improper fraction)
5
×
×
3
)
)
(c) 2 = ( 26 + 5 = 12 + 5 = 17 (d) 10 = ( 10 5 + 3 = 50 + 3 = 53
6 6 6 6 5 5 5 5
(An improper fraction) (An improper fraction)
Ex 3. Find equivalent fractions for the given pairs of fractions, such that their fractional units are the same.
9 5 1 2 8 11 13
(a) and (b) and (c) , and
4 2 10 9 3 4 6
5 52 10
×
Sol. (a) LCM of 4, 2 = 4. ∴ = =
×
2 22 4
9 10 9 5 1
So, and are fractions equivalent to and with the same fractional unit .
4 4 4 2 4
Fractions 199