Page 209 - Ganit Kaushal

1 1
Ex 2. Find the sum of and using Brahmagupta’s method. (NCERT)
6 3
1
1
1
×
Sol. The LCM of 6 and 3 is 6. So, will remain and = 12 = 2 .
6 6 3 32 6
×
÷
1 1 1 2 3 33 1
Therefore, + = + = = = [simplest form]
÷
6 3 6 6 6 63 2
1 1 1
Ex 3. Find the value of +− .
4 3 2
Sol. The LCM of 2, 3 and 4 = 12. So, we can make the denominator of each fraction equal to 12 by
multiplying and dividing it by a suitable number. We get
1 +− 1 = 13 + 14 − 16 = 3 + 4 − 6 = 34 6 = 1
×
1
×
+−
×
×
×
×
4 3 2 43 34 26 12 12 12 12 12
Addition and Subtraction of Mixed Fractions
To add or subtract mixed fractions, first convert them into improper fractions and then add or subtract them as
explained in Brahmagupta’s Method.
For example:
3 1 13 8 13 7 85 91 40 91 40 131 26
+
×
×
(i) 2 + 1 = + = + = + = = = 3
5 7 5 7 57 75 35 35 35 35 35 Note
×
×
5
−
×
×
1 1 13 16 13 5 16 3 65 48 65 48 17 2
(ii) 4 − 3 = − = − = − = = = 1 4 can be written as 4
×
×
5
3 5 3 5 35 53 15 15 15 15 15 1
×
−
+
×
2 1 17 7 4 17 × 3 75 415 51 35 60 76 and LCM (5, 3, 1) = 15.
(iii) 3 − 2 + = − + = − + = =
4
×
5
×
×
5 3 5 3 1 53 35 115 15 15
7.7 MULTIPLICATION OF FRACTIONS
Two or more fractions can be multiplied just by multiplying the numerators and their denominators. If mixed
fractions are involved, we need to convert them to improper fractions first and then multiply. Finally convert
the result to simplest/least form, if required.
×
5 11 511 55 2 5 8 5 40 40 ÷ 2 20
For example: × = = ; 2 × = × = = = (after converting to least form)
7 13 713 91 3 6 3 6 18 18 ÷ 2 9
×
Two fractions are said to be the reciprocals of each other if their product is 1.
13 11 13 11 11 13
×
For example: × = = 1. Therefore and are reciprocals of each other.
11 13 11 13 13 11
×
The reciprocal of a fraction can also be obtained just by interchanging its numerator and denominator.
Solved Examples
Ex 1. Add the following fractions using Brahmagupta’s method: (NCERT)
2 5 6 2 4 3 1 1
(a) + + (b) + (c) ++
7 7 7 3 5 4 3 5
++
Sol. (a) 256 = 13 [ In like fractions, just add the numerators keeping the denominator the same]
7 7
Fractions 207