Page 210 - Ganit Kaushal

(b) The denominators of the given fractions are 3 and 5.

So, LCM (3, 5) = 15
+
×
×
Now, 2 = 25 = 10 and 4 = 43 = 12 ∴ 2 + 4 = 10 12 = 22
×
×
3 35 15 5 53 15 3 5 15 15
(c) The denominators of the given fractions are 4, 3 and 5.
So, LCM (4, 3, 5) = 60
×
×
3 315 45 1 120 20 1 112 12 3 1 1 45 + 20 12 77
×
+
Now, = = ; = = ; = = ∴ ++ = =
×
4 415 60 3 320 60 5 512 60 4 3 5 60 60
×
×
Ex 2. Solve the following using Brahmagupta’s method:
1 2 3 1 2 3 1 1 7 1
(a) 1 + 3 (b) − (c) + + (d) −+ 5
3 3 4 3 3 4 2 2 2 6
+
1 2 4 11 411 15
Sol. (a) 1 + 3 = + = = = 5
3 3 3 3 3 3
(b) Since the denominators of the given fractions are 4 and 3, the LCM of 4 and 3 is 12.
×
×
−
3 1 33 14 9 4 94 5
∴ −= − = − = =
×
×
4 3 43 34 12 12 12 12
(c) Since the denominators of the given fractions are 3, 4 and 2, the LCM of 3, 4, and 2 is 12.
×
×
++ 6
∴ 2 + 3 + 1 = 2 × 4 + 33 + 16 = 8 + 9 + 6 = 89 = 23 = 1 11
×
×
×
3 4 2 34 43 26 12 12 12 12 12 12
1
7
7
(d) 1 −+ 5 = 1 − + 31 (After converting the mixed fraction into an improper fraction)
2 2 6 2 2 6
×
×
= 13 − 73 + 31 ( LCM (2, 6) = 6)
×
23 23 6
×
3 21 31 32131 13 1
−
+
= − + = = = 2
6 6 6 6 6 6
4 5
Ex 3. Find the difference between and .
15 18
Sol. To find the difference, it is important to know which one is greater. Then we will subtract the smaller
one from the greater one. LCM (18, 15) = 3 × 3 × 2 × 5 = 90.
×
×
5 55 25 4 46 24 3 18, 15
Now, = = and = = .
×
18 18 5 90 15 15 6 90 3 6, 5
×
5 4 2 2, 5
∴ > ( 25 > 24) 5 1, 5
18 15 1, 1
−
∴ Difference between 4 and 5 = 5 − 4 = 25 − 24 = 25 24 = 1
15 18 18 15 90 90 90 90
2 3
Ex 4. Rahim mixes 3 litres of yellow paint with 4 litres of blue paint to make green paint. What is the
volume of green paint he has made? (NCERT)
2 3
Sol. Volume of green paint = L + L. The LCM of 3 and 4 is 12.
3 4
×
+
2 3 2 × 4 33 89 17 5
So, + = + = = litres = 1 litres
×
3 4 34 43 12 12 12
×
208 Mathematics-6