Page 202 - Ganit Kaushal

×
1 19 9 2 210 20
×
(b) LCM of 10, 9 = 90. ∴ = = and = = .
×
10 10 9 90 9 910 90
×
9 20 1 2 1
So, and are fractions equivalent to and with the same fractional unit .
90 90 10 9 90
×
×
8 84 32 11 11 3 33 13 13 2 26
×
(c) LCM of 3, 4, 6 = 12. ∴ = = , = = and = =
×
3 34 12 4 43 12 6 62 12
×
×
32 33 26 8 11 13 1
So, , and are fractions equivalent to , and with the same fractional unit .
12 12 12 3 4 6 12
3
Ex 4. Find the equivalent fraction of having:
5
(a) a denominator of 20. (b) a numerator of 9.
×
3 34 12 3 33 9
×
Sol. (a) = = (b) = =
×
5 54 20 5 53 15
×
Ex 5. Find the equivalent fraction of 77 having:
63
(a) a denominator of 18. (b) a numerator of 33.
Sol. Here, we first convert it to the simplest form. HCF (77, 63) = 7 and dividing by the HCF, we get
÷
77 = 77 7 = 11 (Simplest form)
÷
63 63 7 9
(a) Now, multiply both the numerator and the denominator by 2 to get 18 in the denominator i.e.,
×
11 = 11 2 = 22 . This fraction is equivalent to 77 and has a denominator of 18.
×
9 92 18 63
(b) Now, to get the numerator 33, multiply both the numerator and the denominator of the simplest
11
form by 3.
9
×
=
We get 11 11 3 = 33 . This fraction is equivalent to 77 and has a numerator of 33.
9 93 27 63
×
Ex 6. (a) Anil was in a group where 2 cakes were divided equally among 5 children. How much cake would
Anil get?
(b) Now, if there are 10 children in Anil’s group, how many cakes will Anil need so that they get the
same amount of cake as Anil?
(c) What share will each get if we put two such groups together? One group where 2 cakes are divided
equally among 5 children, and another group, again with 4 cakes and 10 children. (NCERT)
2
Sol. (a) 2 cakes are divided into 5 equal parts. ∴ Anil will get of the total cake.
5
2
(b) To get the same amount of cake, we need to find an equivalent fraction to with a denominator
of 10. 5
2 22 4
×
We get = =
5 52 10
×
∴ The number of cakes needed = 4.
(c) Here the total number of cakes = 2 + 4 = 6

Total number of children = 5 + 10 = 15.
6 2
∴ Each child will get = = of the total cake.
15 5

200 Mathematics-6