Page 196 - Ganit Kaushal

Ex 2. In the following figures, identify the error, if any.

(a) (b) (c)

This is 1 This is 1 This is 3
2 4 4
Sol. For expressing in fractions, a whole is divided into equal parts. Here, none of the shapes are divided
into equal parts, therefore none of the figures represent the given fractions.
Ex 3. What fraction of a day is 8 hours?
Sol. A whole day has 24 hours, and 8 hours are considered, therefore 8 hours of a day represent the fraction
8 = of a day.
1
24 3
Ex 4. What fraction of an hour is 40 minutes?
Sol. A whole hour has 60 minutes. If 40 minutes are taken, then the fraction = 40 = 2 .
60 3
Ex 5. Three school friends – Arya, Abhimanyu, and Vivek, used to share lunch during recess. One day, Arya
brought two sandwiches: one made of vegetables and one of jam. The other two boys forgot to bring
their lunch. Arya agreed to share his sandwiches so that each person would have an equal share of each
sandwich. How will Arya do this? What share will each get?

Sol. (a) Arya will divide each sandwich into three equal parts and give one part of each sandwich to each
one of them.
1
1
(b) Each boy will receive 1 × = of each sandwich.
3 3
Ex 6. Write the natural numbers from 2 to 12. What fraction of them are prime numbers?
Sol. The natural numbers from 2 to 12 are: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12; Total numbers = 11.
Prime numbers from 2 to 12 are: 2, 3, 5, 7, 11; Total prime numbers = 5.
5
Hence, the fraction of prime numbers = .
11
Ex 7. Match the entries of column I with those of column II.
Column I Column II

(a) 100 is equivalent to (i) 12 4
,
700 15 5
(b) Fractions are defined as (ii) 5
35
(c) Two equivalent fractions of 11 (iii) represent the same share
14
60 22 33
(d) Two equivalent fractions of (iv) ,
75 28 42
(e) Two equivalent fractions (v) parts of a whole
5
Sol. (a) ↔ (ii) [ Dividing the numerator and denominator by 20 gives .]
(b) ↔ (v) 35
(c) ↔ (iv) [ Multiplying the numerator and denominator by 2, 3 gives 22 and 33 .]
28 42
12 4
(d) ↔ (i) [ Dividing the numerator and denominator by 5, 15 gives 15 and .]
5
(e) ↔ (iii)

194 Mathematics-6