Important Questions with Solutions: Fractions - 1

Q1: Write next three equivalent fractions
Sol: We have:  

3 × 24 × 2 = 68

3 × 34 × 3 = 912

3 × 44 × 4 = 1216
So, 34 = 68 = 912 = 1216
Hence, the equivalent fractions to 34  are  68, 912, 1216

Q2: Find the sum of and

Sol: We have

Q3: Subtract

Sol: We have :

Q4: Express each of the following fractions to its lowest terms :

(a)

(b)

Sol: (a) We have,

So, we can divide the numerator and the denominator by 2 x 3 = 6.

So, 

Thus, the simplest form of

(b) We have,

So, we can divide the numerator and the denominator by 2 x 5 = 10 .

So,

Thus, the Simplest form of

Q5: Subtract

Sol: We have:

Q6: Find the sum of

Sol: We have :

Q7: Compare :

(a)

(b)

Sol: We have:

(a) Consider

Since, 3 > 2, hence

(b) Consider

Since, 7 > 4, hence

Q8: Find an equivalent fraction of  with numerator 8.

Sol: 

To get 8 in the numerator, we multiply 2 by 4, and also 5 by 4.

Hence,  are equivalent fractions.

Q9: Reduce  to its lowest terms.

Sol: We can divide the numerator and the denominator step by step, by their common factors.

Thus,  is in its lowest terms.

Q10: Find an equivalent fraction of  with denominator 15.

Sol: 

To get 15 in the denominator, we multiply 5 by 3 and also 3 by 3.

So,

Hence,are equivalent fractions.

Q11: Are equivalent fractions?

Sol: 2 X 15 = 30, 3 X 10 = 30

Both the products are equal.

Hence,  are equivalent fractions.

Q12: Are  equivalent fractions?

Sol: 

Here, 4 x 18 = 72, 5 x 16 = 80

Products are not the same.

Hence,  are not equivalent fractions.

Q13: Compare
(a)

(b)

Sol: (a) 

Since 9 < 11.

Hence

(b)

Since 14 > 13

Hence

Q14: Compare

Sol: [Multiplying the numerator and the denominator by 4]

[Multiplying the numerator and the denominator by 5]

Clearly,

Hence,

Another method: Two fractions can be compared by using the method of cross multiplication.

Q15: Compare
(a)

(b)

Sol: (a) Given fractions are

 (Cross multiply)

Now 3 x 7 = 21 and 11 x 5 = 55.

Since 21 < 55, hence

(b) Given fractions are

(Cross multiply)
Now 4 x 13 = 52 and 15 x 2 = 30.

Since, 52 > 30, hence,