Practice Questions with Solutions: Fractions - 1

Q1: Write the next three equivalent fractions
Ans:
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 a numerator of 8.
Sol: 
To get 8 in the numerator, we multiply 2 by 4, and also 5 by 4.

Hence,  they 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,  it is in its lowest terms.

Q10: Find an equivalent fraction of  with a denominator of 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 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,