## ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 6 Fractions Ex 6.3

Question 1.

State which of the following fractions are proper, improper or mixed:

Solution:

Question 2.

Convert the following improper fractions into mixed numbers:

Solution:

Question 3.

Convert the following mixed number into improper fractions:

Solution:

Question 4.

Write the fractions representing the shaded regions. Are all these fractions equivalent?

Solution:

Yes, all the fractions are equivalent.

Question 5.

Write the fractions representing the shaded regions and pair up the equivalent fractions from each row:

Solution:

Equivalent fractions are:

(i) ↔ (d)

(ii) ↔ (b)

(iii) ↔ (e)

(iv) ↔ (a)

(v) ↔ (c)

Question 6.

(i) Find the equivalent fraction of \(\frac{15}{35}\) with denominator 7.

(ii) Find the equivalent fraction of \(\frac{2}{9}\) with denominator 63.

Solution:

(i) \(\frac{15}{35}=\frac{ . . .}{7}\)

Let the numerator be a

⇒ 15 × 7 = 35 × a

\(a=\frac{15 \times 7}{35}\)

⇒ a = 3

∴ \(\frac{15}{35}=\frac{3}{7}\)

(ii) \(\frac{2}{9}=\frac{\dots}{63}\)

Let the numerator, which needs to be calculated as x

⇒ 2 × 63 = 9 × x

⇒ \(x=\frac{2 \times 63}{9}\)

⇒ x = 14

∴ \(\frac{2}{9}=\frac{14}{63}\)

Question 7.

Find the equivalent fraction of \(\frac{3}{5}\) having

(i) denominator 30

(ii) numerator 27.

Solution:

(i) \(\frac{3}{5}\) having denominator 30

Multiply and divide the fraction by 6, we get

\(\frac{3}{5} \times \frac{6}{6}=\frac{18}{30}\)

(ii) \(\frac{3}{5}\) having numerator 27

Multiply and divide the fraction by 9, we get

\(\frac{3}{5} \times \frac{9}{9}=\frac{27}{45}\)

Question 8.

Replace ‘…..’ in each of the following by the correct number.

Solution:

Question 9.

Check whether the given pairs of fractions are equivalent:

Solution:

Question 10.

Reduce the following fractions to simplest form:

Solution:

Question 11.

Convert the following fractions into equivalent like fractions:

Solution: