# Ex.2.4 Q2 fractions-and-decimals Solutions-Ncert Maths Class 7

## Question

Find the reciprocals of the following fractions. Classify the reciprocals as proper fractions, improper fractions, and whole numbers.

i) \(\begin{align} \frac{3}{7}\end{align} \)

ii) \(\begin{align} \frac{5}{8}\end{align} \)

iii) \(\begin{align} \frac{9}{7}\end{align} \)

iv) \(\begin{align} \frac{6}{5}\end{align} \)

v) \(\begin{align} \frac{{12}}{7}\end{align} \)

vi) \(\begin{align} \frac{1}{8}\end{align} \)

vii) \(\begin{align} \frac{1}{{11}}\end{align} \)

## Text Solution

**What is known?**

Fractions.

**What is unknown?**

Reciprocal of given fraction.

**Reasoning:**

Reciprocal means interchanging numerator with denominator.

**Steps:**

(1) **Proper fraction:** -In proper fractions numerator is less than the denominator.

(2) **Improper fraction**: - In improper fractions numerator is greater than the denominator.

(3) **Whole number:** - It is a collection of positive integers including \(0\).

i) \(\begin{align} \frac{3}{7}\end{align} \)

Reciprocal of \(\begin{align} \frac{3}{7}\end{align} \) is \(\begin{align} \frac{7}{3}\end{align}\) (Improper fraction)

ii) \(\begin{align} \frac{5}{8}\end{align} \)

Reciprocal of \(\begin{align} \frac{5}{8}\end{align} \) is \(\begin{align} \frac{8}{5}\end{align}\) (Improper fraction)

iii) \(\begin{align} \frac{9}{7}\end{align} \)

Reciprocal of \(\begin{align} \frac{9}{7}\end{align} \) is \(\begin{align} \frac{7}{9}\end{align}\) (Proper fraction)

iv) \(\begin{align} \frac{6}{5}\end{align} \)

Reciprocal of \(\begin{align} \frac{6}{5}\end{align} \) is \(\begin{align} \frac{5}{6}\end{align}\) (Proper fraction)

v) \(\begin{align} \frac{{12}}{7}\end{align} \)

Reciprocal of \(\begin{align} \frac{{12}}{7}\end{align} \) is \(\begin{align} \frac{7}{{12}}\end{align}\) (Proper fraction)

vi) \(\begin{align} \frac{1}{8}\end{align} \)

Reciprocal of \(\begin{align} \frac{1}{8}\end{align} \) is \(\begin{align} \frac{8}{1} = 8\end{align}\) (Whole number)

vii) \(\begin{align} \frac{1}{{11}}\end{align} \)

Reciprocal of \(\begin{align} \frac{1}{{11}}\end{align} \) is \(\begin{align} \frac{{11}}{1} = 11\end{align}\) (Whole number)