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

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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)

  
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