Ex 2.2 Q1 Fractions-and-Decimals-Solutions NCERT Maths Class 7

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Question

 Which of the drawing \((a) \) to \((d) \) show:

i) \(\begin{align}2 \times \frac{1}{5}\end{align}\) 

ii) \(\begin{align}2 \times \frac{1}{2}\end{align}\)

iii) \(\begin{align}3 \times \frac{2}{3}\end{align}\)

iv) \(\begin{align}3 \times \frac{1}{4}\end{align}\)

Text Solution

What is Known?

Fractions and Drawings

What is unknown?

Matching of fractions with shaded part of the drawings.

Reasoning:

Matching can be easily done by comparing the fractions and shaded areas.

Steps:

i)  \(\begin{align}2 \times \frac{1}{5}\end{align}\) matches with \((d)\) since two circles are divided in to five parts and one part of both the circles is shaded.

\[\begin{align} 2 \times \frac{1}{5} = \frac{1}{5} + \frac{1}{5} = \frac{2}{5} \end{align}\]

ii) \(\begin{align}2 \times \frac{1}{2}\end{align}\)matches with \((b)\) as one half of both the drawings is shaded.

\[\begin{align} 2 \times \frac{1}{2} = \frac{1}{2} + \frac{1}{2} = \frac{2}{2} = 1 \end{align}\]

iii) \(\begin{align}3 \times \frac{2}{3}\end{align}\)matches with \((a)\) since two third of the three circles is shaded.

\[\begin{align} 3 \times \frac{2}{3} = \frac{2}{3} + \frac{2}{3} + \frac{2}{3} = 3 \times \frac{2}{3} = 2 \end{align}\]

iv) \(\begin{align}3 \times \frac{1}{4}\end{align}\)matches with \((c)\) since one fourth of three squares is shaded.

\[\begin{align} 3 \times \frac{1}{4} = \frac{1}{4} + \frac{1}{4} + \frac{1}{4} = \frac{3}{4} \end{align}\]