EX 2.1 Q8 Fractions and Decimals Solution- NCERT Maths class 7

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Question

Michael finished coloring picture in \(\begin{align}\frac{7}{{12}}\end{align}\)hours. Vaibhav finished coloring the same picture in \(\begin{align}\frac{3}{4}\end{align}\)hours. Who worked longer? By what fraction was it longer?

Text Solution

What is Known?

Time taken by Michael and Vaibhav to finish coloring the picture.

What is unknown?

Who took longer to finish colouring the picture and how much longer.

Reasoning:

Time is given in unlike fractions. The first step is to change the fractions to like fractions and compare them to decide which one is bigger.

Steps:

Time taken by Michael \(\begin{align} = \frac{7}{{12}}\end{align}\) hour

Time taken by Vaibhav \(\begin{align}=\frac{3}{4}\end{align}\) hour

\[\begin{align} &= \frac{3 \times 3}{4 \times 3}\\&\;\;\;\;(\text{converting into like fractions})\\ & = \frac{9}{12}\text{ hour} \end{align}\]

Since,\( \begin{align}\frac{9}{{12}} > \frac{7}{{12}}\end{align}\)therefore, Vaibhav worked longer.

Difference\( \begin{align} = \frac{9}{{12}} - \frac{7}{{12}} = \frac{2}{{12}} = \frac{1}{6}\end{align}\) hour

Thus, Vaibhav took\( \begin{align}\frac{1}{6}\end{align}\) hour more than Michael.

  
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