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

## 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.