Ex 2.6 Q1 Fractions-and-Decimals-Solutions NCERT Maths Class 7

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Question

 Find

i) \(0.2\times 6\)

 ii) \( 8 \times4.6 \)  

iii) \(2.71\times 5\)   

iv) \(20.1 \times 4\)

v) \(0.05 \times 7\) 

vi) \(211.02 \times 4\) 

vii) \(2 \times 0.86\)

Text Solution

What is known?

One decimal number and one whole number.

What is unknown?

Product of these two numbers.

Reasoning:

Covert decimal number into fraction and then find the product.

Steps:

i) \(0.2\times 6\)

\[\begin{align}0.2 \times 6 &= \frac{2}{{10}} \times 6\\\,\,\,0.2 \times 6 &= \frac{{2 \times 6}}{{10}}\\\,\,\,\,0.2 \times 6 &= \frac{{12}}{{10}}\\\,\,\,\,0.2 \times 6 &= 1.2\\\end{align}\]

 ii) \( 8 \times4.6 \)  

\[\begin{align}8 \times 4.6 &= 8 \times \frac{{46}}{{10}}\\\,\,\,\,\,\,\,8 \times 4.6 &= \frac{{8 \times 46}}{{10}}\\\,\,\,\,\,\,\,\,8 \times 4.6 &= \frac{{368}}{{10}}\\\,\,\,\,\,\,\,\,8 \times 4.6 &= 3.68\end{align}\]

iii) \(2.71\times 5\)   

\[\begin{align}2.71 \times 5 &= \frac{{271}}{{100}} \times 5\\\,\,\,\,\,\,\,\,2.71 \times 5 &= \frac{{271 \times 5}}{{100}}\\\,\,\,\,\,\,\,\,2.71 \times 5 &= \frac{{1355}}{{100}}\\\,\,\,\,\,\,\,\,2.71 \times 5 &= 13.55\end{align}\]

iv) \(20.1 \times 4\)

\[\begin{align}20.1 \times 4 &= \frac{{201}}{{10}} \times 4\\\,\,\,\,\,\,\,20.1 \times 4 &= \frac{{201 \times 4}}{{10}}\\\,\,\,\,\,\,\,20.1 \times 4 &= \frac{{804}}{{10}}\\\,\,\,\,\,20.1 \times 4 &= 80.4\end{align}\]

v) \(0.05 \times 7\)

\[\begin{align}0.05 \times 7 &= \frac{5}{{100}} \times \frac{7}{1}\\\,\,\,\,\,\,0.05 \times 7 &= \frac{{5 \times 7}}{{100}}\\\,\,\,\,\,\,0.05 \times 7 &= \frac{{35}}{{100}}\\\,\,\,\,\,\,0.05 \times 7 &= 0.35\end{align}\]

vi) \(211.02 \times 4\) 

\[\begin{align}211.02 \times 4 &= \frac{{21102}}{{100}} \times \frac{4}{1}\\\,\,\,\,\,\,\,\,\,211.02 \times 4 &= \frac{{21102 \times 4}}{{100}}\\\,\,\,\,\,\,\,\,\,211.02 \times 4 &= \frac{{84408}}{{100}}\\\,\,\,\,\,\,\,\,\,211.02 \times 4 &= 844.08\end{align}\]

vii) \(2 \times 0.86\)

\[\begin{align}2 \times 0.86& = \frac{2}{1} \times \frac{{86}}{{100}}\\\,\,\,\,\,\,\,2 \times 0.86 &= \frac{{2 \times 86}}{{100}}\\\,\,\,\,\,\,\,2 \times 0.86 &= \frac{{172}}{{100}}\\\,\,\,\,\,\,2 \times 0.86 &= 1.72\end{align}\]

  
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