Ex.2.7 Q5 fractions-and-decimals Solutions-Ncert Maths Class 7

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Question

 Find:

i) \(7 ÷ 3.5\)

ii) \(36 ÷ 0.2\)

iii) \(3.25 ÷ 0.5\)

iv) \(30.94 ÷ 0.7\)

v) \(0.5÷ 0.25\)

vi) \(7.75 ÷ 0.25\)

vii) \(76.5 ÷ 0.15 \)

viii) 37.8 ÷ 1.4

ix) \(2.73 ÷ 1.3\)

Text Solution

What is known?

Decimal numbers.

What is unknown?

Quotient of following division.

Reasoning:

Covert decimal into fraction then divide it. To divide fractions, multiply the dividend with reciprocal of divisor.

Steps:

i) \(7 ÷ 3.5\)

\[\begin{align}&= 7 \times \frac{1}{{3.5}} \hfill \\&= \frac{7}{1} \times \frac{{10}}{{35}} \hfill \\
&= \frac{{70}}{{35}} \hfill \\&= \frac{{10}}{5} \hfill \\&= 2 \hfill \\\end{align} \]

ii) \(36 ÷ 0.2\)

\[\begin{align}&= 36 \times \frac{1}{{0.2}} \hfill \\&= \frac{{36}}{1} \times \frac{{10}}{2} \hfill \\
&= \frac{{36 \times 10}}{2} \hfill \\&= 18 \times 10 \hfill \\&= 180 \hfill \\\end{align} \]

iii) \(3.25 ÷ 0.5\)

\[\begin{align}&= 3.25 \times \frac{1}{{0.5}} \\&= \frac{{325}}{{100}} \times \frac{{10}}{5} \\
&= \frac{{65}}{{10}} \\&= 6.5\end{align}\]

iv) \(30.94 ÷ 0.7\)

\[\begin{align}&= 30.94 \times \frac{1}{{0.7}} \\&= \frac{{3094}}{{100}} \times \frac{{10}}{7} \\&= \frac{{3094}}{{70}} \\&= \frac{{442}}{{10}} \\&= 44.2\end{align}\]

v) \(0.5÷ 0.25\)

\[\begin{align}&= 0.5 \times \frac{1}{{0.25}} \hfill \\&= \frac{5}{{10}} \times \frac{{100}}{{25}} \hfill \\
 &= \frac{{50}}{{25}} \hfill \\&= 2 \hfill \\\end{align} \]

vi) \(7.75 ÷ 0.25\)

\[\begin{align}&= 7.75 \times \frac{1}{{0.25}} \hfill \\&= \frac{{775}}{{100}} \times \frac{{100}}{{25}} \hfill \\
&= \frac{{775}}{{25}} \hfill \\&= 31 \hfill \\\end{align} \]

vii) \(76.5 ÷ 0.15 \)

\[\begin{align}&= 76.5 \times \frac{1}{{0.15}} \hfill \\&= \frac{{765}}{{10}} \times \frac{{100}}{{15}} \hfill \\
&= \frac{{7650}}{{15}} \hfill \\&= 510 \hfill \\\end{align} \]

viii) 37.8 ÷ 1.4

\[\begin{align}&= 37.8 \times \frac{1}{{1.4}} \hfill \\&= \frac{{378}}{{10}} \times \frac{{10}}{{14}} \hfill \\&= \frac{{378}}{{14}} \hfill \\&= 27 \hfill \\\end{align} \]

ix) \(2.73 ÷ 1.3\)

\[\begin{align}&= 2.73 \times \frac{1}{{1.3}} \hfill \\&= \frac{{273}}{{100}} \times \frac{{10}}{{13}} \hfill \\
&= \frac{{21}}{{10}} \hfill \\&= 2.1 \hfill \\\end{align} \]

  
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