Excercise 2.7 Fractions and Decimals - NCERT Solutions Class 7

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Question 1

Find

   i) \(0.4 ÷ 2\)

  ii) \(0.35 ÷ 5 \)

 iii) \(2.48 ÷ 4 \)

 iv) \(65.4 ÷ 6\)

  v) \(651.2 ÷ 4 \)

 vi) \(14.49 ÷ 7 \)

 vii) \(3.96 ÷ 4\)

viii) \(0.80 ÷ 5\)

Solution

Video Solution

What is known?

One decimal number and one whole number.

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) \(0.4 ÷ 2\)

\[\begin{align}&=\frac{4}{{10}} \times \frac{1}{2}\left( {0.4 = \frac{4}{{10}}} \right) \\&= \frac{2}{{10}} \\&= \frac{1}{5}\\&= 0.2\\\end{align} \]

ii) \(0.35 ÷ 5 \)

\[\begin{align}&= 0.35 \times \frac{1}{5} \\&= \frac{{35}}{{100}} \times \frac{1}{5} \left( {0.35 = \frac{{35}}{{100}}} \right) \\&= \frac{7}{{100}} \\&= 0.07 \\\end{align} \]

iii) \(2.48 ÷ 4 \)

\[\begin{align}&= 2.48 \times \frac{1}{4} \\&= \frac{{248}}{{100}} \times \frac{1}{4} \left( {\because 2.48 = \frac{{248}}{{100}}} \right) \\&= \frac{{62}}{{100}} \\&= 0.62\end{align}\]

iv) \(65.4 ÷ 6\)

\[\begin{align}&= 65.4 \times \frac{1}{6} \\&= \frac{{654}}{{10}} \times \frac{1}{6} \left( {\because 65.4 = \frac{{654}}{{10}}} \right) \\&= \frac{{109}}{{10}} \\&= 10.9\end{align}\]

v) \(651.2 ÷ 4 \)

\[\begin{align}&= 651.2 \times \frac{1}{4} \\&= \frac{{6512}}{{10}} \times \frac{1}{4} \left( {\because 651.2 = \frac{{6512}}{{10}}} \right) \\&= \frac{{1628}}{{10}} \\&= 162.8\end{align}\]

vi) \(14.49 ÷ 7 \)

\[\begin{align}&= 14.49 \times \frac{1}{7} \\&= \frac{{1449}}{{100}} \times \frac{1}{7}\left( {\because 14.49 = \frac{{1449}}{{100}}} \right) \\&= \frac{{1449}}{{700}}\\&= \frac{{207}}{{100}}\\&= 2.07\end{align}\]

vii) \(3.96 ÷ 4\)

\[\begin{align}&= 3.96 \times \frac{1}{4} \\&= \frac{{396}}{{100}} \times \frac{1}{4} \left( {\because 3.96 = \frac{{396}}{{100}}} \right) \\&= \frac{{396}}{{400}} \\&= \frac{{99}}{{100}} \\&= 0.99\end{align}\]

viii) \(0.80 ÷ 5\)

\[\begin{align}&= 0.80 \times \frac{1}{5} \\&= \frac{{80}}{{100}} \times \frac{1}{5}\left( {\because 0.80 = \frac{{80}}{{100}}} \right) \\&= \frac{{16}}{{100}} \\&= 0.16\end{align}\]

Question 2

Find:

i) \(4.8 ÷ 10 \)

ii) \(52.5 ÷ 10\)

iii) \(0.7 ÷ 10\)

iv) \(33.1 ÷ 10\)

v) \(272.23 ÷ 10\)

vi) \(0.56 ÷ 10 \)

vii) \(3.97 ÷ 10\)

Solution

Video Solution

What is known?

One decimal number and one whole number.

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) \(4.8 ÷ 10 \)

\[\begin{align}&= 4.8 \times \frac{1}{{10}} \\&= \frac{{48}}{{10}} \times \frac{1}{{10}} \\&= \frac{{48}}{{100}} \\ &= 0.48\end{align}\]

ii) \(52.5 ÷ 10\)

\[\begin{align}&= 52.5 \times \frac{1}{{10}} \hfill \\&= \frac{{525}}{{10}} \times \frac{1}{{10}} \hfill \\&= \frac{{525}}{{100}} \hfill \\&= 5.25 \hfill \\\end{align} \]

iii) \(0.7 ÷ 10\)

\[\begin{align}&= 0.7 \times \frac{1}{{10}} \hfill \\&= \frac{7}{{10}} \times \frac{1}{{10}} \hfill \\&= \frac{7}{{100}} \hfill \\&= 0.07 \hfill \\\end{align} \]

iv) \(33.1 ÷ 10\)

\[\begin{align}&= 33.1 \times \frac{1}{{10}} \\&= \frac{{331}}{{10}} \times \frac{1}{{10}} \\&= \frac{{331}}{{100}} \\&= 3.31\end{align}\]

v) \(272.23 ÷ 10\)

\[\begin{align}&= 272.73 \times \frac{1}{{10}} \\&= \frac{{27273}}{{100}} \times \frac{1}{{10}} \\&= \frac{{27273}}{{1000}} \\&= 27.273\end{align}\]

vi) \(0.56 ÷ 10 \)

\[\begin{align}&= 0.56 \times \frac{1}{{10}}\\&= \frac{{56}}{{100}} \times \frac{1}{{10}} \\&= \frac{{56}}{{1000}}\\&= 0.056\end{align}\]

vii) \(3.97 ÷ 10\)

\[\begin{align}&= 3.97 \times \frac{1}{{10}} \\&= \frac{{397}}{{100}} \times \frac{1}{{10}} \\&= \frac{{397}}{{1000}} \\&= 0.397\end{align}\]

Question 3

 Find:

i) \(2.7 ÷ 100\)

ii) \(0.3 ÷ 100 \)

iii) \(0.78 ÷ 100\)

iv) \(432.6 ÷ 100\)

v) \(23.6 ÷ 100\)

vi) \(98.53 ÷ 100 \)

Solution

Video Solution

What is known?

One decimal number and one whole number.

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) \(2.7 ÷ 100\)

\[\begin{align}&= 2.7 \times \frac{1}{{100}} \hfill \\&= \frac{{27}}{{10}} \times \frac{1}{{100}} \hfill \\&= \frac{{27}}{{1000}} \hfill \\&= 0.027 \hfill \\\end{align} \]

ii) \(0.3 ÷ 100 \)

\[\begin{align}&= 0.3 \times \frac{1}{{100}} \hfill \\&= \frac{3}{{10}} \times \frac{1}{{100}} \hfill \\&= \frac{3}{{1000}} \hfill \\&= 0.003 \hfill \\\end{align} \]

iii) \(0.78 ÷ 100\)

\[\begin{align}&= 0.78 \times \frac{1}{{100}}\\&= \frac{{78}}{{100}} \times \frac{1}{{100}} \\ &= \frac{{78}}{{10000}} \\&= 0.0078\end{align}\]

iv) \(432.6 ÷ 100\)

\[\begin{align}&= 432.6 \times \frac{1}{{100}} \hfill \\&= \frac{{4326}}{{10}} \times \frac{1}{{100}} \hfill \\&= \frac{{4326}}{{1000}} \hfill \\&= 4.326 \hfill \\\end{align} \]

v) \(23.6 ÷ 100\)

\[\begin{align}&= 23.6 \times \frac{1}{{100}} \hfill \\&= \frac{{236}}{{10}} \times \frac{1}{{100}} \hfill \\&= \frac{{236}}{{1000}} \hfill \\&= 0.236 \hfill \\\end{align} \]

vi) \(98.53 ÷ 100 \)

\[\begin{align}&= 98.53 \times \frac{1}{{100}} \\&= \frac{{9853}}{{100}} \times \frac{1}{{100}} \\&= \frac{{9853}}{{10000}}\\&= 0.9853\end{align}\]

Question 4

 Find: -

i) \(7.9 ÷ 1000 \)

ii) \(26.3 ÷ 1000\)

iii) \(38.53 ÷ 1000\)

iv) \(128.9 ÷ 1000\)

v) \(0.5 ÷ 1000\)

Solution

Video Solution

What is known?

One decimal number and one whole number.

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) \(7.9 ÷ 1000 \)

\[\begin{align}&= 7.9 \times \frac{1}{{1000}} \hfill \\&= \frac{{79}}{{10}} \times \frac{1}{{1000}} \hfill \\&= \frac{{79}}{{10000}} \hfill \\&= 0.0079 \hfill \\\end{align} \]

ii) \(26.3 ÷ 1000\)

\[\begin{align}&= 26.3 \times \frac{1}{{1000}} \\&= \frac{{263}}{{10}} \times \frac{1}{{1000}} \\&= \frac{{263}}{{10000}} \\&= 0.0263\end{align}\]

iii) \(38.53 ÷ 1000\)

\[\begin{align}&= 38.53 \times \frac{1}{{1000}} \hfill \\&= \frac{{3853}}{{100}} \times \frac{1}{{1000}} \hfill \\&= \frac{{3853}}{{100000}} \hfill \\&= 0.03853 \hfill \\\end{align} \]

iv) \(128.9 ÷ 1000\)

\[\begin{align}&= 128.9 \times \frac{1}{{1000}} \\&= \frac{{1289}}{{10}} \times \frac{1}{{1000}} \\&= \frac{{1289}}{{10000}} \\&= 0.1289\end{align}\]

v) \(0.5 ÷ 1000\)

\[\begin{align}&= 0.5 \times \frac{1}{{1000}} \\&= \frac{5}{{10}} \times \frac{1}{{1000}} \\&= \frac{5}{{10000}} \\&= 0.0005\end{align}\]

Question 5

 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) \(2.73 ÷ 1.3\)

Solution

Video 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) \(2.73 ÷ 1.3\)

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

Question 6

A vehicle covers a distance of \(43.2 \rm\,km\) in \(2.4\) liters of petrol. How much distance will it cover in \(1\) liter of petrol?

Solution

Video Solution

What is known?

A vehicle covers a distance of \(43.2\, \rm{km}\) in \(2.4\) liters of petrol.

What is unknown?

How much distance will it Cover in \(1\) liter of petrol.

Reasoning:

By using Unitary Method, we can simply divide \(43.2\) by \(2.4\) to get how much distance will vehicle cover in \(1\) liter of petrol.

Steps:

Distance covered in \(2.4\) liters of petrol \(= 43.2\rm\, km\)

\(\therefore\)  Distance covered in \(1\) litre of petrol 

\[\begin{align} & =43.2\div 2.4  \\{} & =43.2\times \frac{1}{2.4}  \\ {} & =\frac{432}{10}\times \frac{10}{24}  \\{} & =18\,\text{km}  \\\end{align}\]

Thus, it covers a distance of \(18 \rm\,km\) in \(1\) liter of petrol.

  
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