Ex 2.2 Q7 Fractions-and-Decimals-Solutions NCERT Maths Class 7

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Question

Find

\(\begin{align} {\rm{(a)}}\,\, &\frac{1}{2}\;{\rm{ of }} \\& \qquad ({\rm{ i }})\;\;2\frac{3}{4} \\&\qquad {\rm{ (ii) }}\;4\frac{2}{9}\end{align}\)

\(\begin{align} {\rm{(b)}}\,\, &\frac{5}{8}\;{\rm{ of }}\\ & \qquad ({\rm{ i }})\;\;3\frac{5}{6} \\ &\qquad {\rm{ (ii) }}\;9\frac{2}{3}\end{align}\) 

 Video Solution
Fractions And Decimals
Ex 2.2 | Question 7

Text Solution

What is known?

Fractions

What is unknown?

Product of the given fractions.

Reasoning:

Covert mixed fraction into improper fraction then find the product.

Steps:

(a)

\(\begin{align}({\rm{i}})\;\frac{1}{2}\,{\rm{ of }}\;2\frac{3}{4}\end{align}\)

\(\begin{align}\frac{1}{2}\text{ of }2\frac{3}{4}&=\frac{1}{2}\times 2\frac{3}{4}\\[0.5mm]&=\frac{1}{2}\times \frac{11}{4}\\[0.5mm]&=\frac{11}{8} \\&\left( \text{improper fraction} \right)\end{align}\)

Converting \(\begin{align}\frac{{11}}{8}\end{align}\) into mixed fraction,

we get, \[\begin{align}\frac{{11}}{8} = 1\frac{3}{8}\end{align}\]

\(\begin{align} {\rm{(ii)}} \;\frac{1}{2}\;{\rm{ of }}\;4\frac{2}{9} \end{align}\)

\(\begin{align} \frac{1}{2}\;{\rm{ of }}\;4\frac{2}{9} &= \frac{1}{2} \times \frac{{38}}{9} \\[0.5mm]&= \frac{{19}}{9}\\&({\text{improper fraction}})\end{align}\) 

Converting \(\begin{align}\frac{{19}}{{9}}\end{align}\) into mixed fraction,

we get, \[\begin{align}\frac{{19}}{9} = 2\frac{1}{9}\end{align}\]

(b) \(\begin{align}\frac{5}{8}\;\;{\rm{ of (i) }}\;3\,\frac{5}{6}\quad {\rm{ (ii) }}\;9\frac{2}{3}\end{align}\)

 (i)

\(\begin{align}\;\frac{5}{8}\;{\rm{ of }}\;3\frac{5}{6} &= \frac{5}{8} \times \frac{{23}}{6} \\[0.5mm]&= \frac{{115}}{{48}}\\&({\text{improper fraction)}}\end{align}\)

Converting \(\begin{align}\frac{{115}}{{48}}\end{align}\) into mixed fraction,

we get, \[\begin{align}\frac{{115}}{{48}} = 2\frac{{19}}{{48}}\end{align}\]

 (ii)

\(\begin{align}\frac{5}{8}\;{\rm{ of }}\;9\frac{2}{3} &= \frac{5}{8} \times \frac{{29}}{3} \\[0.5mm]&= \frac{{145}}{{24}}\\&({\text{improper fraction}})\end{align}\)

Converting \(\begin{align}\frac{{145}}{{24}}\end{align}\) into mixed fraction,

we get, \[\begin{align}\frac{{145}}{{24}} = 6\frac{1}{{24}}\end{align}\]

  
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