Ex.2.3 Q2 fractions-and-decimals Solutions-Ncert Maths Class 7

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Question

Multiply and reduce to lowest form (if possible):

(i) \(\begin{align} \frac{2}{3} \times 2\frac{2}{3}\end{align} \)

(ii)\(\begin{align} \frac{2}{7} \times \frac{7}{9}\end{align} \)

(iii) \(\begin{align} \frac{3}{8} \times \frac{6}{4}\end{align} \)

(iv) \(\begin{align} \frac{9}{5} \times \frac{3}{5}\end{align} \)

(v) \(\begin{align} \frac{1}{3} \times \frac{{15}}{8}\end{align} \)

(vi) \(\begin{align} \frac{{11}}{2} \times \frac{3}{{10}}\end{align} \)

(vii) \(\begin{align} \frac{4}{5} \times \frac{{12}}{7}\end{align} \)

Text Solution

What is known?

Expression

What is unknown?

Product of the given expression.

Reasoning:

Find the product by multiplying numerator with numerator and denominator with denominator.

Steps:

(i) \(\begin{align} \frac{2}{3} \times 2\frac{2}{3}\end{align} \)

\[\begin{align}&= \frac{2}{3} \times \frac{8}{3}\\{}&= \frac{{2 \times 8}}{{3 \times 3}}\\&= {\frac{{16}}{9}({\text{ improper fraction }})}\end{align}\]

Converting \(\begin{align} \frac{{16}}{9}\end{align} \) into mixed fraction, we get

 \(\begin{align} = 1\frac{7}{9}\end{align}\)

(ii)\(\begin{align} \frac{2}{7} \times \frac{7}{9}\end{align} \)

\[\begin{align}&= \frac{{2 \times 7}}{{7 \times 9}}\\ &= \frac{{14}}{{63}}\end{align}\]

Reducing \(\begin{align} \frac{{14}}{{63}}\end{align} \)to the lowest form, we get 

 \(\begin{align} = \frac{2}{9}\end{align} \)

(iii) \(\begin{align} \frac{3}{8} \times \frac{6}{4}\end{align} \)

\[\begin{align}&= \frac{{3 \times 6}}{{8 \times 4}}\\&= \frac{{18}}{{32}}\end{align}\]

Reducing\(\begin{align} \frac{{18}}{{32}}\end{align} \) to the lowest form, we get 

   \(\begin{align} = \frac{9}{{16}}\end{align} \)

(iv) \(\begin{align} \frac{9}{5} \times \frac{3}{5}\end{align} \)

\[\,\begin{align}&= \frac{{9 \times 3}}{{5 \times 5}}\\&= \frac{{27}}{{25}}{\text{ (improper fraction) }}\end{align}\] 

Converting \(\begin{align} \frac{{27}}{{25}}\end{align} \)into mixed fraction, we get   

  \(\begin{align} = 1\frac{2}{{25}}\end{align} \)

(v) \(\begin{align} \frac{1}{3} \times \frac{{15}}{8}\end{align} \)

\[\begin{align}&= \frac{{1 \times 15}}{{3 \times 8}}\\&= \frac{{15}}{{24}}\end{align}\]

Reducing \(\begin{align} \frac{{15}}{{24}}\end{align} \) to the lowest form, we get   

   \(\begin{align} = \frac{5}{8}\end{align} \)

(vi) \(\begin{align} \frac{{11}}{2} \times \frac{3}{{10}}\end{align} \)

\[\begin{align}&= \frac{{11 \times 3}}{{2 \times 10}}\\&= \frac{{33}}{{20}}({\text{ improper fraction }})\end{align}\]

Converting \(\begin{align} \frac{{33}}{{20}}\end{align} \) into mixed fraction, we get   

   \(\begin{align} = 1\frac{{13}}{{20}}\end{align} \)

(vii) \(\begin{align} \frac{4}{5} \times \frac{{12}}{7}\end{align} \)

\[\begin{align}&= \frac{{4 \times 12}}{{5 \times 7}}\\&= \frac{{48}}{{35}}{\text{ (improper fraction) }}\end{align}\]

Converting \(\begin{align} \frac{{48}}{{35}}\end{align} \)into mixed fraction, we get \(\begin{align} = 1\frac{{13}}{{35}}\end{align} \)

  
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