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

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)

\[\begin{align}\frac{2}{3} \times 2\frac{2}{3}&= \frac{2}{3} \times \frac{8}{3}\\{}&= \frac{{2 \times 8}}{{3 \times 3}}\\&= {\frac{{16}}{9}}\end{align}\]

(improper fraction)

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

we get,  \(\begin{align} \frac{{16}}{9}\end{align} \) \(\begin{align} = 1\frac{7}{9}\end{align}\)

(ii) 

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

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

we get,  \(\begin{align} \frac{14}{63}= \frac{2}{9}\end{align} \)

(iii)

\[\begin{align}\frac{3}{8} \times \frac{6}{4} &= \frac{{3 \times 6}}{{8 \times 4}}\\&= \frac{{18}}{{32}}\end{align}\]
Reducing\(\begin{align} \frac{{18}}{{32}}\end{align} \) to the lowest form,

we get, \(\begin{align} \frac{18}{32}= \frac{9}{{16}}\end{align} \)

(iv)

\[\begin{align}\frac{9}{3} \times \frac{3}{5}&= \frac{{9 \times 3}}{{5 \times 5}}\\&= \frac{{27}}{{25}}\end{align}\]

(improper fraction)

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

we get,  \(\begin{align}\frac{27}{25} = 1\frac{2}{{25}}\end{align} \)

(v)

\[\begin{align}\frac{1}{3} \times \frac{15}{8} &= \frac{1 \times 15}{3 \times 8}\\[0.5mm]&= \frac{15}{24}\end{align}\]

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

we get,  \(\begin{align}\frac{15}{24} = \frac{5}{8}\end{align} \)

(vi)

\[\begin{align} \frac{11}{2} \times \frac{3}{10} &= \frac{11 \times 3}{2 \times 10}\\[0.5mm] &= \frac{33}{20}\end{align}\]

(improper fraction)

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

we get,  \(\begin{align} \frac{33}{20}= 1\frac{{13}}{{20}}\end{align} \)

(vii)

\[\begin{align}\frac{4}{5} \times \frac{12}{7} &= \frac{4 \times 12}{5 \times 7}\\[0.5mm]&= \frac{48}{35} \end{align}\]

(improper fraction)

Converting \(\begin{align} \frac{{48}}{{35}}\end{align} \)into mixed fraction,

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