Ex.2.3 Q3 fractions-and-decimals Solutions-Ncert Maths Class 7

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Question

 Multiply the following fractions:

i) \(\begin{align} \frac{2}{5} \times 5\frac{1}{4}\end{align} \)

ii) \(\begin{align} 6\frac{2}{5} \times \frac{7}{9} \end{align} \)

iii) \(\begin{align} \frac{3}{2} \times 5\frac{1}{3}\end{align} \)

iv) \(\begin{align} \frac{5}{6} \times 2\frac{3}{7}\end{align} \)

v) \(\begin{align} 3\frac{2}{5} \times \frac{4}{7}\end{align} \)

vi) \(\begin{align} 2\frac{3}{5} \times 3\end{align} \)

(vii) \(\begin{align} 3\frac{4}{7} \times \frac{3}{5}\end{align} \)

Text Solution

What is known?

Expression

What is unknown?

Product of the given expression.

Reasoning:

Covert mixed fraction into improper fraction then find the product.

Steps:

i) \(\begin{align} \frac{2}{5} \times 5\frac{1}{4}\end{align} \)

\(\begin{align} =\frac{2}{5}\times \frac{21}{4}\end{align} \)

Reducing to the lowest form, we get

\[\begin{align}&= \frac{1}{5} \times \frac{{21}}{2}\\&= \frac{{1 \times 21}}{{5 \times 2}}\\&= \frac{{21}}{{20}}({\text{ improper fraction }})\end{align}\]

Converting into mixed fraction, we get \(\begin{align}= 2\frac{1}{{10}}\end{align}\)

ii) \(\begin{align} 6\frac{2}{5} \times \frac{7}{9} \end{align} \)

\[\begin{align}&= \frac{{32}}{5} \times \frac{7}{9}\\&= \frac{{224}}{{45}}({\text{ improper fraction }})\end{align}\]

Converting \(\begin{align} \frac{{224}}{{45}}\end{align} \) into mixed fraction, we get \(\begin{align} = 4\frac{{44}}{{45}} \end{align}\)

iii) \(\begin{align} \frac{3}{2} \times 5\frac{1}{3}\end{align} \)

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

Reducing to the lowest form, we get

\[\begin{align} = \frac{{3 \times 16}}{{2 \times 3}} = 8\quad \text{(This is a whole number) }\end{align}\] 

iv) \(\begin{align} \frac{5}{6} \times 2\frac{3}{7}\end{align} \)

\[\,\begin{align}&= \frac{5}{6} \times \frac{{17}}{7}\\&= \frac{{85}}{{42}}\end{align}\]

Reducing \(\begin{align} \frac{{85}}{{42}}\end{align} \) to the lowest form, we get \(\begin{align} = 2\frac{1}{{42}} \end{align}\)

v) \(\begin{align} 3\frac{2}{5} \times \frac{4}{7}\end{align} \)

\[\begin{align}&= \frac{{17}}{5} \times \frac{4}{7}\\&= \frac{{68}}{{35}}{\text{ (improper fraction) }}\end{align}\]

Converting \(\begin{align} \frac{{68}}{{35}}\end{align} \) into mixed fraction, we get \(\begin{align} = 1\frac{{33}}{{35}}\end{align}\)

vi) \(\begin{align} 2\frac{3}{5} \times 3\end{align} \)

\[\begin{align}&= \frac{{13}}{5} \times \frac{3}{1}\\&= \frac{{13 \times 3}}{{5 \times 1}}\\&= \frac{{39}}{5}{\text{ (improper fraction) }}\end{align}\]

Converting \(\begin{align} \frac{{39}}{5}\end{align} \) into mixed fraction, we get \(\begin{align} = 7\frac{4}{5} \end{align}\)

(vii) \(\begin{align} 3\frac{4}{7} \times \frac{3}{5}\end{align} \)

\[\begin{align}&=\frac{25}{7}\times \frac{3}{5} \\& =\frac{25\times 3}{7\times 5} \\&\\\end{align}\]

 Reducing it to the lowest form, we get

\[\,\,\,~\frac{15}{7}~=~~\left( \text{improper fraction} \right)\]

Converting \(\begin{align} \frac{{15}}{7}\end{align} \) into mixed fraction, we get \(\begin{align}=2\frac{1}{7} \end{align}\)

  
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