Question

please do this question fractions and decimals class 77th ​

Answer 1

Question :-

Multiply the following :

$1.\ \mathtt{4\dfrac{1}{3} \times 9\dfrac{1}{4}}$

$2.\ \mathtt{20 \times 13\dfrac{1}{5}}$

$3.\ \mathtt{17 \times 5\dfrac{2}{3}}$

$4. \ \mathtt{\dfrac{81}{100} \times \dfrac{6}{7}}$

$\begin{gathered} \end {gathered}$

Solution :-

We have,

$\begin{gathered} \end {gathered}$

1. First, Let us Convert Mixed Number into Improper Fractions.

$\mathtt{4\dfrac{1}{3} = \dfrac{3 \times 4 + 1}{3}} = \bold {\dfrac{13}{3}}\: and,$

$\mathtt {9\dfrac{1}{4} = \dfrac{4 \times 9 + 1}{4}} = \bold {\dfrac{37}{4}}$

$\begin{gathered} \end {gathered}$

$\begin {aligned} \mathrm {Now},\: \bold {\dfrac{13}{3} \times \dfrac{37}{4}} &= \dfrac{13\times37}{3\times4}\\\\&= \dfrac{481}{12}\\\\&= \underline {\boxed {\bf 40\dfrac{1}{12}}}\ \star \end{aligned}$

$\begin{gathered} \end {gathered}$

$\begin{aligned}2.\ \bold {20\times13\dfrac{1}{5}} &= 20\times\dfrac{5\times13+1}{5}\\\\&\Rightarrow 20\times\dfrac{66}{5}\\\\&\Rightarrow \dfrac{20\times66}{5}\\\\&\Rightarrow \dfrac{1320}{5} = \underline {\boxed {\bf 264}}\ \star \end{aligned}$

$\begin{gathered} \end {gathered}$

$\begin{aligned} 3.\ \bold {17\times5\dfrac{2}{3}} &= 17 \times \dfrac{3\times5+2}{3}\\\\&\Rightarrow 17\times \dfrac{17}{3}\\\\&\Rightarrow \dfrac{17\times17}{3}\\\\&\Rightarrow \dfrac{289}{3} = \underline {\boxed {\bf 96\dfrac{1}{3}}}\ \star \end{aligned}$

$\begin{gathered} \end {gathered}$

$4.\ \dfrac{81}{100} \times \dfrac{6}{7} \Rightarrow \dfrac{81\times6}{100\times7} \implies \dfrac{486}{700}= \underline {\boxed {\bf \dfrac{243}{350}}}\ \star$

$\begin{gathered} \end {gathered}$

Additional Information :-

MULTIPLICATION of Rational Numbers :-

For any two Rationals $\mathtt {\dfrac{a}{b}}$ and $\mathtt{\dfrac{c}{d}}$, we define :

$\mathtt {\Big (\dfrac{a}{b} \times \dfrac{c}{d}\Big ) = \dfrac{(a \times c)}{(b \times d)}}$