Question

What number should 5/7 be multiplied to give the result 1/21

Answer 1

Given question :

• what number should $\tt\frac{5}{7}$ be multiplied to give the result $\tt\frac{1}{21}$

What to do ?

In this question we have to multiply that number with $\tt\frac{5}{7}$ which which will yield $\tt\frac{1}{21}$. So, we can assume that number to be x and try to answer.

S O L U T I O N:

$\bf{{\colorbox{yellow} {\green{{assumption : }}}}}$

Let x number should multiplied with $\tt\frac{5}{7}$ to give $\tt\frac{1}{21}$

$\bf{{\colorbox{black} {\color{white}{{now : }}}}}$

$\Rightarrow\tt \pmb{x \times \frac{5}{7} = \frac{1}{21} }$

$\Rightarrow \tt \pmb{x = \frac{1}{21} \times \frac{7}{5} } \: {\small (reciprocalled)}$

$\Rightarrow \tt \pmb{x = \frac{1}{ \cancel{{21}} \: \orange{3}} \times \frac {\cancel{{7}} \: \orange{1}}{5} }$

$\Rightarrow \tt \pmb{x = \frac{1 \times 1}{3 \times 5} }$

$\boxed{ \tt \pmb{x = \frac{1}{15} }}$

Verification:

$\boxed{ \green{ \tt{lhs = rhs}}}$

$\Rightarrow \tt \pmb{ \frac{1}{15} \times \frac{5}{7} = \frac{1}{21} }$

$\Rightarrow\tt \pmb{ \frac{1}{ \cancel{{15}} \: \red{3}} \times \frac {\cancel{{5}} \: \red{1}}{7} = \frac{1}{21} }$

$\Rightarrow \tt \pmb{ \frac{1 \times 1}{7 \times 3} = \frac{1}{21} }$

$\boxed{\tt \pmb{ \frac{1}{21} = \frac{1}{21} }}$

$\bf{{\colorbox{lightpink} {\color{white}{{hence \: proved }}}}}$

So,the answer is 1/15

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