Question

10/ The product of a fraction and the sum of 31 and 3-1 is
9
Find the fraction.
5
10
10​

Answer 1

Answer:

you can solve like this

Step-by-step explanation:

hope it would be helpful for you

Answer 2

Question:

The product of a fraction and the sum of $\displaystyle{\sf\:3\:\dfrac{1}{5}\:\&\:3\:\dfrac{1}{10}}$ is $\displaystyle{\sf\:\dfrac{9}{10}}$. Find the fraction.

Answer:

$\displaystyle{\boxed{\red{\sf\:The\:fraction\:=\:\dfrac{1}{7}}}}$

Step-by-step-explanation:

Let the numerator of the fraction be x.

And the denominator of the fraction be y.

$\displaystyle{\therefore\:\sf\:The\:fraction\:=\:\dfrac{x}{y}}$

From the given condition,

$\displaystyle{\sf\:\dfrac{x}{y}\:\times\:\left(\:3\:\dfrac{1}{5}\:+\:3\:\dfrac{1}{10}\:\right)\:=\:\dfrac{9}{10}}$

$\displaystyle{\implies\sf\:\dfrac{x}{y}\:\times\:\left(\:\dfrac{5\:\times\:3\:+\:1}{5}\:+\:\dfrac{10\:\times\:3\:+\:1}{10}\:\right)\:=\:\dfrac{9}{10}}$

$\displaystyle{\implies\sf\:\dfrac{x}{y}\:\times\:\left(\:\dfrac{15\:+\:1}{5}\:+\:\dfrac{30\:+\:1}{10}\:\right)\:=\:\dfrac{9}{10}}$

$\displaystyle{\implies\sf\:\dfrac{x}{y}\:\times\:\left(\:\dfrac{16}{5}\:+\:\dfrac{31}{10}\:\right)\:=\:\dfrac{9}{10}}$

$\displaystyle{\implies\sf\:\dfrac{x}{y}\:\times\:\left(\:\dfrac{16\:\times\:2}{5\:\times\:2}\:+\:\dfrac{31}{10}\:\right)\:=\:\dfrac{9}{10}}$

$\displaystyle{\implies\sf\:\dfrac{x}{y}\:\times\:\left(\:\dfrac{32}{10}\:+\:\dfrac{31}{10}\:\right)\:=\:\dfrac{9}{10}}$

$\displaystyle{\implies\sf\:\dfrac{x}{y}\:\times\:\left(\:\dfrac{32\:+\:31}{10}\:\right)\:=\:\dfrac{9}{10}}$

$\displaystyle{\implies\sf\:\dfrac{x}{y}\:\times\:\dfrac{63}{\cancel{10}}\:=\:\dfrac{9}{\cancel{10}}}$

$\displaystyle{\implies\sf\:\dfrac{x}{y}\:\times\:63\:=\:9}$

$\displaystyle{\implies\sf\:\dfrac{x}{y}\:=\:\cancel{\dfrac{9}{63}}}$

$\displaystyle{\implies\boxed{\red{\sf\:\dfrac{x}{y}\:=\:\dfrac{1}{7}}}}$

$\displaystyle{\therefore\:\underline{\boxed{\red{\sf\:The\:fraction\:=\:\dfrac{1}{7}}}}}$