Question

Q5: The numerator of a fraction is
a fraction is to less than denominator
If the numerator is increased by 19 and
the denominator is decreased by 1. the number
obtained is 3 Find the rational number.​

Answer 1

✬ Rational Number = 8/10 ✬

Step-by-step explanation:

Given:

• The numerator of a fraction is 2 less than denominator.
• After increasing numerator by 19 and decreasing denominator by 1 the number obtained is 3.

To Find:

• What is the rational number ?

Solution: Let the denominator of fraction be x. Therefore,

➫ Numerator = 2 less than x

➫ Numerator = (x – 2)

[ Adding 19 to numerator & subtracting 1 from denominator ]

➫ New numerator = (x – 2 + 19)

➫ New denominator = (x – 1)

A/q

• New number obtained is 3.

$\implies{\rm }$ (x – 2 + 19)/(x – 1) = 3

$\implies{\rm }$ (x + 17)/(x – 1) = 3

$\implies{\rm }$ (x + 17) = 3(x – 1)

$\implies{\rm }$ x + 17 = 3x – 3

$\implies{\rm }$ 17 + 3 = 3x – x

$\implies{\rm }$ 20 = 2x

$\implies{\rm }$ 20/2 = x

$\implies{\rm }$ 10 = x

So,

➯ Denominator is x = 10

➯ Numerator is (x – 2) = 10–2 = 8

∴ Fraction = Numerator/Denominator

➯ 8/10

Answer 2

Step-by-step explanation:

$\sf \red {\underline{\underline{Given:-}}}$

• The numerator of a fraction in two less than denominator

• If the numerator is increased by 19 and
• the denominator is decreased by 1 , the number
• obtained is 3 .

$\sf \blue{\underline{\underline{To\:Find:-}}}$

• The original rational number

$\sf \green {\underline{\underline{Solution:-}}}$

According to the given question:-

Condition 1:-

$\rm Let \: the \: denominator \: be \: (x)$

$\rm The \: numerator \: = (x-2)$

Condition 2:-

$\rm\rightarrow The\:numerator = x - 2 + 19$

$\rm\rightarrow x + 17$

$\rm The \: denomirator \: = x -1$

Therefore:-

$\rm \rightarrow \dfrac{x + 17}{x - 1} = 3$

$\rm By\:cross\:multiplication$

$\rm \rightarrow {x + 17} = {3(x - 1)}$

$\rm \rightarrow {x + 17} = {3x - 3}$

$\rm \rightarrow {3x - x} = {17 + 3}$

$\rm \rightarrow {2x} = {20}$

$\rm \rightarrow x = \dfrac{20}{2}$

$\rm \rightarrow x = 10$

Therefore:-

$\rm The \: denominator = {x} = {10}$

$\rm The \: numerator= {x - 2} = {10 - 2} = 8$

Hence;

$\boxed{ \rm \purple{ \therefore The \: rational \: number \: is \: \: \frac{8}{10} }}$