Question

The numerator of a rational number is smaller than its denominator by 3. If the numerator is decreased by 1 and the denominator is increased by 2, the number becomes 1/3. Find the rational number.​

Answer 1

Answer:

4/7

Step-by-step explanation:

1-x+3/x+2=1/3

3 (1-x+3)=1 (x+2)

3-3x+9=x+2

-3x+12=x+2

-3x-x=2-12

-4x =-10

4x =10

x =10/4

x =5/2

according to the question

2+2=4

5+3-1=7

=4/7

Hope it helps

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Answer 2

$\sf \large{ \underline{Given -} }$

The numerator of a rational number is smaller than its denominator by 3.

If the numerator is decreased by 1 and the denominator is increased by 2, the number becomes 1/3.

$\sf \large{ \underline{To \: find -} }$

$\sf \dashrightarrow Original \: fraction = \: ?$

$\sf \large{ \underline{Solution -} }$

$\sf Let \: us \: assume \: that,$

$\sf \dashrightarrow The \: numerator \: of \: the \: fraction \: be \: x$

$\sf \dashrightarrow Then, \: the \: denominator \: will \: be \: x+3$

$\sf According \: to \: question,$

$\sf \dashrightarrow Equation = \bf \red{ \dfrac{(x) + 1}{(x + 3) + 2} = \dfrac{1}{3} }$

$\sf \dashrightarrow \dfrac{x + 1}{x + 5} = \dfrac{1}{3}$

$\sf Do \: cross \: multiplication,$

$\sf \dashrightarrow 3(x + 1) = 1(x + 5)$

$\sf \dashrightarrow 3x + 3 = x + 5$

$\sf \dashrightarrow 3x + 3 - x = 5$

$\sf \dashrightarrow 2x + 3 = 5$

$\sf \dashrightarrow 2x = 5 - 3$

$\sf \dashrightarrow 2x = 2$

$\sf \dashrightarrow x = \cancel{\dfrac{2}{2} }$

$\sf \dashrightarrow x = 1$

$\bf Now,$

$\sf \dashrightarrow Numerator \: (x) = 1$

$\sf \dashrightarrow Denominator \: (x+3) = (1+3) = 4$

$\bf Therefore,$

$\sf \dashrightarrow \underline{\boxed{ \sf Original \: fraction = \dfrac{1}{4} }}$

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$\sf \large{ \underline{Verification -} }$

$\bf \dashrightarrow \dfrac{(x) + 1}{(x + 3) + 2} = \dfrac{1}{3}$

$\sf \dashrightarrow \dfrac{(1) + 1}{(1 + 3) + 2} = \dfrac{1}{3}$

$\sf \dashrightarrow \dfrac{1 + 1}{(4) + 2} = \dfrac{1}{3}$

$\sf \dashrightarrow \dfrac{2}{4+ 2} = \dfrac{1}{3}$

$\sf \dashrightarrow \cancel{\dfrac{2}{6}} = \dfrac{1}{3}$

$\sf \dashrightarrow \dfrac{1}{3} = \dfrac{1}{3}$

LHS and RHS are equal.

Hence verified !!