Question

The denominater of a fraction is greater than its numerator by 12.1f the mumerator
is decreased by 2 and the denominator is increased by 7. the new fraction is equivalent with 1/2. find the fraction​

Answer 1

Step-by-step explanation:

let, x be numerator

The denominater of a fraction is greater than its numerator by 12 andthe denominator is increased by 7

denominator=x+12+7=x+19

numerator id decreased by 2

numerator=x-2

the new fraction is equivalent with 1/2

x-2/x+19=1/2

2x-4=x+19

2x-x=19+4

x=23

numerator=x-2=23-2=21

denominator=x+19=21+19=40

fraction=21/40

Answer 2

Given:-

• Denominator of a fraction is greater than its numerator by 12.
• If the numerator is decreased by 2 and the denominator is is increased by 7, the new fraction becomes 1/2.

To Find:-

• The fraction

Assumption:-

• Let us assume the numerator to be x
• Hence, denominator = x + 12

Solution:-

We are told that when the numerator is decreased by 2 and the denominator is increased by 7 the fraction becomes 1/2

Hence,

ATQ,

$\sf{\dfrac{x - 2}{x + 12 + 7} = \dfrac{1}{2}}$

= $\sf{\dfrac{x - 2}{x + 19} = \dfrac{1}{2}}$

By Cross - multiplying,

$\sf{\implies 2(x - 2) = x + 19}$

$\sf{\implies 2x - 4 = x + 19}$

$\sf{\implies 2x - x = 19 + 4}$

$\sf{\implies x = 23}$

Now,

Substituting the respective values:-

Numerator = x = 23

Denominator = x + 12 = 23 + 12 = 35

Therefore the fraction is as follows:-

$\sf{\dfrac{x}{x+12} = \dfrac{23}{35}}$

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Verification!!

Lets see whether, when the denominator is increased by 7 and the numerator is decreased by 2, we get the fraction to be equivalent to 1/2 or not.

Original fraction 23/35

Now,

decreasing the numerator by 2

= 23 - 2 = 21

Increasing the denominator by 7

= 35 + 7 = 42

The fraction:-

$\sf{\dfrac{21}{42}}$

= $\sf{\dfrac{1}{2}}$

Hence, Verified!!!

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