Question

Q5. The sum of denominator and numerator of a fraction is 3 less than twice
the denominator. If each of the numerator and denominator is denominator is
decreased by 1, the fraction becomes 1/2. Find the fraction.​

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Definition

The sum of the numerator and denominator of a fraction is 3 less than twice the denominator. If the numerator and denominator are decreased by 1, the numerator becomes half the denominator. Determine the fraction.

SOLUTION

Let the numerator and denominator of the fraction be x and y respectively. Then the fraction is

xy

The sum of the numerator and denominator of the fraction is 3 less than twice the denominator. Thus, we have

x+y=2y-3

⇒x+y-2y+3=0

⇒x-y+3=0

If the numerator and denominator are decreased by 1, the numerator becomes half the denominator. Thus, we have

x-1=12(y-1)

⇒x-1y-1=12

⇒2(x-1)=y-1

⇒2x-2=y-1

⇒2x-y-1=0

So, we have two equations

x-y+3=0

2x-y-5=0

Here x and y are unknowns. We have to solve the above equations for x and y.

By using cross-multiplication, we have

x(-1)×(-1)-(-1)×3=-y1×(-1)-2×3=11×(-1)-2×(-1)

⇒x1+3=-y-1-6=1-1+2

⇒x4=-y-7=11

⇒x4=y7=1

⇒x=4,y=7

Hence, the fraction is

47