Question

the denominator of a fraction is 3 more than the numerator. if 5 is added to both parts,the resulting fraction is equivalent to 4/5. find the fraction

Answer 1

Let the numerator be x then the denominator will be x + 3.

Given that if 5 is added to both parts the resulting will be 4/5.

x + 5/x + 8 = 4/5

5x + 25 = 4x + 32

x = 7.

Then the denominator will be x + 3 = 7 + 3 = 10


The fraction is 7/10.

Answer 2

Concept

In mathematics, fractions are used to represent  whole percentages / parts. It represents the same part of the whole. Fractions have two parts: the numerator and the denominator. The upper number  is called the numerator and the lower number  is called the denominator. The numerator defines the number of equal parts and the denominator defines the total number of equal parts in total

Given

We have given that the denominator of a fraction is 3 more than the numerator and when 5 is added to both parts, the resulting fraction is equivalent to 4/5 .

Find

We are asked to find the fraction

Solution

Let a numerator of a fraction be x and denominator be y

Then , fraction will be  $\frac{x}{y}$ .

According to the first statement i.e denominator is 3 more than that  numerator that means $y=3+x$  ...(1)

According to the second statement if 5 is added to both parts then , fraction becomes equals to 4/5 .

Then , numerator will be $x+5$ and denominator will be $y+5$ .

Fraction will be  $\frac{x+5}{y+5} =\frac{4}{5}$

On cross multiplication, we get

$5(x+5)=4(y+5)\\5x+25=4y+20\\5x-4y=-5$

Putting value of y from equation (1) in above equation, , we get

$5x-4(x+3)=-5\\5x-4x-12=-5\\x=7$

Putting x = 7 in equation, , we get

$y=7+3\\y=10$

Hence , the fraction is  $\frac{7}{10}$ .

Therefore, the fraction is  7 / 10.

#SPJ2