Question

sum of numerator and denominator is 8.write three such fractions. how many such fractions are possible?​

Answer 1

Answer:

Step-by-step explanation:

Sum of numerator and denominator of a feaction is 8. If 3 is added to both numerator and denominator the fraction becomes 3/4.

To Find:

Fraction

Solution:

Let the numerator be x and denominator be y

then,

➤ According to 1st condition :-

Numerator + Denominator = 8

➭ x + y = 8

➭ x = 8 - y. --(1)

➤ According to 2nd condition :-

Num + 3 / Den + 3 = 3/4

\implies \:  \frac{x + 3}{y + 3}  =  \frac{3}{4}  \\  \\  \\  \implies \: 4(x + 3) = 3(y + 3) \\  \\  \\  \implies \: 4x + 12 = 3y + 9 \\  \\  \\  \implies \: 4x - 3y = 9 - 12 \\  \\  \\  \implies \: 4x - 3y =  - 3

➭ 4x - 3y = -3. --(2)

\rule{200}2

Put the value of (1) in (2) , we get,

➭ 4x - 3y = -3

➭ 4(8 - y) - 3y = -3

➭ 32 - 4y - 3y = -3

➭ 32 - 7y = -3

➭ -7y = -3 - 32

➭ -7y = -35

➭ y = -35/-7

➭ y = 5

Put y = 5 in (1) , we get,

➭ x = 8 - y

➭ x = 8 - 5

➭ x = 3

Hence,

Numerator = x = 3

Denominator = y = 5

Therefore,

Fraction is x/y = 3/5

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