Question

Write a fraction for which the sum of the numerator and denominator is 20, and the value of the

fraction is equal to 2/3

Answer 1

`(8)/(12)`

Explanation:

Let the unknown fraction be:

• 
  `(a)/(b)`

If the sum of the numerator and denominator is 20 then:

`\implies a+b=20`

Rewrite the equation to isolate b:

`\implies b=20-a`

If the fraction is equal to 2/3 then:

`\implies (a)/(b)=(2)/(3)`

Cross multiply:

`\implies 3a=2b`

Substitute the expression for b into the cross-multiplied equation and solve for a:

`\implies 3a=2(20-a)`

`\implies 3a=40-2a`

`\implies 5a=40`

`\implies a=8`

Substitute the found value of a into the equation for b and solve for b:

`\implies b=20-8`

`\implies b=12`

Therefore, the fraction for which the sum of the numerator and denominator is 20, and the value of the fraction is equal to 2/3 is:

• 
  `(8)/(12)`