Student Question

# In a fraction the numerator is 1 less than the denominator. If 1 is added to the numerator and 5 to the denominator, the fractions becomes 1/2 find the original number?

Suppose that the denominator of the fraction is x; then, the original fraction is:

(x - 1)/x

When we add 1 and 5 in the numerator and denominator respectively, we have the following equation:

[(x - 1) + 1]/(x + 5) = 1/2

Solving for the variable x:

x/(x + 5) = 1/2

2x = x+5

x = 5

Then, the initial fraction is:

(x - 1)/x

(5 – 1)/5 = 4/5

Let's check:

[(x - 1) + 1]/(x +5) = 1/2

x/(x + 5) = 1/2

5/10 = 1/2

1/2 = 1/2

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Let the numerator be `x` , then the denominator becomes `x+1.`

`therefore ` the fraction = `x/(x+1)`

According to the question, 1 is added to the numerator and 5 is added to denominator,i.e. `x+1 ` and `x+1+5,` which equals to `1/2`

`(x+1)/(x+1+5) = 1/2`

`(x+1)/(x+6) = 1/2`

By cross-multiplication you get

`2(x+1) = 1(x+6)`

`2x +2 = x+6`

Combine x terms

`2x - x = 6 - 2`

`x = 4`

`x+1 = 4+1 = 5`

`therefore ` the required fraction is `4/5`