Question

What number should be deducted by the numerator and the denominator of the fraction `7/13` to obtain the fraction `1/3`?

Answer 1

8/39

Explanation:

Suppose the value that will be deducted from `7/13` is `x` to form `1/3`

So,

`7/13 -x=1/3`

Solve the equation

`x=7/13 -1/3`

`x=((7xx3)-(13xx1))/39`

`x= (21 -13)/39`

`x=8/39`

Answer 2

Just to show that you get the same answer if you approach it a very slightly different way

Deduct `8/39`

Explanation:

Let the unknown value be represented by `x`

Complying with the wording of the question gives:

`color(green)(7/13color(red)(-x)=1/3)" ".......Equation(1)`

But what happens if we change the sign from subtract to add ?

`color(green)(7/13color(red)(+x)=1/3)" ".....Equation(2)`

Subtract `7/13` from both sides

`color(green)(color(red)(+x)= 1/3-7/13)`

Multiply by 1 and you do not change the value. However, 1 comes in many forms.

`color(green)(x=color(white)(.) [1/3color(red)(xx1)]color(white)(".")-color(white)(".")[7/13color(red)(xx1)]`

`color(green)(x= [1/3color(red)(xx13/13)]-[7/13color(red)(xx3/3)]`

`color(green)(x=color(white)("ddd")13/39color(white)("ddd")-color(white)("ddd")21/39)`

`color(green)(x=-8/39`
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Substitute into `Equation(2)`

`color(green)(7/13color(red)(+(x))=1/3)`

`color(green)(7/13color(red)(+(-8/39))=1/3)`

Two signs that are not the same give a minus. So `+(-8/39)` becomes just `-8/39`

`color(green)(7/13color(red)(-8/39)=1/3) larr" Format as required by the question"`

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So it works out correctly whichever way you chose as long as you 'fully' follow the rules of mathematics.