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

2 Answers

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

Apr 11, 2018

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.