Question

If the same number is added to the numerator and subtracted from the denominator of LaTeX: \frac{23}{12}23 12, the resulting fraction is equivalent to the reciprocal of LaTeX: \frac{2}{3}2 3 . What is the number?

Answer 1

Hence, -45 is the number which when added to the given fraction will give 2/3

Further explanation:

Given fraction is:

$\frac{23}{12}$

Let x be the number which has to be added to numerator and denominator

Then

$\frac{23+x}{12+x}=\frac{2}{3}$

Cross-multiplying

$\frac{23+x}{12+x}=\frac{2}{3} \\3(23+x)=2(12+x)\\69+3x=24+2x\\3x-2x=24-69\\x=-45$

Hence, -45 is the number which when added to the given fraction will give 2/3

Keywords: Linear equation in one variable, Cross-multiplication

Learn more about linear equation at:

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