Math CentralQuandaries & Queries


Question from Derrick, a student:

If the numerator and denominator of a fraction are both decreased by 1 the fraction becomes 2/3. If the numerator and denominator are both increased by 1 the fraction will be 3/4. Find the original fraction. How to do?

Hi Derrick,

Suppose the fraction is $\large \frac{a}{b}.$ The first sentence of the problem says that

\[\frac{a - 1}{b - 1} = \frac23.\]

Simplifying his expression gives a linear equation ia $a$ and $b.$ The second sentence gives another linear equation is $a$ and $b.$ Solve for $a$ and $b.$


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