A fraction is given in which numerator is less than denominator by three. If we add number seven in the numerator and subtract one from the denominator, $\frac{3}{2}$ is the new fraction which we get. Find the original fraction? [4 MARKS]

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Solution

Visualizing the situation : 1 Mark
Steps : 2 Marks
Result : 1 Mark

Let the numerator of a rational number $= x$

Then the denominator of a rational number $= x + 3$

When numerator is increased by 7, then new numerator $= x + 7$

When denominator is decreased by 1, then new denominator $= x + 3 - 1$

The new number formed $= \frac{3}{2}$

According to the question,

$\frac{x + 7}{x + 3 - 1} = \frac{3}{2}$

$\Rightarrow \frac{x + 7}{x + 2} = \frac{3}{2}$

$\Rightarrow 2 (x + 7) = 3 (x + 2)$

$\Rightarrow 2 x + 14 = 3 x + 6$

$\Rightarrow 3 x - 2 x = 14 - 6$

$\Rightarrow x = 8$

Numerator = 8, then denominator = 8+3 = 11

Original fraction $= \frac{8}{11}$

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A fraction is given in which numerator is less than denominator by three. If we add number seven in the numerator and subtract one from the denominator, 32 is the new fraction which we get. Find the original fraction? [4 MARKS]

A fraction is given in which numerator is less than denominator by three. If we add number seven in the numerator and subtract one from the denominator, $\frac{3}{2}$ is the new fraction which we get. Find the original fraction? [4 MARKS]