Lorena Beard

2022-07-06

When the numerator of a fraction is increased by 4, the fraction increases by 2/3...
When the numerator of a fraction is increased by 4, the fraction increases by 2/3. What is the denominator of the fraction?
I tried,
Let the numerator of the fraction be x and the denominator be y.
Accordingly,
$\frac{x+4}{y}=\frac{x}{y}+\frac{2}{3}$
I am not able to find the second equation.

Elianna Wilkinson

Expert

Again, you've got a fine start:
You wrote:
$\begin{array}{}\text{(1)}& \frac{x+4}{y}=\frac{x}{y}+\frac{2}{3}\end{array}$
But note that
$\begin{array}{}\text{(2)}& \frac{x+4}{y}=\frac{x}{y}+\frac{4}{y}\end{array}$
From (1),(2), it must follow that
$\frac{4}{y}=\frac{2}{3}\phantom{\rule{thickmathspace}{0ex}}⟺\phantom{\rule{thickmathspace}{0ex}}2y=4\cdot 3=12\phantom{\rule{thickmathspace}{0ex}}⟺\phantom{\rule{thickmathspace}{0ex}}y=\frac{12}{2}=6$
So the denominator, y is 6.

racodelitusmn

Expert

Given,
$\frac{n+4}{d}=\frac{n}{d}+\frac{2}{3}$
So,
$\frac{n}{d}+\frac{4}{d}=\frac{n}{d}+\frac{2}{3}$
Or,
$\frac{4}{d}=\frac{2}{3}$
That, gives us $d=6$

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