Lorena Beard

Answered

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.

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.

Answer & Explanation

Elianna Wilkinson

Expert

2022-07-07Added 11 answers

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

${\frac{4}{y}=\frac{2}{3}}\phantom{\rule{thickmathspace}{0ex}}\u27fa\phantom{\rule{thickmathspace}{0ex}}2y=4\cdot 3=12\phantom{\rule{thickmathspace}{0ex}}\u27fa\phantom{\rule{thickmathspace}{0ex}}y=\frac{12}{2}=6$

So the denominator, y is 6.

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

${\frac{4}{y}=\frac{2}{3}}\phantom{\rule{thickmathspace}{0ex}}\u27fa\phantom{\rule{thickmathspace}{0ex}}2y=4\cdot 3=12\phantom{\rule{thickmathspace}{0ex}}\u27fa\phantom{\rule{thickmathspace}{0ex}}y=\frac{12}{2}=6$

So the denominator, y is 6.

racodelitusmn

Expert

2022-07-08Added 5 answers

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 $d=6$

$\frac{n+4}{d}=\frac{n}{d}+\frac{2}{3}$

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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