Question

Find a number which when added to the numerator and denominator of the fraction 3/5 gives 4/5

Answer 1

Let the number we need to find be \( x \).

According to the problem, when \( x \) is added to both the numerator and the denominator of the fraction \( \frac{3}{5} \), the result should be \( \frac{4}{5} \).

We can express this mathematically as:

\[
\frac{3 + x}{5 + x} = \frac{4}{5}
\]

To eliminate the fraction, we can cross-multiply:

\[
5(3 + x) = 4(5 + x)
\]

Expanding both sides gives:

\[
15 + 5x = 20 + 4x
\]

Now, we'll isolate \( x \) by first moving \( 4x \) to the left side and \( 15 \) to the right side:

\[
5x - 4x = 20 - 15
\]

This simplifies to:

\[
x = 5
\]

Thus, the number we need is \( \boxed{5} \).

To verify, let's substitute \( x = 5 \) back into the fraction:

\[
\frac{3 + 5}{5 + 5} = \frac{8}{10} = \frac{4}{5}
\]

Since this is correct, the solution \( x = 5 \) is verified.