Question

How can a ratio's number can be changed without changing the ratio itself

Answer 1

Answer:

The ratio is a fraction that tells us how many times longer a thing is compared to another thing. In mathematics, we express a ratio as the relationship between two numbers, namely $a \ and \ b$, so the ratio can be written as:

$r=\frac{a}{b}$

If we can change this number without changing the ration we need to multiply  both the numerator and the denominator by the same number. For instance, if we have the following ratio:

$r=\frac{2}{3}$

We can multiply both the numerator and denominator, say, by 7. Then:

$r=\frac{7\times 2}{7 \times 3}=\frac{14}{21}$

As you can see, the ratio's number has changed but without changing the ratio itself because:

$\frac{2}{3}=\frac{14}{21}$