According to Wikipedia, a proportion is a mathematical statement expressing the equality of two ratios, and a ratio shows how many times one number contains another.
$$a : b = c : d$$
$a$ and $d$ are called the extremes, and $b$ and $c$ are called the means. Proportions can be written as fractions:
$$ \frac{a}{b} = \frac{c}{d} $$
Properties of proportions
$$\frac{a+c}{b+d} = \frac{a}{b} = \frac{c}{d}$$
Why is this true? Consider that if $ \frac{a}{b} = \frac{c}{d}$, then there is some nunber $x$ that we can multiply $a$ by to get $c$ (i.e: $a\cdot x = c$), which is the same number that we can multiply $b$ by to get $d$ (i.e: $b\cdot x = d$):
$$ \frac{a}{b} = \frac{a}{b} \cdot \frac{x}{x} = \frac{a \cdot x}{b \cdot x} = \frac{c}{d} $$
We can multiply a ratio by $1$ and not change it. Consider multiplying the ratio by a fancy version of $1$ that equals $\frac{(1+x)}{(1+x)}$
$$\frac{a}{b} = \frac{a}{b} \cdot \frac{(1+x)}{(1+x)} = \frac{a \cdot (1+x)}{b \cdot (1+x)} = \frac{a + a \cdot x}{b + b \cdot x} = \frac{a + c}{b + d}$$