[Arithmetic 6] Ratio of two numbers

I. RATIO OF TWO NUMBERS

_ The quotient in the division of number $a$ by number $b$ ($b$ $\ne$ 0) is called the ratio of $a$ to $b$.
_ The  ratio of $a$ to $b$ is denoted by $a$ : $b$ or $\dfrac{a}{b}$.
Example: 1.7 : 3.12; $\dfrac{1}{5}:\dfrac{3}{4}$; $- 3\dfrac{1}{4}:5$; ... are ratios.
* Note: When we say ratio $\dfrac{a}{b}$, then $a$ and $b$ can be integers, fractions, mixed numbers, …, on the other hand, for fraction $\dfrac{a}{b}$, both $a$ and $b$ must be integers.

II. PERCENTAGE
Rule: To find the percentage of $a$ to $b$, we compute $\dfrac{{a.100}}{b}\%$.

Example: Find the percentage of:

a) $5$ và $8$

The percentage of $5$ to $8$ is:

$\dfrac{5}{8} = \dfrac{{5 \times 100}}{8}\%  = 62.5\%$

b) 25kg và $\dfrac{3}{{10}}$quintal

$\dfrac{3}{{10}}$quintal = $\dfrac{3}{{10}}$ $\times$ 100kg = 30kg

The percentage of 25kg to $\dfrac{3}{{10}}$quintal is:

$\dfrac{{25}}{{30}} = \dfrac{5}{6} = \dfrac{{5 \times 100}}{6}\%  = 83.3\%$ 

III. SCALE

Scale $T$ of a drawing (or a map) is the ratio of distance $a$ between two points on the drawing (or the map) to distance $b$ between two points in corresponding reality: $T = \dfrac{a}{b}$ (a, b have the same unit of measurement).

Example: If the distance $a$ on a map is 1cm, the actual distance $b$ is 1km, the map scale $T$ is 1 : 100000.