Prerequisites
Arithmetic | 11 of 17
Prerequisites: Fractions, Decimals. Enables: Algebra.
Ratio
A ratio compares two quantities by division.
A ratio can be written as:
$$
a:b
$$
or
$$
\frac{a}{b}
$$
where
$$
b \ne 0
$$
Example:
$$
3:5 = \frac{3}{5}
$$
Rate
A rate compares quantities with different units.
Example:
$$
\frac{180\text{ miles}}{3\text{ hours}} = 60\text{ miles/hour}
$$
Unit rate:
$$
60\text{ mph}
$$
Proportion
A proportion states that two ratios are equal.
$$
\frac{a}{b}=\frac{c}{d}
$$
where
$$
b \ne 0,\quad d \ne 0
$$
Cross products are equal:
$$
ad = bc
$$
Solving a proportion
Example:
$$
\frac{x}{12}=\frac{5}{8}
$$
Cross multiply:
$$
8x = 12\cdot5
$$
$$
8x = 60
$$
$$
x = 7.5
$$
Scale factor
A scale factor multiplies every corresponding length.
If a figure is scaled by factor $k$, then:
$$
\text{new length} = k(\text{old length})
$$
If $k>1$, the figure is enlarged.
If $0<k<1$, the figure is reduced.