Chapter 5.CT, Problem 1CT

Reduce to its simplest form:

a) The ratio $12:20$

b) The rate $\frac{200 \mathrm{m}\mathrm{i}\mathrm{l}\mathrm{e}\mathrm{s}}{8 \mathrm{g}\mathrm{a}\mathrm{l}\mathrm{l}\mathrm{o}\mathrm{n}\mathrm{s}}$

To determine

a)

To simplify:

The ratio $12:20$.

Answer to Problem 1CT

Solution:

$3:5$

Explanation of Solution

Ratio:

A ratio is the quotient $\frac{a}{b}$ (where $b\ne 0$) that provides comparison between the numbers a and b.

The ratio sometimes written as a:b.

The numbers a and b are often called term of the ratio.

Calculation:

Given ratio, $12:20$

$\frac{12}{20}=\frac{3}{5}$

$\frac{12}{20}=3:5$

Final statement:

The simplest form of 12:20 is 3:5.

To determine

b)

To simplify:

The rate $\frac{200 miles}{8 gallons}$.

Answer to Problem 1CT

Solution:

25 miles per gallon

Explanation of Solution

Rate:

A rate is a quotient that relates two quantities that are incommensurable.

Given, $\frac{200 miles}{8 gallons}$

$\frac{200}{8}=25$

Therefore, 25 miles per gallon.

Final statement:

The rate of $\frac{200 miles}{8 gallons}$ is 25 miles per gallon.