Ratio Tables

Concept

A ratio table is a structured list of equivalent (equal value) ratios that helps us understand the relationship between the ratios and the numbers. Ratios are proportional if they represent the same relationship.

Rules

The order of the values in a ratio relates directly to the order of the quantities described.
To find an equivalent ratio, multiply or divide both quantities by the same number.
To determine whether two ratios are equivalent, write them as simplified fractions. If the fractions are equal, the ratios are equivalent.

Example

Complete the table so that a and b are always in the same ratio.

Solution

1. Find the missing quantities by finding equivalent fractions.
$\fn_phv \frac{201}{69}=\frac{67}{x}$
$\fn_phv \frac{201 \div 3}{69\div 3}=\frac{67}{23}$
2. Find the remaining equivalent fractions using the first or the simplest ratio.
$\fn_phv \frac{67}{23}=\frac{{\color{Red} x}}{46}$ $\fn_phv \frac{67\times 2}{23\times 2}=\frac{{\color{Red} 134}}{46}$
$\fn_phv \frac{67}{23}=\frac{{\color{Red} x}}{92}$ $\fn_phv \frac{67\times 4}{23\times 4}=\frac{{\color{Red} 268}}{92}$