Relationship between ratios, rates and proportions with percentages, fractions and decimals

Relationship between Ratios, Rates and Proportions, with Percentages, Fractions and Decimals

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Relationship between Ratios, Rates and Proportions, with Percentages, Fractions and Decimals

The relationship between percentages and ratios:

A percentage is a fraction with a denominator of \(100\).
The ratio that compares the number of parts to \(100\) parts can be expressed in the form of fraction, decimal and percentage.

Example

In a class, the ratio of the number of girls to the number of boys is \(3 : 2\).

Calculate the percentage of the girls in the class.

The ratio of the number of girls to the total number of students is \(3:5=\dfrac{3}{5}\).

Thus, the percentage of the girls in the class is

\(\begin{aligned}\dfrac{3}{ 5}& =\dfrac{ 3 × 20}{ 5 × 20} \\\\&=\dfrac{60}{100} \\\\&=60\%. \end{aligned}\)

The percentage of a quantity by applying the concept of proportions:

A proportion is a relationship that states that two ratios are equal.

Example

A box contains \(8\) ribbons.

Two of the ribbons are red.

What is the percentage of red ribbons in the box?

Let the percentage of red ribbons in the box be \(x\).

\(\begin{aligned} \dfrac{x}{100}&=\dfrac{\text{Number of red ribbons}}{\text{Total number of ribbons}} \\\\\dfrac{x}{100}&=\dfrac{2}{8} \\\\8\times x&=2\times100 \\\\x&=\dfrac{200}{8} \\\\&=25. \end{aligned}\)

Thus, the percentage of red ribbons in the box is \(25\%\).