Ratios: Explanations, examples

Friday Lessons with Uncle Jay

In a classroom, there are 60 girls and 40 boys.

How can we can represent the number of girls to the number of boys and vice versa?

In another case, 2 kg of rice and 3 kg of beans are used to prepare a meal, how can we represent the weight of the rice to the weight of beans in the meal?

Such kind of situations raises the need of ratios.

Ratios are frequently used in our daily life to simplify problems by expressing numbers into their correct perspective.

The origin of the ratio is not very well known.

There are many examples of ratios where the people are applying it in their daily lives but unaware of it.

What is a ratio?

In mathematics, a ratio is defined as a tool used to compare the size of two or more quantities in relation to each other.

Ratios allow us to measure and express quantities by making them easier to interpret.

A ratio is a kind of a fraction where the numerator is referred to as antecedent and the denominator is termed as the consequent.

We use a colon symbol (:) to denote a ratio.

For instance, 3: 4, 1: 3, 5:7, 1:1, etc. are examples of ratios.

Let us take a look at some of the properties of ratios.

Ratios only represent quantities of the same unit.

Ratios are dimensionless.

The first item in the sentence comes first in a ratio.

Equivalent ratios have equivalent corresponding fractions.

In the ratio such as a: b, a is the antecedent and b is the consequent

The positions of antecedent and consequent in a ratio cannot be interchanged.

Ratios can be used to represent multiple quantities.

For example, a: b: c: d

How to calculate ratio?

There several different ways of calculating a ratio.

One the most common method is comparing two quantities is using a colon.

For example, if there are 20 boys and 30 girls in a classroom.

The ratio of boys to girls can be represented as 20: 30 which simplifies to 2:3.

Another method of calculating the ratio is by expressing the quantities as a fraction.

The first quantity is usually represented as the numerator while the second quantity represents the denominator.

For example, the ratio of boys to girls can as well be represented as 2/3.

Other methods of finding the ratio between numbers include the use the word “to” between the numbers themselves and calculating a ratio in decimal form.

For example, a ratio 3:10 can be expressed as 3 to 10 and 0.3 in decimal format.

Example

A component is composed 30 percent copper, 60 percent brass and 10 percent gold.

Use this information to calculate:

Ratio of copper to brass

Copper = 30 percent

Practice questions

1. A gym has 65 members.

If 35 are men and the rest are women, what is the ratio of the female members to the total members of the gym?

2. If you draw all hearts from a deck of 52 cards, what is the ratio of the remaining cards to the whole deck?

3. A band comprises 55 seniors, 63 sophomores, 55 juniors, and 127 freshmen.

What is the ratio of freshmen to juniors?