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What a ratio is; How to compare quantities; Different ways to write ratios; Why order matters in ratios; Real-life examples of ratios

Understanding Ratios

Mathematics

Understanding Ratios

Learn to compare quantities using ratios.

Agenda

• What a ratio is

• How to compare quantities

• Different ways to write ratios

• Why order matters in ratios

• Real-life examples of ratios

What is a Ratio?

A ratio compares two amounts, showing how much of one thing there is compared to another. For example, if you have 3 red apples and 2 green apples, the ratio of red to green apples is 3 to 2. This shows a 'part-to-part' comparison.

Four shiny green apples on a wooden surface.

Comparing Quantities

Ratios help us compare different groups or items. For example, if a classroom has 12 boys and 15 girls, we can use a ratio to compare the number of boys to the number of girls. This helps us understand the relationship between these two parts of the group.

Children's heights compared: taller, shorter, tallest, shortest.

Parts of a Ratio

• A ratio compares two specific amounts.

• These amounts are called the "parts."

• Example: 5 boys to 6 girls in a class.

• Example: 3 red apples to 2 green apples.

Identifying Quantities

To write a ratio, first identify the two specific things you want to compare in a situation. For instance, if you look at a desk, you might compare the number of pencils to the number of erasers. Knowing what you are comparing is the first step to writing a ratio.

Pencils on a desk, comparing quantities for ratios.

Ratio of Cats to Dogs

A ratio compares two different quantities or parts. For example, if there are 5 cats and 6 dogs in a room, you can compare the number of cats to the number of dogs. This 'part-to-part' ratio is written as 5 to 6, or 5:6.

Feline family gathering: eight cats in a cozy indoor setting.

Writing Ratios: Using 'to'

• Use the word "to" between the two numbers.

• Example: 5 cats to 6 dogs.

• Example: 7 boys to 8 girls in a class.

• Compares one part of a group to another part.

Writing Ratios: Using a Colon

Another common way to write a ratio is by using a colon (:). You place the colon between the two numbers that represent the quantities. For example, if you have 3 red apples and 5 green apples, the ratio of red apples to green apples is 3:5.

Ten apples illustrate divisibility, grouped for even distribution.

Writing Ratios: Using a Fraction

Ratios can also be written like fractions. The first number in the ratio becomes the top number (numerator) and the second number becomes the bottom number (denominator). For example, if you have 3 red apples to 5 green apples, the ratio as a fraction is 3/5.

Apples illustrate equivalent fractions and ratios.

Understanding Ratios

What a ratio is; How to compare quantities; Different ways to write ratios; Why order matters in ratios; Real-life examples of ratios

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