Understanding Ratios for 12-Year-Old Students: A Step-by-Step Guide

What is a Ratio?

A ratio is a way to compare two quantities or amounts. It tells us how much of one thing there is compared to another.

How Does a Ratio Work?

A ratio shows the relationship between two numbers. For example, if you have 4 apples and 2 oranges, the ratio of apples to oranges is 4 to 2. This ratio can be written in different ways:

• 4:2
• 4 to 2
• ⁴⁄₂

All of these mean the same thing: for every 4 apples, there are 2 oranges.

Simplifying Ratios

Just like fractions, ratios can be simplified. If we take the ratio 4:2, we can divide both numbers by their greatest common divisor, which is 2:

• 4 ÷ 2 = 2
• 2 ÷ 2 = 1

So, the simplified ratio is 2:1. This means for every 2 apples, there is 1 orange.

Using Ratios in Real Life

Ratios help us understand proportions in everyday situations. For example, if a recipe calls for 3 cups of flour and 2 cups of sugar, the ratio of flour to sugar is 3:2.

Practice Example

If there are 10 boys and 15 girls in a class, what is the ratio of boys to girls?

Answer: 10:15. We can simplify this by dividing both numbers by 5, so the ratio becomes 2:3.

Summary

• A ratio compares two quantities.
• It can be written as a:b, a to b, or a/b.
• Ratios can be simplified like fractions.
• Ratios are useful to understand parts of a whole or to compare amounts.