6th Grade Math

Ratios, proportions, and algebraic thinking for sixth grade students.

Basic Concepts

Understanding Ratios

What are Ratios?

Ratios are a way to compare two quantities. They show how much of one thing there is compared to another. You can think of ratios as a recipe—if you use 2 cups of flour for every 3 cups of sugar, the ratio of flour to sugar is 2 to 3.

How Do You Write Ratios?

There are three common ways to write ratios:

  • Using a colon: 2:3
  • As a fraction: \( \frac{2}{3} \)
  • With the word “to”: 2 to 3

Visualizing Ratios

Imagine you have 4 red marbles and 6 blue marbles. The ratio of red to blue marbles is 4:6, or, in simplest form, 2:3.

Why Ratios Matter

Ratios are everywhere! They help us understand recipes, map scales, and even the odds in games.

Tips for Simplifying

Always try to write ratios in their simplest form by dividing both numbers by their greatest common factor.

Examples

  • If a fruit salad has 3 apples and 6 oranges, the ratio of apples to oranges is 3:6 or 1:2.

  • A class has 8 boys and 12 girls. The ratio of boys to girls is 8:12, which simplifies to 2:3.

In a Nutshell

Ratios show how two quantities compare and can be written in several ways.

Key Terms

Ratio
A comparison of two quantities by division.
Simplest Form
The form of a ratio when both numbers are divided by their greatest common divisor.