6th Grade Math

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

Understanding Ratios

What Are Ratios?

Ratios help us compare two or more quantities. Imagine you have 4 apples and 6 oranges. The ratio of apples to oranges is 4 to 6, or written as \(4:6\) or \(\frac{4}{6}\).

How Do We Use Ratios?

Ratios can show relationships in many ways:

  • \(2:3\)
  • \(\frac{2}{3}\)
  • "2 to 3"

You can simplify ratios just like fractions. For example, \(4:6\) simplifies to \(2:3\).

Why Are Ratios Important?

Ratios are everywhere! They help us with recipes, maps, mixing paint, or comparing scores.

How to Simplify Ratios

Find the greatest common factor (GCF) of both numbers and divide each by that number.

Real-World Uses

If a recipe needs 2 cups of flour for every 3 cups of sugar, the ratio is \(2:3\).

Examples

  • A classroom has 10 boys and 15 girls. The ratio of boys to girls is 10:15 or 2:3.

  • If a map shows 1 inch represents 5 miles, the ratio is 1:5.

In a Nutshell

Ratios compare two or more quantities and can be simplified.

Key Terms

Ratio
A comparison of two quantities by division.
Simplify
To reduce a ratio to its smallest whole numbers.
6th Grade Math Content & Lessons - Comprehensive Study Guide | Practice Hub