6th Grade Math

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

Understanding RatiosIntroduction to ProportionsAlgebraic Thinking: Expressions and Variables
Solving Ratio and Proportion ProblemsUsing Variables to Write and Solve EquationsRecognizing Patterns and Relationships
Using Ratios in Cooking and RecipesProportions in Maps and ModelsAlgebra in Everyday Decisions
Breaking Down Word ProblemsChecking Your Answers
Understanding RatiosIntroduction to Prop...Algebraic Thinking: ...Solving Ratio and Pr...Using Variables to W...Recognizing Patterns...Using Ratios in Cook...Proportions in Maps ...Algebra in Everyday ...Breaking Down Word P...Checking Your Answer...
Basic Concepts

Introduction to Proportions

What Is a Proportion?

A proportion is when two ratios are equal. It helps us find missing values and solve problems where things change at the same rate.

Writing Proportions

If \(\frac{a}{b} = \frac{c}{d}\), then these ratios form a proportion.

Solving Proportions

To find a missing number, use cross-multiplication: \[ \frac{a}{b} = \frac{c}{d} \implies a \times d = b \times c \]

Everyday Uses

Proportions help you scale recipes, convert measurements, or determine distances on a map.

Examples

  • If 3 pencils cost $6, how much do 5 pencils cost? Set up the proportion: 3/6 = 5/x.

  • On a map, 1 inch represents 8 miles. If two cities are 3.5 inches apart, they are 28 miles apart.

In a Nutshell

Proportions show when two ratios are equal and help solve for unknowns.

Next
Algebraic Thinking: Expressions and Variables