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...
Advanced Topics

Solving Ratio and Proportion Problems

Steps to Solve Ratio and Proportion Problems

  1. Write the ratios as fractions.
  2. Set up the proportion.
  3. Use cross-multiplication to find the missing value.
  4. Check your answer by plugging it back in.

Tips for Solving Problems

  • Always simplify ratios first!
  • Label your quantities to avoid confusion.
  • Practice makes perfect—draw pictures or use tables for tricky questions.

Example with Formula

If \( \frac{a}{b} = \frac{c}{x} \), then \( x = \frac{b \times c}{a} \).

Key Formula

\[x = \frac{b \times c}{a}\]

Examples

  • If 4 pens cost $12, how much do 7 pens cost? Set up 4/12 = 7/x and solve for x.

  • A model car is built at a 1:24 scale. If the real car is 12 feet long, the model is 0.5 feet (6 inches).

In a Nutshell

You can solve for unknowns in proportions using cross-multiplication.

Key Terms

Cross-multiplication
A method for solving proportions by multiplying across the equals sign.
Next
Using Variables to Write and Solve Equations