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Common Core Math6th GradeRatios & Proportions

6.RP.3: Solve Ratio, Rate and Percent Problems

Also written as 6.RP.A.3 and CCSS.MATH.CONTENT.6.RP.A.3 · Cluster: Understand ratio concepts and use ratio reasoning to solve problems.

Make 6.RP.3 Word ProblemsAll 29 6th Grade Math Standards

The Official Wording

Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

Common Core State Standards, Grade 6, Ratios & Proportional Relationships · Read it at the source · Checked October 14, 2026

What 6.RP.3 Means in Plain English

This is the workhorse standard of 6th grade. Students fill in ratio tables and plot the pairs, find unit prices and speeds, take a percent of a number (30% of 50 is 15), find the whole from a part and a percent, and convert units like feet to inches.

The tools matter as much as the answers: tables of equivalent ratios, tape diagrams and double number lines, not cross-multiplying. Proportions as equations wait for 7th grade, where 7.RP.3 solves multistep percent problems like tax, discount and percent change, and 7.RP.2 names the constant of proportionality.

6.RP.3 I Can Statements

  • I can complete a ratio table and plot its pairs.
  • I can find a percent of a number and the whole from a part.
  • I can convert units with a ratio, like 3 feet to 36 inches.

6.RP.3 Worked Example

A percent problem run backwards: the part and the percent are known, the whole is not, and a double number line finds it without a formula.

Problem

Maya has read 60 pages, which is 40% of her book. How many pages does the book have?

Finding the whole from a part and a percent
  1. Draw a double number line: percents on top from 0% to 100%, pages underneath. Mark 40% directly above 60 pages.0% ... 40% ... 100% over 0 ... 60 ... ?
  2. Find what 10% is worth. 40% is four 10%s, so divide 60 by 4.60 ÷ 4 = 15 pages per 10%
  3. The whole book is 100%, which is ten 10%s.10 × 15 = 150 pages
  4. Write the same reasoning as a ratio table, so students see both tools agree.40% : 60 pages, 10% : 15 pages, 100% : 150 pages
AnswerThe book has 150 pages.

Check it: Take 40% of 150: 40/100 × 150 = 60 pages, the part we started with.

Common Mistakes with 6.RP.3

Taking the percent of the part

40% of 60 = 24, so “the book has 24 pages”

Try this: Ask whether the answer should be bigger or smaller than 60. The whole book is more than 60 pages, so 24 cannot be right.

Scaling one column of a ratio table

3 lawns in 7 hours, so 6 lawns in 7 hours

Try this: Multiply both quantities by the same number, every row. Doubling the lawns doubles the hours too: 6 lawns in 14 hours.

Converting units in the wrong direction

5 feet = 5 ÷ 12 inches

Try this: Write the conversion as a ratio first, 12 inches for every 1 foot, so 5 feet is 5 × 12 = 60 inches.

Where 6.RP.3 Fits

Comes Before6.RP.1Write ratios and describe them with “for every” language.6.RP.2Find the unit rate behind a ratio.5.MD.1Convert measurement units within one system, like 5 feet to 60 inches.
Alongside6.EE.9Write an equation for two quantities that change together, like d = 65t.6.NS.3Compute with decimals when prices are involved.
Comes Next7.RP.2Recognize proportional relationships and find the constant of proportionality.7.RP.3Solve multistep ratio and percent problems: tax, tips, discounts, percent change.

Practice 6.RP.3

Word Problem GeneratorFree ToolUnit-price, speed and percent stories, so students pick the tool (table, tape diagram or double number line) and show it.Ratios and ratesPercentGrade 6
Make Word Problems
Graph Paper GeneratorFree ToolGrid paper for plotting ratio-table pairs on the coordinate plane. Equivalent ratios land on a straight line from the origin.1 cm squaresOne pagePrint
Make Graph Paper

Quick Check

  1. A machine fills 6 bottles in 4 minutes. At that rate, how many bottles does it fill in 30 minutes?
  2. What is 30% of 80?
  3. 18 is 25% of what number?

6.RP.3: Other Names

6.RP.36.RP.A.3CCSS.MATH.CONTENT.6.RP.A.3

Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. Official wording from the Common Core State Standards PDFs at corestandards.org, last checked October 14, 2026. The explanation, I can statements, example, mistakes and practice on this page are EMStudio’s own, written beside the official wording. They are not part of the standard.