Skip to main content
Common Core Math7th GradeRatios & Proportions

7.RP.3: Multi-Step Percent Problems

Also written as 7.RP.A.3 and CCSS.MATH.CONTENT.7.RP.A.3 · Cluster: Analyze proportional relationships and use them to solve real-world and mathematical problems.

Make 7.RP.3 Word ProblemsAll 24 7th Grade Math Standards

The Official Wording

Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

Common Core State Standards, Grade 7, Ratios & Proportional Relationships · Read it at the source · Checked October 14, 2026

What 7.RP.3 Means in Plain English

Seventh graders use proportions to work percent problems in two or more steps: a $40 jacket marked down 25% and then taxed at 8% costs 40 × 0.75 × 1.08 = $32.40. The same thinking covers tips, commissions, simple interest and percent increase or decrease.

Percent error joins the list: a guess of 48 for a true 50 is off by 2/50 = 4%. Sixth grade found a percent of a quantity (6.RP.3). Here the whole relationship is proportional, which 8th grade turns into linear equations (8.EE.7) and functions (8.F.4).

7.RP.3 I Can Statements

  • I can find a price after a discount and then sales tax.
  • I can calculate simple interest, a tip or a commission.
  • I can find a percent increase, decrease or percent error.

7.RP.3 Worked Example

A markdown followed by sales tax: two percents, two different wholes, and a shortcut that does both in one line.

Problem

Sneakers priced at $60 are on sale for 30% off. Sales tax is 5%. What is the final price?

A $60 pair of sneakers, 30% off, plus 5% sales tax
  1. A 30% discount leaves 70% of the price. Set up the proportion: 70 per 100 is x per 60.70/100 = x/60, so x = 0.70 × 60 = 42
  2. Tax is charged on the sale price, not the original. Paying 5% tax means paying 105% of $42.1.05 × 42 = 44.10
  3. Both steps are multiplications by a factor, so they chain into one expression.60 × 0.70 × 1.05 = 44.10
  4. Round to cents and label it.Final price: $44.10
Answer$44.10

Check it: Estimate: 30% of $60 is $18, leaving about $42. 5% of $42 is about $2, so a final price a little over $44 makes sense.

Common Mistakes with 7.RP.3

Taxing the original price

60 × 0.70 = 42, then 60 × 0.05 = 3, so $45

Try this: Ask what the store actually charges tax on: the amount paid, $42. Each percent in a problem needs its own whole.

Adding and subtracting the percents

30% off then 5% tax is 25% off, so 60 × 0.75 = $45

Try this: Compute the two steps separately once, then compare: 60 × 0.70 × 1.05 = 44.10, not 45. Percents of different wholes do not combine.

Dividing a percent change by the new amount

The price rose from $40 to $50: 10 ÷ 50 = 20% increase

Try this: Divide the change by the original amount, the “from” number: 10 ÷ 40 = 25%. The starting value is always the whole.

Where 7.RP.3 Fits

Comes Before6.RP.3Find a percent of a quantity, like 30% of 60, as a rate per 100.7.RP.2Recognize that a percent problem is a proportional relationship.
Alongside7.EE.2See that a 5% increase is the same as multiplying by 1.05.7.EE.3Solve multi-step problems with decimals and fractions, checked by estimating.
Comes Next8.EE.7Solve linear equations, including ones built from percent situations.
HSF-LE.1See repeated percent change, like compound interest, as exponential growth.

Practice 7.RP.3

Word Problem GeneratorFree ToolTax, tip, discount and interest stories with two or more steps, so the second percent has to find its own whole.PercentsMulti-stepGrade 7
Make Word Problems
Math Worksheet GeneratorFree ToolPercent-of drills and percent-change pairs with an answer key, for the arithmetic underneath the stories.Percent of a numberPercent changeAnswer key
Make a Worksheet

Quick Check

  1. A $48 meal plus an 18% tip. What is the total?
  2. What is the simple interest on $800 at 4% per year for 3 years?
  3. A class predicted 120 people would come to a concert and 150 came. What is the percent error?

7.RP.3: Other Names

7.RP.37.RP.A.3CCSS.MATH.CONTENT.7.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.