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Common Core Math7th GradeThe Number System

7.NS.3: Word Problems with Rational Numbers

Also written as 7.NS.A.3 and CCSS.MATH.CONTENT.7.NS.A.3 · Cluster: Apply and extend previous understandings of operations with fractions.

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

The Official Wording

Solve real-world and mathematical problems involving the four operations with rational numbers.

Common Core State Standards, Grade 7, The Number System · Read it at the source · Checked October 14, 2026

What 7.NS.3 Means in Plain English

Seventh graders combine everything from 7.NS.1 and 7.NS.2 in one problem, with negative fractions and decimals. A lunch account holding $40 is charged $12.75 a week for 4 weeks: 40 + 4 × (-12.75) = -11, so it is $11 in the red.

Every answer gets a sense check: a submarine at -80 feet that dives 25 more cannot end at -55. These problems feed the multi-step work of 7.EE.3, and in 8th grade the same arithmetic sits inside the linear equations of 8.EE.7.

7.NS.3 I Can Statements

  • I can choose the operations a signed-number word problem needs.
  • I can compute with negative fractions and decimals in one problem.
  • I can check that my answer makes sense in the story.

7.NS.3 Worked Example

Five days of profits and losses at a school store: the average needs addition and division with signs, and the forecast needs multiplication.

Problem

The school store’s profit for five days was -$2.40, $1.15, -$0.85, $3.10 and -$1.50. What was the average daily change? At that average, what would 20 school days add up to?

The school store’s average day
  1. An average is the total divided by the number of days. Group the gains and the losses first, which the commutative and associative properties allow.(1.15 + 3.10) + (-2.40 - 0.85 - 1.50)
  2. Add each group.4.25 + (-4.75)
  3. The signs differ, so subtract the sizes and keep the sign of the larger one.4.25 + (-4.75) = -0.50
  4. Divide the total by the 5 days. A negative divided by a positive is negative.-0.50 ÷ 5 = -0.10
  5. Twenty days at that average is a multiplication, positive times negative.20 × (-0.10) = -2.00
AnswerAn average change of -$0.10 a day, a 10-cent loss, which comes to -$2.00 over 20 days

Check it: Estimate with whole dollars: gains about 1 + 3 = 4 and losses about 2 + 1 + 2 = 5, so a small net loss is right. Multiply back: 5 × (-0.10) = -0.50, the exact total.

Common Mistakes with 7.NS.3

Losing a sign when copying the data

2.40 + 1.15 - 0.85 + 3.10 - 1.50 = 4.30, so the store made money

Try this: Have students circle every negative in the problem and in their first line, then compare: three circles in each place.

Accepting an answer that cannot be right

It is 3 °F and falls 2.5 degrees an hour for 4 hours: 3 + 10 = 13 °F

Try this: Ask whether the answer should be above or below the start: falling temperatures end lower, so 3 + 4 × (-2.5) = -7 °F.

Rounding too early

A pool loses 5/6 inch a day: -5/6 ≈ -0.8, so 12 days is 12 × (-0.8) = -9.6 inches

Try this: Keep the fraction until the last step: 12 × (-5/6) = -60/6 = -10 inches. Round only the final answer, if at all.

Where 7.NS.3 Fits

Comes Before6.NS.3Add, subtract, multiply and divide multi-digit decimals fluently.6.NS.5Use signed numbers for opposite directions, like a gain and a loss.
Alongside7.NS.1Add and subtract signed numbers, the first half of the toolkit.7.NS.2Multiply and divide signed numbers, the second half.7.EE.3Solve multi-step problems in any number form, checked by estimating.
Comes Next8.EE.7Solve linear equations with rational coefficients, like 0.4x - 3 = -1.8.8.EE.4Compute with numbers in scientific notation and decimal form in the same problem.

Practice 7.NS.3

Word Problem GeneratorFree ToolMoney, temperature, elevation and sports stories where the numbers carry signs and every problem needs more than one operation.IntegersMulti-stepGrade 7
Make Word Problems
Number Line GeneratorFree ToolA line from -50 to 50 in fives for elevation and temperature stories: students sketch the start, each move and the end before computing.-50 to 50Step 5Labeled
Make a Number Line

Quick Check

  1. A diver at -12 feet descends 2.5 feet a minute for 6 minutes. What is her depth now?
  2. Three friends split a $22.50 restaurant debt evenly. Write each share as a signed number.
  3. At 6 p.m. it was 5 °F, and the temperature fell 3/4 of a degree each hour until midnight. What was it at midnight?

7.NS.3: Other Names

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