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Common Core Math7th GradeThe Number System

7.NS.1: Add and Subtract Rational Numbers

Also written as 7.NS.A.1 and CCSS.MATH.CONTENT.7.NS.A.1 · Cluster: Apply and extend previous understandings of operations with fractions.

Make a 7.NS.1 Number LineAll 24 7th Grade Math Standards

The Official Wording

Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

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

What 7.NS.1 Means in Plain English

Seventh graders add and subtract positive and negative numbers on a number line: -3 + 8 starts at -3 and moves 8 to the right, landing on 5. Opposites cancel, so a $40 deposit and a $40 withdrawal combine to 0.

Subtraction becomes adding the opposite: 2 - 6 = 2 + (-6) = -4. The distance from -4.5 to 3 is |3 - (-4.5)| = 7.5, and properties let students regroup -3/4 + 5 + 3/4 as 5. In 8th grade, solving equations (8.EE.7) leans on these moves.

7.NS.1 I Can Statements

  • I can add positive and negative numbers on a number line.
  • I can rewrite any subtraction as adding the opposite.
  • I can find the distance between two numbers with absolute value.

7.NS.1 Worked Example

A morning below zero and a noon above it: one subtraction of a negative, checked on a thermometer, which is the vertical number line the standard names.

Problem

At 6 a.m. the temperature was -7.5 °F. By noon it was 12 °F. How many degrees did the temperature rise?

How far did the temperature rise from -7.5 °F to 12 °F?
  1. A rise is the end minus the start. Put the negative start in parentheses so its sign stays visible.12 - (-7.5)
  2. Subtracting a number is adding its opposite. The opposite of -7.5 is 7.5.12 - (-7.5) = 12 + 7.5
  3. Add.12 + 7.5 = 19.5
  4. Picture the thermometer as a vertical number line: from -7.5 up to 0 is 7.5 degrees, and from 0 up to 12 is 12 more.7.5 + 12 = 19.5 degrees
  5. The distance between two readings is the absolute value of their difference, so subtracting in the other order gives the same size.|-7.5 - 12| = |-19.5| = 19.5
AnswerThe temperature rose 19.5 °F

Check it: Add the rise back to the start: -7.5 + 19.5 = 12, the noon reading. Estimate too: about 8 degrees to reach zero and 12 more is about 20.

Common Mistakes with 7.NS.1

Subtracting the negative as if it were positive

12 - (-7.5) = 12 - 7.5 = 4.5

Try this: Rewrite every subtraction as adding the opposite before computing: 12 - (-7.5) becomes 12 + 7.5, which is 19.5.

Adding the sizes when the signs differ

-9 + 4 = -13

Try this: Start at -9 on a number line and move 4 to the right. The jump goes toward 0, so the answer is -5.

Reporting a negative distance

Diver at -30 ft, gull at 18 ft: -30 - 18 = -48, so they are -48 ft apart

Try this: Take the absolute value of the difference: |18 - (-30)| = |48| = 48 feet. Distance on a number line is never negative.

Where 7.NS.1 Fits

Comes Before6.NS.5Use positive and negative numbers for opposite directions, like a deposit and a withdrawal.6.NS.7Read absolute value as distance from 0, like |-45| = 45.
Alongside7.NS.2Multiply and divide the same positive and negative numbers.7.NS.3Solve word problems that use all four operations with signed numbers.
Comes Next8.EE.7Solve linear equations where every step adds or subtracts signed numbers.8.NS.1Extend the number system past the rationals to irrational numbers like √2.

Practice 7.NS.1

Number Line GeneratorFree ToolLines from -20 to 20 marked by ones, or -5 to 5 by halves for the fractions, so every sum is drawn as a start point and a jump.-20 to 20Step 0.5Labeled
Make a Number Line
Math Worksheet GeneratorFree ToolMixed sums and differences of integers, fractions and decimals, with a subtracted negative in every row and an answer key.IntegersAdd and subtractAnswer key
Make a Worksheet

Quick Check

  1. Compute -8 + 13 and -8 - 13.
  2. Compute -2/3 - (-1/4).
  3. A submarine at -120 feet rises to -45 feet. Write the subtraction and find how far it rose.

7.NS.1: Other Names

7.NS.17.NS.A.1CCSS.MATH.CONTENT.7.NS.A.1

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.