7.NS.A.1c 7th Grade The Number System

Subtracting Integers

Understand subtraction of rational numbers as adding the additive inverse, and show that distance on a number line is the absolute value of the difference.

How to explain it

Students subtract integers by rewriting every difference as adding the additive inverse (Keep–Change–Change), model the rewritten sum as a jump on the number line, and interpret the distance between two integers as the absolute value of their difference in real-world contexts.

The anchor students hold onto: KCC: Keep the first number · Change subtraction to addition · Change the sign of the second — then use SUMS.

Where this leads next, students will multiply integers, where the sign rules tighten into one pattern: same signs give a positive product, different signs give a negative one — fluency here makes that automatic.

Worked examples

Example 1 Subtract a Positive

5 − 8

Step 1KCC: 5 + (−8)

Step 2Unlike signs: 8 − 5 = 3

Step 3|−8| > |5| → negative

Step 4A: −3

Answer−3

Example 2 Subtract a Negative

3 − (−5)

Step 1KCC: 3 + (+5)

Step 2Same signs: add

Step 33 + 5 = 8

Step 4A: 8

Answer8

Common mistakes

What students write Did not add the opposite: (−6) − (−4) = −10

The fix Add the opposite — (−6) + 4 = −2 (Keep, Change, Change)

Try this Devon says (−6) − (−4) = −10. Find his mistake, then show the correct work using KCC.

What students write Changed the operation but not the second sign: 7 − (−5) = 2

The fix Change BOTH: 7 + 5 = 12 — keep, change, change.

Try this Mara says 7 − (−5) = 2. She changed subtraction to addition but her answer is still wrong. Explain what she forgot, and give the correct difference.

Teacher tip

Head off the two predictable errors before they happen. First: Add the opposite — (−6) + 4 = −2 (Keep, Change, Change) Second: Change BOTH: 7 + 5 = 12 — keep, change, change.