math class 678 4-in-1 skill sheets
7.NS.A.1d 7th Grade The Number System

Adding & Subtracting Rationals

Apply properties of operations as strategies to add and subtract rational numbers.

How to explain it

Students add and subtract positive and negative fractions, mixed numbers, and decimals by rewriting every subtraction as adding the additive inverse (Keep–Change–Change), applying the SUMS sign rules over a common denominator, representing sums and differences as jumps on the number line, and interpreting results in real-world contexts.

The anchor students hold onto: See subtraction? KCC it: Keep the first number · Change − to + · Change the second sign. Then SUMS finishes — fractions get a common denominator first.

Worked examples

Example 1 Unlike Denominators
(,[object Object],) + ,[object Object]
Step 1LCD = 4: 1/2 = 2/4
Step 2Signs differ → 3/4 − 2/4 = 1/4
Step 3Larger value is negative → −1/4
Step 4A: −1/4
Answer−1/4
Example 2 KCC a Subtraction
[object Object], − ,[object Object]
Step 1KCC: 2/5 + (−4/5)
Step 2Signs differ → 4/5 − 2/5 = 2/5
Step 3Larger value is negative → −2/5
Step 4A: −2/5
Answer−2/5

Common mistakes

What students write Adding tops and bottoms: 1/4 + 2/3 = 3/7
The fix Denominators never add — find the LCD first: 3/12 + 8/12 = 11/12
Try this Noah says 1/4 + 2/3 = 3/7 because "you add the tops and add the bottoms." Find his mistake, then show the correct work.
What students write Subtracting a negative still subtracts: 3/5 − (−1/5) = 2/5
The fix KCC changes BOTH signs: 3/5 + 1/5 = 4/5 — subtracting a negative ADDS
Try this Mia says 3/5 − (−1/5) = 2/5 because "subtracting makes it smaller." Explain her error, then give the correct answer.

Teacher tip

Head off the two predictable errors before they happen. First: Denominators never add — find the LCD first: 3/12 + 8/12 = 11/12 Second: KCC changes BOTH signs: 3/5 + 1/5 = 4/5 — subtracting a negative ADDS