Zero Pairs Additive Inverse Worksheet
Grade 7 Math 7.NS.A.1 • Rational Numbers
Zero Pairs & Additive Inverses
Name:
Date: Period:
Key Rule: The Additive Inverse of any number \( a \) is \( -a \). When opposites combine, their sum is always zero: \( a + (-a) = 0 \). Opposite numbers lie at the exact same distance from zero in opposite directions on a horizontal number line.
1
Visual Number Line Hops: Returning to Zero
Analyze the model, then draw the return jump and write the matching addition equation that sums to zero.
Example Model: Start at 0 → Jump +6 → Return with -6 Equation: \( 6 + (-6) = 0 \)
-8 -6 -4 -2 0 +2 +4 +6 +8 +6 -6
A. Start at -5. Show the additive inverse jump that returns to zero. Equation:
-8 -6 -4 -2 0 +2 +4 +6 +8
B. Start at +7. Show the additive inverse jump that returns to zero. Equation:
-8 -6 -4 -2 0 +2 +4 +6 +8
2
Opposite Match-Up & Zero-Sum Sort
Write the letter of the correct additive inverse:
1. \( 14 \) → [ ] A. \( -\frac{3}{4} \)
2. \( -9.2 \) → [ ] B. \( -14 \)
3. \( \frac{3}{4} \) → [ ] C. \( 9.2 \)
4. \( -2\frac{1}{3} \) → [ ] D. \( 2\frac{1}{3} \)
5. \( 0 \) → [ ] E. \( 0 \)
Expression Bank:
\( 8 + (-8) \) \( -6 + (-6) \) \( -15 + 15 \) \( 4.5 - 4.5 \) \( 10 - (-10) \) \( -\frac{2}{5} + \frac{2}{5} \)
Equals 0
Does NOT Equal 0
Page 1 of 2 • Additive Inverse Concepts & Models
Zero Pairs & Additive Inverses: Practice & Application
Name:
3
Real-World "Zero-Out" Situations
Write an integer for the given event, state its additive inverse, and write a sentence describing what action brings the total back to zero.
| Real-World Situation | Initial Integer | Additive Inverse | Action to "Zero Out" |
|---|
| A submarine dives 120 feet below sea level. | -120 | +120 | Ascend 120 feet to surface. |
| Maya deposits $45 into her checking account. | | | |
| The temperature drops 8°F overnight. | | | |
| A football team loses 15 yards on a penalty. | | | |
| A hiker climbs 350 meters up a mountain. | | | |
4
Finding Zero Pairs to Simplify Expressions
Identify zero pairs first by crossing them out or circling them, then find the final simplified value.
Problem 1: \( (-7) + 12 + 7 \)
Zero Pair:
Remaining Value: Answer: _____
Problem 2: \( 15 + (-9) + (-15) + 4 \)
Zero Pair:
Remaining Value: Answer: _____
Problem 3: \( (-3.4) + 8.1 + 3.4 + (-2.1) \)
Zero Pair:
Remaining Value: Answer: _____
Problem 4: \( \frac{5}{8} + \left(-\frac{1}{4}\right) + \left(-\frac{5}{8}\right) \)
Zero Pair:
Remaining Value: Answer: _____
5
Error Analysis & Deep Reasoning
Student Claim: "Jordan says that \( 10 - (-10) = 0 \) because 10 and -10 are opposites, so they cancel out to make zero."
Is Jordan correct? Explain why or why not using what you know about subtracting negative numbers and additive inverses:
Page 2 of 2 • Practice, Applications & Conceptual Reasoning
