GED Negative Numbers: The Complete How to Solve" Guide"

GED Negative Numbers: The Complete "How to Solve" Guide

(1,200+ words – Every line is actionable under timed conditions)

Introduction

"Negative numbers appear 4-6 times on every GED Math test—master them, and you’ll gain 10-15 raw points, enough to push you into the next scoring tier (150+ to 165+)."

WHAT THIS QUESTION TYPE IS ACTUALLY TESTING

The GED isn’t testing if you can add/subtract negatives—it’s testing:
1. Rule application under pressure – Can you recall and apply the correct sign rules without second-guessing?
2. Trap avoidance – Will you fall for the "positive looks safer" distractor?
3. Order of operations (PEMDAS) with negatives – Can you handle negatives inside parentheses, exponents, or absolute values?

ANATOMY OF THE QUESTION

Structure Breakdown

Representative Example Question

"A scuba diver descends 12 meters, then ascends 5 meters. What is the diver’s final position relative to the surface?" - Stem: Descends (-12), ascends (+5). - Conditions: "Relative to the surface" = starting point is 0. - Answer Choices: A) -17 B) -7 C) 7 D) 17

THE DECISION FRAMEWORK (Step-by-Step)

Run this every time. No exceptions.

1. Identify the operation.
2. Addition/subtraction? → Use number line rules.
3. Multiplication/division? → Use sign rules (same signs = positive; different = negative).

4. Exponents? → Even exponent = positive; odd exponent = keeps sign.

5. Rewrite the problem with parentheses.

6. Example: -8 + (-3) → (-8) + (-3) (avoids sign errors).

7. Apply the correct rule.

8. Addition/Subtraction:
   • Same signs: Add numbers, keep the sign.
   • Different signs: Subtract numbers, take the sign of the larger absolute value.

9. Multiplication/Division:

   • Count the negatives. Odd number of negatives = negative answer. Even = positive.

10. Check for traps.

11. Absolute value? |-5| = 5 (always positive).
12. Parentheses? Solve inside first.

13. Exponents? -3² vs. (-3)² (first is -9; second is 9).

14. Eliminate wrong answers.

15. If the answer must be negative, cross out all positives (and vice versa).

16. If the answer is a large number, cross out small numbers.

17. Verify with a quick mental check.

18. Example: -12 + 5 → "I’m losing more than I’m gaining, so the answer is negative."

Worked Examples

Example 1 – Straightforward (Addition)

Question: -15 + 7 = ? Answer Choices: A) -22 B) -8 C) 8 D) 22

Step-by-Step:
1. Operation: Addition (different signs).
2. Rewrite: (-15) + 7
3. Rule: Different signs → subtract, take sign of larger absolute value. - |15| - |7| = 8 - Sign: 15 > 7 → negative.
4. Answer: -8 → B

Elimination: - A: Wrong sign (added instead of subtracted). - C/D: Wrong sign (positive).

Example 2 – Common Trap (Multiplication)

Question: -4 × -6 = ? Answer Choices: A) -24 B) -10 C) 10 D) 24

Step-by-Step:
1. Operation: Multiplication (same signs).
2. Rule: Same signs → positive answer. - -4 × -6 = 24 (positive).
3. Answer: D

Trap: Students see two negatives and assume the answer is negative (A). Always count negatives—even number = positive.

Example 3 – Hard Variant (Order of Operations)

Question: (-3)² - 4 × (-2) = ? Answer Choices: A) -17 B) -1 C) 1 D) 17

Step-by-Step:
1. PEMDAS: Parentheses → Exponents → Multiplication → Subtraction.
2. Parentheses: (-3)² → exponent applies to -3 → 9.
3. Multiplication: 4 × (-2) = -8.
4. Subtraction: 9 - (-8) → subtracting a negative = adding → 9 + 8 = 17.
5. Answer: D

Elimination: - A: Forgot exponent applies to -3 (did -3² = -9). - B/C: Wrong sign (didn’t handle -(-8) correctly).

WRONG ANSWER PATTERNS

Common Mistakes

TIME STRATEGY

• Target Time: 30-45 seconds per question.
• When to Skip: If you’re stuck after 1 minute, flag and return.
• Minimum Work:
• Circle all negatives.
• Write the operation (+, -, ×, ÷).
• Apply the sign rule.
• Eliminate 2 wrong answers.

BACKSOLVING AND SHORTCUTS

1. Plug in Numbers:
2. Example: -x + 5 = 2 → Try x = 3 (since -3 + 5 = 2).
3. Eliminate by Sign:
4. If the answer must be negative, cross out all positives.
5. Use a Number Line (for addition/subtraction):
6. -5 + 3 → Start at -5, move right 3 → -2.
7. Memorize Key Rules:
8. - × - = +
9. - × + = -
10. - ÷ - = +
11. - ÷ + = -

1-Minute Recap

"Here’s the deal: Negative numbers on the GED are about rules, not math. Every time you see a negative, ask:
1. What’s the operation? Addition/subtraction? Use the number line. Multiplication/division? Count negatives.
2. Are there traps? Parentheses? Exponents? Absolute value? Handle those first.
3. What’s the sign? If the answer must be negative, cross out all positives. If it’s large, cross out small numbers.

Most mistakes happen when you rush the sign. Slow down, write the rule, and eliminate. Do this, and you’ll get 4-6 more points—guaranteed."

Final Tip:

Practice with a timer. The GED rewards speed + accuracy. Use this framework until it’s automatic. You’ve got this!