ACT Math: Master Negative Numbers in Order of Operations

When a negative sign appears before parentheses, it distributes (multiplies) to every term inside. Example: -(3+5)=-3-5=-8, not -3+5. Many students drop the negative or apply it selectively, causing errors. The rule: a negative sign before parentheses flips the sign of every term inside. Example: -(2x+3y-5)=-2x-3y+5. Notice that the -5 becomes +5 because the negative sign flips it. This detail separates students who get -2 right from those who get -1.

Subtraction vs. negation: Subtraction a-b is the same as a+(-b), so you can always rewrite subtraction as addition of a negative. Example: 5-3=5+(-3)=2. This reframe helps with order of operations because you can track signs more carefully.

Step 1: Before you start order of operations, distribute any negative signs outside parentheses. Step 2: Simplify inside parentheses (if any remain). Step 3: Apply exponents, noting that (-2)^2=4 but -2^2=-4 (the negative is not squared). Step 4: Multiply and divide left to right, tracking signs carefully. Step 5: Add and subtract left to right. Example: -3^2+(-2)(4)-5. Step 1: No distribution needed. Step 3: -3^2=-9 (the negative is not part of the exponent). Step 4: (-2)(4)=-8. Step 5: -9+(-8)-5=-9-8-5=-22. Following these steps in order prevents the vast majority of negative number errors.

Practice: Compute -2^2+(-3)^2-(-5). Step 3: -2^2=-4 and (-3)^2=9. Step 1 (distribute): -(-5)=+5. Step 5: -4+9+5=10. The answer is 10, not a smaller number, because you correctly handled the negative distribution.

Mistake 1: Confusing -x^2 and (-x)^2. Fix: -x^2=-(x^2) (the negative is not squared). (-x)^2=(negative times itself)=positive. Example: -3^2=-9 but (-3)^2=9. Mistake 2: Forgetting to flip signs when distributing a negative. Fix: Write out every sign flip. -(a-b)=-a+b, not -a-b. Mistake 3: Subtracting a negative and getting the sign wrong. Fix: a-(-b)=a+b. Subtraction of a negative is addition. Example: 5-(-3)=5+3=8. Mistake 4: Multiplying negatives and forgetting the result is positive. Fix: negative×negative=positive. negative×positive=negative. These four mistakes cause 80% of negative number errors on ACT Math.

Drill: Compute. (1) -4^2. (2) (-4)^2. (3) 3-(-2). (4) -(5-8). (5) -2×(-3). Answers: (1) -16, (2) 16, (3) 5, (4) 3, (5) 6. If you missed any, redo them using the step-by-step method.

Negative numbers appear in nearly every ACT Math problem at some level: solving equations, simplifying expressions, interpreting graphs. If you flip signs randomly, you'll accumulate errors across multiple problems. Students who own negative number operations can solve complex expressions in one clean pass, while others guess and make careless mistakes.

Spend this week doing five problems a day with negatives, using the step-by-step method. Write out every sign. By test day, handling negatives will feel as natural as handling positive numbers. That reliability will show in your overall accuracy and confidence.