Don't navigate away from this page too quickly! You will absolutely need to know negatives on the ACT® Math section. Maybe you're thinking, "I already know negatives…" I'm expecting you to know negatives already. So many students lose points on these questions when they misapply, or forget to apply, a negative sign.
A formal term for numbers with positive and negative signs is signed numbers. That's the term I'll use throughout my math review to be more concise.
This is one of the most important sections a student can review to improve their math score. The ACT® Math is purposefully trying to trick you on negatives.
Students assume that negatives are easy because they learned them in grade school. A few stray negative signs later and your score becomes less representative of your math skills.
Let's make sure you get all the points you deserve. I'm not going to spend too much time reteaching negatives (you can check out Khan Academy).
Instead, I'm going to show you several questions with tricky negative rules. Learning to be careful in your application of these rules can help you a lot on the ACT® Math section.
Practice Section
Question 1:
Calculate: 7 - (-3) + 2 × (-4)
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Step-by-Step Solution:
- Identify and simplify operations inside parentheses: 7 - (-3) + 2 × (-4) becomes 7 + 3 + 2 × (-4)
- Rewrite the expression: 7 + 3 + 2 × (-4)
- Perform multiplication first (order of operations): 2 × (-4) = -8
- Rewrite the expression with the result of the multiplication: 7 + 3 - 8
- Perform addition and subtraction from left to right: 7 + 3 = 10, 10 - 8 = 2
Final Answer: 2
Question 2:
Calculate: -5 + 6 × (-3) - (-2)
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Step-by-Step Solution:
- Identify and simplify operations inside parentheses: -5 + 6 × (-3) - (-2) becomes -5 + 6 × (-3) + 2
- Rewrite the expression: -5 + 6 × (-3) + 2
- Perform multiplication first (order of operations): 6 × (-3) = -18
- Rewrite the expression with the result of the multiplication: -5 - 18 + 2
- Perform addition and subtraction from left to right: -5 - 18 = -23, -23 + 2 = -21
Final Answer: -21
Question 3:
Calculate: (-2) × (4 - 6) + 3²
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Step-by-Step Solution:
- Simplify inside parentheses: (-2) × (4 - 6) + 3² becomes (-2) × (-2) + 3²
- Rewrite the expression with simplified parentheses: (-2) × (-2) + 3²
- Perform multiplication and exponentiation (order of operations): (-2) × (-2) = 4, 3² = 9
- Rewrite the expression with results of multiplication and exponentiation: 4 + 9
- Perform addition: 4 + 9 = 13
Final Answer: 13
Question 4:
Calculate: 5 - 3 × (-4) + (-6) ÷ 2
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Step-by-Step Solution:
- Identify and simplify multiplication and division: 5 - 3 × (-4) + (-6) ÷ 2
- Perform multiplication: 3 × (-4) = -12
- Perform division: (-6) ÷ 2 = -3
- Rewrite the expression with the results of multiplication and division: 5 - (-12) + (-3)
- Simplify subtraction of a negative number: 5 + 12 + (-3)
- Perform addition and subtraction from left to right: 5 + 12 = 17, 17 + (-3) = 14
Final Answer: 14
Question 5:
Calculate: -8 + (-2)³ - 4 ÷ (-2)
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Step-by-Step Solution:
- Identify and simplify exponentiation and division: -8 + (-2)³ - 4 ÷ (-2)
- Perform exponentiation: (-2)³ = -8
- Perform division: 4 ÷ (-2) = -2
- Rewrite the expression with the results of exponentiation and division: -8 + (-8) - (-2)
- Simplify subtraction of a negative number: -8 + (-8) + 2
- Perform addition and subtraction from left to right: -8 + (-8) = -16, -16 + 2 = -14
Final Answer: -14
These questions require careful application of arithmetic rules, especially the handling of negative numbers, order of operations, and understanding how subtraction of negative numbers transforms them into addition.
How is this going to show up on the ACT® Math Section? The importance of positive and negative signs on the ACT® Math section cannot be overstated.
Many questions will weave different positives or negatives in. The more the test does this, the more students lose points on the math.
Conclusion
You have to be vigilant whenever you notice a sign changing. Follow it through to the end of the equation, and you'll be well set up to earn more points on the ACT® Math Section.