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ACT Math : Negative Numbers

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Example Questions

Example Question #1 : Negative Numbers

What is 1 + (–1) – (–3) + 4 ?

Possible Answers:

Correct answer:

Explanation:

You simplify the expression to be 1 – 1 + 3 + 4 = 7

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Example Question #1 : How To Subtract Negative Numbers

Solve the following equation for $\displaystyle x$:

$\displaystyle x-(-13)+26-(-23)=-3$

Possible Answers:

x=-65 $\displaystyle x=-65$

x=65 $\displaystyle x=65$

x=4 $\displaystyle x=4$

x=15 $\displaystyle x=15$

x=-13 $\displaystyle x=-13$

Correct answer:

x=-65 $\displaystyle x=-65$

Explanation:

To begin, we need to recall how to subtract negative numbers. Remember, when subtracting a negative number, the two negatives cancel out, creating a positive.

So, this:

$\displaystyle x-(-13)+26-(-23)=-3$

Becomes this:

$\displaystyle x+13+26+23=-3$

We can combine like terms on the left to get:

x+62=-3 $\displaystyle x+62=-3$

Then, we can subtract $\displaystyle 62$ from both sides in order to get $\displaystyle x$ by itself:

x=-3-62 $\displaystyle x=-3-62$

In this case, we are subtracting from a negative number, which is just like adding two negative numbers, or subtracting from a positive number. The result will be more negative, because we will be moving further to the left on the number line.

x=-65 $\displaystyle x=-65$

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Example Question #91 : Negative Numbers

Compute the following: $\displaystyle -12 -(-3)-(-4)+5$

Possible Answers:

$\displaystyle 6$

$\displaystyle -14$

$\displaystyle -24$

$\displaystyle 0$

$\displaystyle -6$

Correct answer:

$\displaystyle 0$

Explanation:

Convert all the double signs to a single sign before solving. Remember, two minus (negative) signs combine to form a plus (positive) sign, and a plus (positive) sign and a minus (negative) sign combine to form a minus (negative) sign.

$\displaystyle -12 -(-3)-(-4)+5$

$\displaystyle -12+3+4+5=0$

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Example Question #1 : How To Multiply Negative Numbers

If a = –2 and b = –3, then evaluate a³ + b²

Possible Answers:

Correct answer:

Explanation:

When multiplying negative numbers, we get a negative answer if there are an odd number of negative numbers being multiplied. We get a positive answer if there are an even number of negative numbers being multiplied.

a³ + b² becomes (–2)³ + (–3)² which equals –8 + 9 = 1

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Example Question #1 : Negative Numbers

Evaluate:

–3 * –7

Possible Answers:

–10

–21

Correct answer:

Explanation:

Multiplying a negative number and another negative number makes the product positive.

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Example Question #11 : Concepts

Evaluate.

$\dpi{100} \small (-8\times 6) - (5\times -3)$ $\displaystyle \dpi{100} \small (-8\times 6) - (5\times -3)$

Possible Answers:

$\dpi{100} \small 32$ $\displaystyle \dpi{100} \small 32$

$\dpi{100} \small -63$ $\displaystyle \dpi{100} \small -63$

$\dpi{100} \small 62$ $\displaystyle \dpi{100} \small 62$

$\dpi{100} \small 33$ $\displaystyle \dpi{100} \small 33$

$\dpi{100} \small -33$ $\displaystyle \dpi{100} \small -33$

Correct answer:

$\dpi{100} \small -33$ $\displaystyle \dpi{100} \small -33$

Explanation:

$\dpi{100} \small (-8\times 6) - (5\times -3)$ $\displaystyle \dpi{100} \small (-8\times 6) - (5\times -3)$

Multiplying a negative and a positive number creates a negative product:

$\dpi{100} \small (-48)-(-15)$ $\displaystyle \dpi{100} \small (-48)-(-15)$

$\dpi{100} \small -48+15$ $\displaystyle \dpi{100} \small -48+15$

$\dpi{100} \small -33$ $\displaystyle \dpi{100} \small -33$

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Example Question #2 : How To Multiply Negative Numbers

Solve.

$(6-8)\times 11=$ $\displaystyle (6-8)\times 11=$

Possible Answers:

$13$ $\displaystyle 13$

$-13$ $\displaystyle -13$

$5$ $\displaystyle 5$

$-22$ $\displaystyle -22$

$22$ $\displaystyle 22$

Correct answer:

$-22$ $\displaystyle -22$

Explanation:

$(6-8)=-2$ $\displaystyle (6-8)=-2$

$-2\times 11=-22$ $\displaystyle -2\times 11=-22$

A negative number multiplied by a positive number will always be negative.

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Example Question #1 : How To Multiply Negative Numbers

Evaluate 3x³ + x² if x = –2

Possible Answers:

–22

–20

Correct answer:

–20

Explanation:

When multiplying a negative number an odd number of times, the answer is negative. When multiplying a negative number an even number of times, the answer is positive. Order of operations also applies: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction, from left to right. A mnemonic to remember the order of operations is “Please excuse my dear Aunt Sally.”

3(–2)³ + (–2)²

= 3(–8) + (4)

= –24 + 4

= –20

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Example Question #3 : How To Multiply Negative Numbers

Simplify the following expression: (–4)(2)(–1)(–3)

Possible Answers:

–16

–24

Correct answer:

–24

Explanation:

First, we multiply –4 and 2. A negative and a positive number multiplied together give us a negative number, so (–4)(2) = –8. A negative times a negative is a positive so (–8)(–1) = 8. (8)(–3) = –24.

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Example Question #2 : Negative Numbers

Evaluate the following:

-6*-4 $\displaystyle -6*-4$

Possible Answers:

$\displaystyle 10$

$\displaystyle 24$

$\displaystyle -24$

$\displaystyle -10$

Correct answer:

$\displaystyle 24$

Explanation:

Two odd numbers multiplied always result in an even number. Simply multiple the two as though they were even. Thus

$\displaystyle -6*-4=6*4=24$

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ACT Math : Negative Numbers

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1 : Negative Numbers

Example Question #1 : How To Subtract Negative Numbers

Example Question #91 : Negative Numbers

Example Question #1 : How To Multiply Negative Numbers

Example Question #1 : Negative Numbers

Example Question #11 : Concepts

Example Question #2 : How To Multiply Negative Numbers

Example Question #1 : How To Multiply Negative Numbers

Example Question #3 : How To Multiply Negative Numbers

Example Question #2 : Negative Numbers

All ACT Math Resources

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