ACT Math : How to multiply negative numbers

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #10 : Arithmetic

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

Possible Answers:

17

1

8

5

9

Correct answer:

1

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

Example Question #34 : Integers

Evaluate:

–3 * –7

Possible Answers:

21

4

–21

–10

10

Correct answer:

21

Explanation:

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

Example Question #35 : Integers

Evaluate.    

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

Possible Answers:

\dpi{100} \small 62

\dpi{100} \small -33

\dpi{100} \small 32

\dpi{100} \small -63

\dpi{100} \small 33

Correct answer:

\dpi{100} \small -33

Explanation:

\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)      

\dpi{100} \small -48+15

\dpi{100} \small -33

Example Question #36 : Integers

Solve.

(6-8)\times 11=

Possible Answers:

-13

-22

5

22

13

Correct answer:

-22

Explanation:

(6-8)=-2

-2\times 11=-22

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

Example Question #37 : Integers

Evaluate 3x3 + x2 if x = 2

 

Possible Answers:

14

22

28

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 

 

Example Question #38 : Integers

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

Possible Answers:

12

24

–24

–16

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. 

Example Question #39 : Integers

Evaluate the following:

Possible Answers:

Correct answer:

Explanation:

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

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