ACT Math : How to subtract integers

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #1 : Operations

On an airline flight of 250 people there is a choice of pasta, salad, or pizza for dinner. If 113 passengers choose pasta and 30% choose salad, how many passengers choose pizza?

Possible Answers:

100

62

53

75

Correct answer:

62

Explanation:

30% of 250 is 75. Therefore, 250 – 75 – 113 = 62

Example Question #2 : How To Subtract Integers

At a store, a t-shirt costs \(\displaystyle \$12\). If Shane bought \(\displaystyle 2\) t-shirts and shoes from the store for \(\displaystyle \$55\), how much were the shoes?

Possible Answers:

\(\displaystyle \$24\)

\(\displaystyle \$31\)

\(\displaystyle \$43\)

\(\displaystyle \$20\)

Correct answer:

\(\displaystyle \$31\)

Explanation:

If one shirt costs \(\displaystyle \$12\), then two shirts must cost \(\displaystyle \$24 (12 \times 2 = 24)\). The difference of the total and this number is the cost of the the shoes.

\(\displaystyle \$55 - \$24 = \$31\)

Example Question #1 : How To Subtract Integers

\(\displaystyle (a+b+2c)-(3a+6b-4c)\) is equivalent to which of the following?

Possible Answers:

\(\displaystyle 3a+6b-8c\)

\(\displaystyle -2a+6b-2c\)

\(\displaystyle 4a+7b-2c\)

\(\displaystyle -3a-6b+8c\)

\(\displaystyle -2a-5b+6c\)

Correct answer:

\(\displaystyle -2a-5b+6c\)

Explanation:

To answer this question, we must remember how to distribute a negative when we are subtracting an entire expression.

To distribute a negative, you change the sign of everything within the expression being subtracted from positive to negative or negative to positive. You then add the resulting expression. So, for this data:

\(\displaystyle (a+b+2c)-(3a+6b-4c)=(a+b+2c)+(-3a-6b+4c)\)

We can then add the like expressions normally (combine \(\displaystyle a\) with \(\displaystyle a\), \(\displaystyle b\) with \(\displaystyle b\), and \(\displaystyle c\) with \(\displaystyle c\)). Therefore, for this data:

\(\displaystyle (a+b+2c)+(-3a-6b+4c)=-2a-5b+6c\)

Therefore, our answer is \(\displaystyle -2a-5b+6c\).

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