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Algebra 1 : How to multiply integers

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Example Questions

Example Question #1 : How To Multiply Integers

Evaluate 5x + 3y when x = 7 and y = 9.

Possible Answers:

–62

–66

Correct answer:

Explanation:

Plug in 7 for x and 5 for y, giving you 5(7) + 3(9). This is equal to 35 + 27, which equals 62.

5x + 3y

5(7) + 3(9)

35 + 27 = 62

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Example Question #2 : How To Multiply Integers

A plane flies at a rate of 210mi/h. If the plane has flown for five hours, how many miles has it traveled?

Possible Answers:

1050mi

840mi

215mi

42mi

1000mi

Correct answer:

1050mi

Explanation:

Multiply the rate of travel (210 mi/hr) by the time traveled (5 hours), and you get the total distance, 1050 miles.

distance = rate * time

distance = (210mi/hr)(5hr)

distance = 1050mi

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Example Question #2 : How To Multiply Integers

Find the volume of a cube that is five feet on each side.

Possible Answers:

125ft³

10ft³

5ft³

25ft³

15ft³

Correct answer:

125ft³

Explanation:

To find the volume of a cube, you cube the side length, raising it to the thrid power. 5cubed is 125.

(5ft)³ = 5ft*5ft*5ft = 125ft³

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Example Question #3 : How To Multiply Integers

What is the square root of 81?

Possible Answers:

40.5

–9

Correct answer:

Explanation:

9 * 9 = 81, and thus 9 is the square root of 81. It is true that (–9) * (–9) = 81, but it is a convention that "the square root" refers to the positive value. Had the question asked for "a square root" or "the square roots" of 81, –9 would be acceptable.

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Example Question #3 : How To Multiply Integers

What is (–16) * (–2)?

Possible Answers:

–32

–8

Correct answer:

Explanation:

When multiplying two negative numbers, the negatives cancel each other out, leaving a positive solution, thus, we can think of (–16)(–2) as (16)(2), which is 32.

(–16) * (–2)

(–1)(16) * (–1)(2)

(–1)(–1) * (16)(2)

(1) * (16)(2)

16 * 2

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Example Question #2 : How To Multiply Integers

Solve:

$\frac{(3\cdot 7-4)}{2\cdot 4^3}$ $\displaystyle \frac{(3\cdot 7-4)}{2\cdot 4^3}$

Possible Answers:

$\frac{9}{128}$ $\displaystyle \frac{9}{128}$

0.13 $\displaystyle 0.13$

7.5 $\displaystyle 7.5$

None of the available answers

$\frac{17}{128}$ $\displaystyle \frac{17}{128}$

Correct answer:

$\frac{17}{128}$ $\displaystyle \frac{17}{128}$

Explanation:

$\frac{(3\cdot 7-4)}{2\cdot 4^3}$ $\displaystyle \frac{(3\cdot 7-4)}{2\cdot 4^3}$

$\frac{(3\cdot 7-4)}{2\cdot 64}$ $\displaystyle \frac{(3\cdot 7-4)}{2\cdot 64}$

$\frac{(21-4)}{128}$ $\displaystyle \frac{(21-4)}{128}$

$\frac{17}{128}$ $\displaystyle \frac{17}{128}$

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Example Question #4 : How To Multiply Integers

If $\displaystyle p$ is an integer, which of the following must be odd?

Possible Answers:

3p+1 $\displaystyle 3p+1$

p-1 $\displaystyle p-1$

$\displaystyle 7p$

2p+1 $\displaystyle 2p+1$

$\displaystyle 3p$

Correct answer:

2p+1 $\displaystyle 2p+1$

Explanation:

While all of the answers could result in an odd answer, only 2p+1 $\displaystyle 2p+1$ guarantees an odd answer. Since any integer multiplied by 2 is even, adding 1 will always give the next consecutive odd integer.

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Example Question #1 : How To Multiply Integers

What is $\displaystyle (9) * (-7)$ ?

Possible Answers:

$\displaystyle -56$

$\displaystyle 2$

$\displaystyle -16$

$\displaystyle -63$

$\displaystyle 63$

Correct answer:

$\displaystyle -63$

Explanation:

Multiply the absolute values to get the magnitude of the answer.

9*7=63 $\displaystyle 9*7=63$

Remember the following rules:

Positive * negative = negative

Positive * positive = positive

Negative * negative = positive

Since we are dealing with a positive and a negative, our answer will be negative.

$\displaystyle 9*-7=-63$

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Example Question #4 : How To Multiply Integers

$100-30\times4+25\times 2= ?$ $\displaystyle 100-30\times4+25\times 2= ?$

Possible Answers:

610 $\displaystyle 610$

$\displaystyle 10$

230 $\displaystyle 230$

$\displaystyle 90$

$\displaystyle 30$

Correct answer:

$\displaystyle 30$

Explanation:

$\textup{Order of operations: Perform multiplication functions before addition/subtraction.}$ $\displaystyle \textup{Order of operations: Perform multiplication functions before addition/subtraction.}$

$100-30\times4+25\times 2= \;\;100-120+50\;\;\;= \;\;\;30$ $\displaystyle 100-30\times4+25\times 2= \;\;100-120+50\;\;\;= \;\;\;30$

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Example Question #2 : How To Multiply Integers

$\frac{\left ( 2-4 \right )^{3}}{3\times 6}=$ $\displaystyle \frac{\left ( 2-4 \right )^{3}}{3\times 6}=$

Possible Answers:

$-\frac{4}{9}$ $\displaystyle -\frac{4}{9}$

$\frac{4}{9}$ $\displaystyle \frac{4}{9}$

$-\frac{9}{4}$ $\displaystyle -\frac{9}{4}$

$\frac{9}{4}$ $\displaystyle \frac{9}{4}$

Correct answer:

$-\frac{4}{9}$ $\displaystyle -\frac{4}{9}$

Explanation:

$\frac{\left ( 2-4^ \right )^{3}}{3\times 6}= \frac{-2^{3}}{18}=\frac{-8}{18}=\frac{4}{9}$ $\displaystyle \frac{\left ( 2-4^ \right )^{3}}{3\times 6}= \frac{-2^{3}}{18}=\frac{-8}{18}=\frac{4}{9}$

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Algebra 1 : How to multiply integers

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #1 : How To Multiply Integers

Example Question #2 : How To Multiply Integers

Example Question #2 : How To Multiply Integers

Example Question #3 : How To Multiply Integers

Example Question #3 : How To Multiply Integers

Example Question #2 : How To Multiply Integers

Example Question #4 : How To Multiply Integers

Example Question #1 : How To Multiply Integers

Example Question #4 : How To Multiply Integers

Example Question #2 : How To Multiply Integers

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