# 8.3: Homework

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• Submit homework separately from this workbook and staple all pages together. (One staple for the entire submission of all the unit homework)
• Start a new module on the front side of a new page and write the module number on the top center of the page.
• Answers without supporting work will receive no credit.
• Some solutions are given in the solutions manual.
• You may work with classmates but do your own work.

## HW #1

How would you explain to someone what the "absolute value of a number" means? Explain without using examples.

## HW #2

Simplify each of the following:

 b. | 8 | – | 10 | c. | 8 – 10 | d. | 35 | e. | 10 – 18 | f. | 10 | – | 18 |

## HW #3

Write any and all numerals that have the given absolute value:

 a. 4 b. 0

HW #4

For each vector drawn, write the number that the vector represents:

 a. Vector a b. Vector b c. Vector c d. Vector d

## HW #5

Look again at the four vectors shown in exercise 4. If someone had drawn those vectors to find the difference of two numbers using the missing addend approach, write the four subtraction problems which generated those vectors.

## HW #6

Use vectors on the number line to add -8 + 5 + (-3) using vectors as actions. Mark and LABEL your number line with at least zero and a point on either side. Explain how to read the answer.

-8 + 5 + -3 = _____ since ______________________________________________

## HW #7

Use vectors on the number line to compute the 8 – 5 + -7 – -4 using vectors to DO and UNDO actions. Mark and LABEL your number line with at least zero and a point on either side. Explain how to read the answer.

______________________________________________8 – 5 + -7 – -4 = _____ since ______________________________________________.

## HW #8

Use the missing addend approach to perform the following subtractions. Label the vector on the number line.

 a. 5 – 11 c. 5 – (-11)

HW #9

Use red and green counters to add the following integers. For each problem, explain and show each of the steps involved.

## HW #10

For each problem, use positive and negative counters. First, state what the problem means, and then explain and show each step you need to take to find the answer. Each problem requires 3 or 4 steps.

 a. 6 – 8

HW #11

For each of the following sets, determine if the set is closed under the operation given. Provide a counterexample if it is not closed.

 a. Negative Integers under addition b. Positive Integers under subtraction c. {..., -10, -5, 0, 5, 10, ...} under addition d. {0, 3, 6, 9, ...} under subtraction e. Positive Integers under multiplication f. Negative Integers under multiplication

## HW #12

Use your counters to do each of the following multiplication problems using the definition of multiplying two integers with positive and negative counters. Then, explain what the multiplication problem given means in terms of the counters, and explain and show each of the individual steps.

This page titled 8.3: Homework is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Julie Harland via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.