# Absolute Value-Magnitude and Distance

Examples, videos, and solutions to help Grade 6 students understand the absolute value of a number as its distance from zero on the number line.

Students use absolute value to find the magnitude of a positive or negative quantity in a real-world situation.

New York State Common Core Math Grade 6, Module 3, Lesson 11

Opening Exercises
What is the relationship between the following pairs of numbers? How do each pair of numbers relate to zero?
-4 and 4
-2 1/2 and 2 1/2
-10 and 10

What is the absolute value of a number?

The absolute value of a number is the distance between the number and zero on a number line. Every number and it opposite are the same distance from zero on the number line.In other words, a number and its opposite have the same absolute value.

What is the absolute value of 6?
What is the absolute value of -6?
Both 6 and -6 are six units from zero.
What is the absolute value of 0?

Example 1: The Absolute Value of a Number

The absolute value of ten is written as |10|. On the number line, count the number of units from 10 to 0. How many units is 10 from 0?
What other number has an absolute value of ? Why?

The absolute value of a number is the distance between the number and zero on the number line.

Example 2: Using Absolute Value to Find Magnitude

Mrs. Owens received a call from her bank because she had a checkbook balance of dollars. What was the magnitude of the amount overdrawn?

The magnitude of a quantity is found by taking the absolute value of its numerical part

Exercises
4. Maria was sick with the flu and her weight change as a result of it is represented by -4 pounds. How much weight did Maria lose?
5. Jeffrey owes his friend \$5. How much is Jeffrey’s debt?
6. The elevation of Niagara Falls, which is located between Lake Erie and Lake Ontario, is 326 feet. How far is this above sea level?
7. How far below zero is -16 degrees Celsius?
8. Frank received a monthly statement for his college savings account. It listed a deposit of \$100 as +100.00. It listed a withdrawal of \$25 as -25.00. The statement showed an overall ending balance of \$835.50. How much money did Frank add to his account that month? How much did he take out? What is the total amount Frank has saved for college?
9. Meg is playing a card game with her friend Iona. The cards have positive and negative numbers printed on them. Meg exclaims: “The absolute value of the number on my card equals 8!” What is the number on Meg’s card?
10. List a positive and negative number whose absolute value is greater than . Explain how to justify your answer using the number line.
11. Which of the following situations can be represented by the absolute value of10? Check all that apply.
The temperature is degrees below zero. Express this as an integer.
Determine the size of Harold’s debt if he owes .
Determine how far is from zero on a number line.
degrees is how many degrees above zero?
12. Julia used absolute value to find the distance between 0 and 6 on a number line. She then wrote a similar statement to represent the distance between and . Below is her work. Is it correct? Explain.
|6| = 6, |-6| = -6
13. Use absolute value to represent the amount, in dollars, of a \$238.25 profit.
14. Judy lost 15 pounds. Use absolute value to represent the number of pounds Judy lost.
15. In math class, Carl and Angela are debating about integers and absolute value. Carl said two integers can have the same absolute value and Angela said one integer can have two absolute values. Who is right? Defend your answer.
16. Jamie told his math teacher: “Give me any absolute value, and I can tell you two numbers that have that absolute value.” Is Jamie correct? For any given absolute value, will there always be two numbers that have that absolute value?
17. Use a number line to show why a number and its opposite have the same absolute value.
18. A bank teller assisted two customers with transactions. One customer made a \$25.00 withdrawal from a savings account. The other customer made a \$15 deposit. Use absolute value to show the size of each transaction. Which transaction involved more money?
19. Which is farther from zero: -7 3/4 or 7 1/2? Use absolute value to defend your answer.

Closing

I am thinking of two numbers. Both numbers have the same absolute value. What must be true about the two numbers?
Can the absolute value of a number ever be a negative number? Why or why not?
How can we use absolute value to determine magnitude? For instance, how far below zero is -18 degrees?

Kelly owes Taylor \$35. Tracy owes Taylor \$65.
a. Write the integer represented by each amount.
b. Who owes more money? Write an inequality statement to represent the situation.

Problem Set
For each of the following two quantities in Problems 1–4, which has the greater magnitude? (Use absolute value to defend your answers.)

1. 33 dollars and -52 dollars
2. -14 feet and 23 feet
3. -24.6 pounds and -24.58 pounds
4. -11 1/4 degrees and 11 degrees
For Problems 5–7, answer true or false. If false, explain why.
5. The absolute value of a negative number will always be a positive number.
6. The absolute value of any number will always be a positive number.
7. Positive numbers will always have a higher absolute value than negative numbers.
8. Write a word problem whose solution is |20| = 20.
9. Write a word problem whose solution is |-70| = 70.
10. Look at the bank account transactions listed below, and determine which has the greatest impact on the account balance. Explain.
a. A withdrawal of \$60
b. A deposit of \$55
c. A withdrawal of \$58.50

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. 