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Videos, examples, lessons, and solutions to help Grade 7 students learn how to find the distance between two rational numbers.
Grade 7, Module 2, Lesson 6 Worksheets (pdf)
Change may be positive or negative. For instance, there is a -4° change when the temperature goes from 7° to 3°
Exercise 1
Use the number line to answer each of the following:
What is the distance between - 4 and 5?
What is the distance between 5 and - 4?
What is the distance between -5 and -3?
What is the distance between -3 and -5?
What is the distance between 7 and -1?
What is the distance between -1 and 7?
Why did you both get the same answers for all three problems?
What represents the distance between a number and zero on the number line?
If the distance between 5 and 0 can be calculated using |5 - 0| or |5 |, do you think we might be able to calculate the distance between -4 and 5 using absolute value? Take a minute to see if it works.
Exercise 2
Use the number line to answer each of the following:
a. What is the distance between 0 and -8?
b. What is the distance between -2 and -1 1/2?
c. What is the distance between -6 and -10?
Example 1: Formula for the Distance Between Two Rational Numbers
For two rational numbers p and q, the distance between p and q is |p - q|.
Example 2: Change in Elevation vs. Distance
Distance is positive. Change in elevation or temperature may be positive or negative depending on whether it is increasing or decreasing (going up or down).
Exercise 3
The distance between a negative number and a positive number is 12 1/2. What are the numbers?
Exercise 4
Use the distance formula to find each answer. Support your answer using a number line diagram.
a. Find the distance between -7 and -4.
b. Find the change in temperature if the temperature rises from -18°F to 15°F (use a vertical number line).
c. Would your answer for part (c) be different if the temperature dropped from 15°F to -18°F?
d. Beryl is the first person to finish a %K race and is standing 15 feet beyond the finish line. Another runner, Jeremy, is currently trying to finish the race and has approximately 14 feet before he reaches the finish line. What is the minimum possible distance between Beryl and Jeremy?
e. What is the change in elevation from 140 feet above sea level to 40 feet below sea level? Explain.
|-19 -12|
|19 - (-12)|
Describe any patterns you see in the answers to the problems in the left and right-hand columns. Why do you think this pattern exists?
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