Distance, Subtraction, and Absolute Values

Lesson 3.3 focuses on applying subtraction to rational numbers in word problems. It explains how to identify when to use addition or subtraction based on context clues. Examples include calculating temperature changes and ranges. The lesson emphasizes understanding range as a positive distance and concludes with choosing the correct expression for a given situation. The lesson ends with a transition to lesson 3.4, which will cover multiplying rational numbers with different signs.

Which of the following clue words would indicate the use of subtraction in a word problem?

• Increase

• Difference

• Ascend

• Total

In the temperature example, what is the resulting temperature when 3.2 degrees is subtracted from 2.1 degrees?

• 1.1 degrees

• -1.1 degrees

• -0.9 degrees

• 0.9 degrees

How do you determine the sign of the result when subtracting two numbers with unlike signs?

• Always use a negative sign

• Always use a positive sign

• Use the sign of the number with the smaller absolute value

• Use the sign of the number with the greater absolute value

What is the range in temperature if the coldest night was -2.75 degrees and the warmest was 1.5 degrees?

• 5.25 degrees

• 2.25 degrees

• 3.25 degrees

• 4.25 degrees

Why is the range of values always a positive number?

• Because it is calculated using addition

• Because it is a measure of time

• Because it represents a distance, which is non-directional

• Because it is always measured in degrees

What does the term 'distance' refer to in mathematical problems?

• The total time taken to move

• How far an object moves, regardless of direction

• The speed of an object

• The direction an object moves

If you run 2 miles east and then 2 miles west, what is the total distance covered?

• 0 miles

• 2 miles

• 1 mile

• 4 miles

In the elevation problem, what is the correct expression to find the distance between the rock and the treasure?

• Negative 6.25 minus 8.5

• Absolute value of negative 6.25 minus 8.5

• 8.5 minus negative 6.25

• Absolute value of negative 6.25 plus 8.5

Why do we use absolute values when calculating distances?

• To avoid using decimals

• To simplify the calculation

• To ensure the result is always positive

• To make the calculation faster

What is the distance between two points if one is at 8.5 meters and the other at -6.25 meters?

• 10.75 meters

• 12.75 meters

• 2.25 meters

• 14.75 meters