Suppose you took a job as a peer tutor and the person you were tutoring asked you to give examples of the Commutative Property of Addition, Associative Property of Addition, and Identity Property of Addition. Could you do it? Would you be able to distinguish between the different properties? After completing this Concept, you'll have a firm understanding of these properties so that you can easily add integers.
Addition of IntegersSDSAD ASD
A football team gains 11 yards on one play, then loses 5 yards on the next play, and then loses 2 yards on the third play. What is the total loss or gain of yardage?
When the value that is being added is positive, we jump to the right. If the value is negative, we jump to the left (in a negative direction).
Solution: Begin by making a point at 2. The expression represents subtraction, so we will count three jumps to the left.
Algebraic Properties of Addition
In the previous Concept, you learned the Additive Inverse Property. This property states that the sum of a number and its opposite is zero. Algebra has many other properties that help you manipulate and organize information.
To commute means to change locations, so the Commutative Property of Addition allows you to rearrange the objects in an addition problem.
To associate means to group together, so the Associative Property of Addition allows you to regroup the objects in an addition problem.
This property allows you to use the fact that the sum of any number and zero is the original value.
These properties apply to all real numbers, but in this lesson we are applying them to integers, which are just a special kind of real number.
Nadia and Peter are building sand castles on the beach. Nadia built a castle two feet tall, stopped for ice-cream, and then added one more foot to her castle. Peter built a castle one foot tall before stopping for a sandwich. After his sandwich, he built up his castle by two more feet. Whose castle is taller?
Simplify the following using the properties of addition:
In exercises 1 and 2, write the sum represented by the moves on the number line.
In 3 – 6, which property of addition does each situation involve?
- Shari’s age minus the negative of Jerry’s age equals the sum of the two ages.
- Kerri has 16 apples and has added zero additional apples. Her current total is 16 apples.
- A blue whale dives 160 feet below the surface and then rises 8 feet. Write the addition problem and find the sum.
- The temperature in Chicago, Illinois one morning was
−8∘F. Over the next six hours the temperature rose 25 degrees Fahrenheit. What was the new temperature?
- Find the opposite of –72.
- What is the domain and range of the following:
- Write a rule for the following table:
||Mass (in grams)|