1. Bell Quiz

2. Objectives Subtract real numbers. Discuss the definition of additive inverse. Write an equivalent addition statement in order to subtract real numbers.

3. Subtracting Real Numbers Two numbers with the same absolute value but different signs are called opposites. Another name for the opposite of a number is additive inverse. The sum of a number and its opposite is 0 Inverse Property of Addition For every real number a, a + (– a) = (– a) + a = 0. Example: 5 + (– 5) = 0

4. Subtracting Real Numbers Addition and subtraction are inverse operations. Subtracting a number is the same as adding the inverse of the number. Rules for Subtracting Real Numbers To subtract a number, add its inverse. Then follow the rules for adding real numbers. Example: 3 – 5 = 3 + (– 5) = –2

5. Example 1 Subtracting Real Numbers Find each difference. a.(– 12) – 21 b.(– 19) – (–8) c.3.2 – (– 5.1) d.(– 3/5) – (– 1/5)

6. Lesson Practice Find each difference. a.14 – (– 22) b.(– 7) – 16 c.(– 23.4) – 18.72 d.(– 2/3) – (– 1/6)

7. Example 2 Determining Closure Over Subtraction Determine whether each statement is true or false. a.The set of integers is closed under subtraction. b.The set of real numbers is closed under subtraction.

8. Lesson Practice Determine whether each statement is true or false. a.The set of whole numbers is closed under subtraction. b.The set of rational numbers is closed under subtraction.

9. Example 3 Application: Dive Depth Sam collected a water sample at a depth of 23 meters from the surface. He descended another 12 meters to collect a plant sample. Where was Sam in relation to the surface when he retrieved the plant sample?

10. Lesson Practice On January 23, 1960, the Trieste dove to a record depth of 37,800 feet below sea level. The record set previously, on January 7 th of the same year was, 13,800 feet less than the dive on January 23 rd. What was the record set on January 7 th in relation to sea level?