Tallahassee Community College 4 I. Understanding Addition ADDITION OF WHOLE NUMBERS (DEFINITIONS AND PROPERTIES) 1. Define addition. 2. Draw a picture of 3 apples + 2 apples. 3. Write the directions for adding on the number line. 4. Show how to add 3 + 2 on the number line. 0 1 2 3 4 5 6 7 8 5. Know the names of the parts of an addition problem. a. 3 + 2 = 5 addend addend sum b. 6 + 4 = 10 Give the number for each name. 6 is a(an) 4 is a(an) 10 is a(an) c. Write a problem with addends of 7, 3 and 9. What is the sum? = II. Properties of Addition It is very important to know what can be done and what cannot be done when you are adding. Study the Properties of Addition in your text so that you: 1. can recognize what property has been used. 2. can use the property correctly yourself. Write each property. Then answer the questions which follow that property.
A. Addition Property of Zero 1. This property tells what happens when zero is a(an) (What part of an addition problem?) 2. Fill in the blanks to make true statements: a. 6 + 0 = c. 3 + = 3 e. + 0 = 4 b. 0 + 7 = d. + 9 = 9 f. 0 + = 8 3. In your own words describe what happens when zero is added to a number. B. Commutative Property of Addition EXAMPLE: 1. The Commutative Property of Addition lets us know that we can change the of the without changing the answer when we are adding. 2. Use the Commutative Property of Addition to rewrite each problem. Show that both sums are the same. a. 5 + 9 = 9 + 5 b. 6 + 7 = c. 11 + 9 = 14 = 14 = = d. (2 + 5) + 4 = ( + ) + 4 e. (6 + 7) + 3 = 3 + (6 + 7) + 4 = + 4 13 + 3 = 3 + 13 = = 3. NOTICE in d. and e. that the same addends are in the parentheses. What was changed in d. and e.? 4. What property is illustrated in each problem in #2? C. Associative Property of Addition 2
1. The Associative Property of Addition lets us know that we can change the of the without changing the answer when we are adding. 2. What symbol is used to group numbers? When is the operation inside the parentheses done? Be sure you understand the following section: 3. a. (6 + 4) + 8 What numbers are grouped together here? b. 6 + (4 + 8) What numbers are grouped together here? c. NOTICE the order of the addends is 6, 4, 8 in both examples (a and b). The of the addends did not change in a and b. The of the addends in a and b did change. d. What property is used below? (6 + 4) + 8 = 6 + (4 + 8) How do you know the property you named is correct? The of the addends changed. 4. Add: Show each step: a. (2 + 7) + 8 = 2 + (7 + 8) + 8 = 2 + = What property is used? b. 6 + (5 + 8) = (6 + 5) + 8 + = + = What property is used? 3
PART III. 3 D. Practice Identifying Properties: Name the property illustrated. Tell why you chose the property. 1. 17 + 0 = 17 2. 17 + 0 = 0 + 17 because because 3. (5 + 8) + 7 = 5 + (8 + 7) 4. 6 + (2 + 3) = 6 + (3 + 2) 5. 7 + (9 + 4) = (9 + 4) + 7 ANSWERS: I. 1. Addition is the process of finding the total of two or more numbers. 2. + = 3. 1. Start at zero. 2. Move distance of first addend. 3. Move distance of second addend. 4. The sum is where you stop. 3 + 2 4. 0 1 2 3 4 5 6 7 5b. 6, 4 addends 5c. 7 + 3 + 9 is the problem 10 sum 19 is the sum II. A. Zero added to a number does not change the number. 1. addend 4
2. a. 6 c. 0 e. 4 b. 7 d. 0 f. 8 3. Your statement should tell that a number added to zero is the same number. B. Two numbers can be added in either order. The sum will be the same. 1. Order of the addends. 2. b. 6 + 7 = 7 + 6 c. 11 + 9 = 9 + 11 13 = 13 20 = 20 d. (2 + 5) + 4 = (5 + 2) + 4 7 + 4 = 7 + 4 11 = 11 e. 16 = 16 3. Order of addends. (The same numbers are grouped in parentheses.) 4. Commutative Property of Addition. C. Grouping of addends does not change the answer in addition. 1. grouping of the addends 2. parentheses. The operation inside the parentheses is done first. 3. a. 6 and 4 b. 4 and 8 c. order did not change; grouping did change. d. Associative Property of Addition (because the grouping changed) 4. a. (2 + 7) + 8 2 + (7 + 8) 9 + 8 2 + 15 17 17 Associative Property of Addition b. 6 + (5 + 8) (6 + 5) + 8 6 + 13 11 + 8 19 19 Associative Property of Addition D. 1. Addition Property of Zero (because 0 is an addend; answer is the other addend) 5
2. Commutative Property of Addition because the order of the addends changed. This example did not tell the sum.) 3. Associative Property of Addition because (5 + 8) and (8 + 7) have different addends inside the parentheses. The order is 5, 8, 7 in each. 4. Commutative Property of Addition. The order of the addends changed. (2 + 3) and (3 + 2) have the same addends inside parentheses, but the order changed. 5. Commutative Property of Addition. The order of the addends changed 7 is the first addend on one side of the = and the last addend on the other side. The groupings are the same (9 and 4 are in both pairs of parentheses). 6