Lesson 10. adding integers. 46 Lesson 10 ~ Adding Integers
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1 adding integers Lesson 10 explore! integer chips Integer chips are helpful for modeling integer operations. Each blue chip will represent the integer 1. Each red chip will represent the integer 1. When a positive integer chip is combined with a negative integer chip, the result is zero. This pair of integer chips is called a zero pair. 1 1 = 0 step 1: Model 4 ( 2) with integer chips. step 2: Group as many zero pairs as possible. step 3: Because zero pairs are worth zero, remove all zero pairs. What is the result? step 4: Write an expression for the following model. Create the same model using your own integer chips. step 5: Group as many zero pairs as possible and remove them. What is the result of your expression? step 6: Model 5 ( 3) with integer chips. step 7: Are there any zero pairs? If so, remove them. What is the result of 5 ( 3)? step 8: Write an integer addition expression. Model it with integer chips to find the sum. step 9: Use integer chips to help you determine what type of answer (positive, negative or zero) you think you will get for each situation. Explain your reasoning. a. the sum of two positive numbers b. the sum of two negative numbers c. the sum of a number and its opposite d. the sum of a negative and positive integer 46 Lesson 10 ~ Adding Integers
2 Number lines are another way to model integer addition. Look at these integer sums on a number line: Find the value of 4 ( 2) using a number line. Start at 0 Move 4 to the right for 4 Move 2 to the left for The value of 4 ( 2) = 2. Find the value of 5 ( 3) using a number line. Start at 0 Move 5 to the left for 5 Move 3 to the left for The value of 5 3 = 8. example 1 Find the sum using integer chips or a number line. a. 1 ( 4) b. 6 ( 3) a. 1 ( 4) Using integer chips: = = 5 Using a number line: 4 1 b. 6 ( 3) Using integer chips: = = 3 Using a number line: 6 3 Lesson 10 ~ Adding Integers 47
3 The following rules may help you add two integers without using integer chips or a number line.? example 2 Janell descended 16 feet and then rose 21 feet in elevation on a hike. Write an integer addition expression to represent this situation. determine her overall change in elevation. JaNell descended 16 feet and then rose 21 feet. Integer expression: Determine the sign. One integer is negative and the other is positive so use the sign of the number that has the larger absolute value. Since 21 > 16, the sign of the answer is positive. Find the sum. Subtract the lesser absolute value from the larger absolute value = 5 JaNell s overall change in elevation is 5 feet. example 3 Find the value of 5 ( 2) 1. Find the sum of the first two numbers. Add the third number to the sum. 5 ( 2) 1 = = = 6 48 Lesson 10 ~ Adding Integers
4 exercises use a number line to find each sum ( 1) 2. 6 ( 2) ( 3) 6. 8 ( 2) Find each sum. use integer chips, a number line or the integer addition rules ( 7) ( 10) ( 1) ( 8) ( 6) ( 30) ( 15) 19. Jason withdrew $14 from his account on Monday. He deposited $8 in his account on Tuesday. What integer represents the total change in his account over the last two days? 20. Maria is in a two-day golf tournament. She scored 3 on the first day. On the second day, her score is 5. What is her overall score for the entire tournament? 21. Ishmael s stock went up $17 on Thursday and then down $13 on Friday. What was the total change in the value of the stock? Find each sum ( 4) ( 1) ( 5) ( 7) ( 12) ( 4) ( 2) ( 3) ( 4) 28. Yesterday Kirk borrowed $13 from his friend. Today he borrowed $8 more. He plans to give his friend $15 tomorrow. What will Kirk s balance be? 29. Find three different integer addition expressions that equal Santiago ran up 72 stairs. He realized he forgot something and went down 32 stairs. He finished by going up 65 more stairs. a. Write an integer addition expression to show Santiago s movement up and down the stairs. b. What was Santiago s ending location on the stairs? Lesson 10 ~ Adding Integers 49
5 31. Esther opened a checking account by depositing $60. Her next four transactions are shown in the table. Copy and complete the table by writing an integer to represent each transaction. Find her balance at the end of this transaction period. transaction Integer Deposited $60 60 Withdrew $22 Withdrew $6 Deposited $35 Withdrew $20 Balance transaction Integer Deposited $44 44 Withdrew $30 Withdrew $20 Deposited $15 Withdrew $10 Withdrew $25 Balance 32. Corey deposited $44 in a new checking account. His next five transactions are shown in the table. Copy and complete the table by writing an integer to represent each transaction. Find his balance at the end of this transaction period. review order the integers from least to greatest , 4, 1, , 6, 10, 2, , 3, 1, 2, 7 Find each absolute value _ 3 50 Lesson 10 ~ Adding Integers
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Knowing WHEN to add or subtract Adding and Subtracting All Sorts of Numbers We use addition when we know the parts and want to find the total. We use subtraction when we know the total and want to take
EXAMPLE: Multiplying Integers with the Same Sign. Recall that multiplication is repeated addition. 3 2 means to add 3 groups of 2.
1.4 Multiplying Integers COMMON CORE STATE STANDARDS 7.EE. 7.NS.2a 7.NS.2c negative, or zero? How can you tell? 1 Use repeated addition to find 2. Is the product of two integers positive, : Multiplying