Lesson 1-5 Warm-Up

“Adding Integers” (1-5) What is the “Identity Property of Addition”? What is the “Inverse Property of Addition”? How can you use a number line to add integers? Identity Property of Addition: A number plus 0 is equal to the original number [In other words, the number keeps its identity (doesn’t change) when 0 is added to it.] Examples: 5 + 0 = 5 n + 0 = n Inverse Property of Addition: A number plus its additive inverse (its opposite = same number with the opposite sign) is equal to zero. Examples: 17 + (-17) = 0 n + (-n) = 0 To add integers using a number line, start at the first number and move / jump the number of units right (+) or left (-) the second number tells you to.

Examples: Use a number line to simplify each expression. Adding Integers LESSON 1-5 Additional Examples Examples: Use a number line to simplify each expression. a. 3 + (–5) Start at –3. Move left 5 units. 3 + (–5) = –2 Start at –3. Move right 5 units. b. –3 + 5 –3 + 5 = 2 c. –3 + (–5) Start at –3. Move left 5 units. –3 + (–5) = –8

“Adding Integers” (1-5) To add integers using a model, create a symbol (like a yellow box) to represent (stand for) one positive unit and another symbol (like a red box) to represent one negative unit. Then, model the espression and cancel out each positive (yellow) and negative (red) pair, since Example: Use a model to find 2 + (-5). 2 + (-5) = -3.

– 4 Group and remove zero pairs. Adding Integers LESSON 1-5 Additional Examples Use models to find (–7) + 3. (–7) + 3 Model the sum. – 4 Group and remove zero pairs. Write the integer that the simplified model represents. (–7) + 3 = – 4

To add positive 4, move right 4 units to –16. Adding Integers LESSON 1-5 Additional Examples From the surface, a diver goes down 20 feet and then comes back up 4 feet. Find –20 + 4 to find where the diver is. Start at 0. To represent –20, move left 20 units. To add positive 4, move right 4 units to –16. –20 + 4 = –16 The diver is 16 feet below the surface.

“Adding Integers” (1-5) What are the rules for adding integers with the same and different signs? Rule: Adding Numbers With the Same Signs: To add to numbers with the same signs, add their absolute values (add them) and use the same sign as both the addends (the numbers you’re adding) Examples: 2 + 6 = 8 -2 + (-6) = -8 Rule: Adding Numbers With Different Signs: To add to numbers with different signs, find the difference of their absolute values (subtract them) and use the same sign as the addend with the greatest absolute value (take the sign from the bigger number). Examples: -2 + 6 = 4 2 + (-6) = -4

Since both integers are negative, the sum is negative. Adding Integers LESSON 1-5 Additional Examples Find each sum. a. –20 + (–15) Since both integers are negative, the sum is negative. –20 + (–15) = –35 b. 13 + (–17) Find the difference of the absolute values. |–17| – |13| = 17 – 13 = 4 Simplify. Since –17 has the greater absolute value, the sum is negative. 13 + (–17) = – 4

Find the difference of the absolute values. |–30| – |22| = 30 – 22 Adding Integers LESSON 1-5 Additional Examples A player scores 22 points. He then gets a penalty of 30 points. What is the player’s score after the penalty? Write an expression. 22 + (–30) Find the difference of the absolute values. |–30| – |22| = 30 – 22 = 8 Simplify. Since –30 has the greater absolute value, the sum is negative. 22 + (–30) = – 8 The player’s score is – 8.

The sum of the two negative integers is negative. –11 + 13 + (–5) Adding Integers LESSON 1-5 Additional Examples Find –7 + (– 4) + 13 + (–5). Add from left to right. –7 + (– 4) + 13 + (–5)  The sum of the two negative integers is negative. –11 + 13 + (–5) |13| – |11| = 2. Since 13 has the greater absolute value, the sum is positive. 2 + (–5) –3 |5| – |2| = 3. Since –5 has the greater absolute value, the sum is negative. –7 + (– 4) + 13 + (–5) = –3

Find each sum. 1. –37 + (–5) 2. 14 + (–4) Adding Integers LESSON 1-5 Lesson Quiz Find each sum. 1. –37 + (–5) 2. 14 + (–4) 3. –100 + 5 + (–3) 4. 33 + ( 21) –42 10 – + ( 12) – –98