Learn to add integers.

Adding Integers To add two integers with the same sign, find the sum of their absolute values. Use the sign of the two integers. To add two integers with different signs, find the difference of their absolute values. Use the sign of the integer with the greater absolute value.

The integers are the set of whole numbers and their opposites The integers are the set of whole numbers and their opposites. Including zero. The whole numbers are the counting numbers and zero: 0, 1, 2, 3, . . . . Remember!

The opposite of a number is the same distance from 0 on a number line as the original number. Zero is its own opposite. –4 and 4 are opposites –4 4 • • –5–4–3–2–1 0 1 2 3 4 5 Negative integers Positive integers 0 is neither positive nor negative

A number’s absolute value is its distance from 0 on a number line. They are always positive or zero. The symbol is read as “the absolute value of.” For example -3 is the absolute value of -3. Reading Math

Example 1: Modeling Integer Addition Use a number line to find each sum. –7 + (–4) +(–4) –7 2 –14 –12 –10 –8 –6 –4 –2 0 Start at 0. Move left 7 spaces. Then move left 4 more spaces. –7 + (–4) = –11

Example 2: Modeling Integer Addition Use a number line to find each sum. –12 + 19 19 –12 2 4 6 8 –12 –10 –8 –6 –4 –2 0 Start at 0. Move left 12 spaces. Then move right 19 spaces. –12 + 19 = 7

Insert Lesson Title Here Example 3 Use a number line to find each sum. –4 + (–5) +(–5) –4 2 –14 –12 –10 –8 –6 –4 –2 0 Start at 0. Move left 4 spaces. Then move left 5 more spaces. –4 + (–5) = –9

Insert Lesson Title Here Example 4 Use a number line to find each sum. –7 + 12 12 –7 2 4 6 8 –12 –10 –8 –6 –4 –2 0 Start at 0. Move left 7 spaces. Then move right 12 spaces. –7 + 12 = 5

Example 5: Adding Integers Using Absolute Values Find each sum. –4 + 8 The signs are different. Find the difference of the absolute values. –4 + 8 Think: 8 – 4 = 4. Use the sign of the integer with the greater absolute value. 4

Example 6: Adding Integers Using Absolute Values Find each sum. 23 + (–35) The signs are different. Find the difference of the absolute values. 23 + (–35) Think: 35 – 23 = 12. Use the sign of the integer with the greater absolute value. –12

Insert Lesson Title Here Example 7 Find each sum. –5 + 3 The signs are different. Find the difference of the absolute values. –5 + 3 Think: 5 – 3 = 2. Use the sign of the integer with the greater absolute value. –2

Insert Lesson Title Here Example 8 Find each sum. –13 + (–24) The signs are the same. Find the sum of the absolute values. –13 + (–24) Think: 13 + 24 = 37. –37 Use the sign of the two integers.

Insert Lesson Title Here Example 9 The French Club was raising money for a trip to Washington D.C. Their car wash raised $730. They had expenses of $52. Use integer addition to find the club’s total profit or loss. 730 + (–52) Use negative for the expenses. Find the differences of the absolute values. 730 – 52 678 The answer is positive. The club earned $678.

Insert Lesson Title Here Exit Ticket Use a number line to find the sum. 1. –7 + (–6) Find each sum. 2. –15 + 24 + (–9) 3. –24 + 7 + (–3) 4. Evaluate x + y for x = –2 and y = –15. –13 2 –14 –12 –10 –8 –6 –4 –2 0 –20 –17

Insert Lesson Title Here The math club’s income from a bake sale was $217. Advertising expenses were $32. Use integer addition to find the club’s total profit or loss? $185 profit