Main Idea and New Vocabulary

Example 1:Add Integers with the Same Sign

Key Concept: Add Integers with the Same Sign

Example 2:Add Integers with the Same Sign

Key Concept: Additive Inverse Property

Example 3: Add Integers with Different Signs

Example 4: Add Integers with Different Signs

Key Concept: Add Integers with Different Signs

Example 5: Add Integers with Different Signs

Example 6: Add Integers with Different Signs

Example 7: Add Integers with Different Signs

Example 8: Real-World Example

• Add integers.

• opposites

• additive inverse

Add Integers with the Same Sign

Find –6 + (–3).

• Start at 0. Move 6 units to the left to show –6.

• From there, move 3 units to the left to show –3.

Answer: So, –6 + (–3) = –9.

–6–3

A. –4

B. –2

C. 0

D. 4

Find –2 + (–2).

Find –34 + (–21).

Add Integers with the Same Sign

–34 + (–21) = –55 Both integers are negative, so the sum is negative.

Answer: So, –34 + (–21) = –55.

A. 22

B. 6

C. –6

D. –22

Find –14 + (–8).

Add Integers with Different Signs

Find 8 + (–7).

Answer: So, 8 + (–7) = 1.

+8–7

A. –4

B. –2

C. 2

D. 4

Find 3 + (–1).

Find –5 + 4.

Add Integers with Different Signs

Answer: So, –5 + 4 = –1.

–5+4

A. –11

B. –7

C. 7

D. 11

Find –9 + 2.

Add Integers with Different Signs

Find 2 + (–7).

2 + (–7) = –5 Subtract absolute values; 7 – 2 = 5. Since 7 has the greater absolute value, the sum is negative.

Answer: So, 2 + (–7) = –5.

A. 14

B. 2

C. –2

D. –14

Find 6 + (–8).

Add Integers with Different Signs

Find –9 + 6.

–9 + 6 = –3 Subtract absolute values; 9 – 6 = 3. Since 9 has the greater absolute value, the sum is negative.

Answer: So, –9 + 6 = –3.

A. 12

B. 10

C. –10

D. –12

Find –11 + 1.

Add Integers with Different Signs

Find 11 + (–4) + (–11).

11 + (–4) + (–11) = 11 + (–11) + (–4)Commutative Property (+)

= [11 + (–11)] + (–4)Associative Property (+)

= 0 + (–4) Additive Inverse Property

= –4 Additive Identity Property

Answer: The solution is –4.

A. –12

B. –10

C. –7

D. –2

Find 5 + (–7) + (–5).

FINANCIAL LITERACY Small businesses manage their inventory using integers. The cost of goods sold is calculated as starting inventory plus cost of items bought during the year plus a negative value on the ending inventory for the year. For example, a small horse farm owner might have a starting inventory of horses valued at $9,500, purchase a colt during the year for $2,000, and have an ending inventory value of $6,000. What is the cost of goods sold? Write an addition sentence to describe this situation. Then find the sum and explain its meaning.

$9,500 + $2,000 + (–$6,000) = $11,500 + (–$6,000) $9,500 + $2,000 = $11,500

= $5,500 Subtract the absolute values. Since $11,500 has the greater absolute value, the sum is positive.

Answer: The cost of goods sold is $5,500.

A. Point E is 4 feet lower than point A.

B. Point E is 6 feet lower than point A.

C. Point E is 8 feet lower than point A.

D. Point E is 10 feet lower than point A.

ROLLER COASTERS The graphic shows the change in height at several points on a roller coaster. Write an addition sentence to find the height at point E in relation to point A.

20 + (–32) + 16 + (–10) = –6