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Main Idea and New Vocabulary
NGSSS
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
Five-Minute Check
• Add integers.
• opposites
• additive inverse
MA.7.A.3.1 Use and justify the rules for adding, subtracting, multiplying, dividing, and finding the absolute value of integers.
Also addresses MA.7.A.3.2.
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
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.
Add Integers with Different Signs
Find 8 + (–7).
Answer: So, 8 + (–7) = 1.
+8–7
Find –5 + 4.
Add Integers with Different Signs
Answer: So, –5 + 4 = –1.
–5+4
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.
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.
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.
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
A. –50 + 10 = –40; the bird is 40 feet below where it started.
B. 50 + (–10) = 40; the bird is 40 feet above where it started.
C. 50 + 10 = 60; the bird is 60 feet above where it started.
D. –50 + (–10) = –60; the bird is 60 feet below where it started.
Write an addition expression to describe the situation. Then find the sum and explain the meaning. A bird flies up 50 feet and swoops back down 10 feet.
A. –14 + 10 = –4; Teresa still owes her brother $4.
B. –14 – 10 = –24; Teresa still owes her brother $24.
C. 14 + (–10) = 4; Teresa’s brother now owes her $4.
D. 14 + 10 = 24; Teresa’s brother now owes her $24.
Write an addition expression to describe the situation. Then find the sum and explain the meaning.Teresa owes her brother $14. She finds $10 and gives it to him.
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