Adding Integers With The Same Sign Practice And Problem Solving ... - Free Printable

Let's solve the problem step by step based on the worksheet titled "Adding Integers with the Same Sign".

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Section 1: Find each sum. Write counters are positive, black counters are negative.

#### Problem 1: -4 + (-3)

- a. How many counters are there?
→ We have 4 negative counters (from -4) and 3 more negative counters (from -3).
→ Total = 4 + 3 = 7 counters

- b. Do the counters represent positive or negative integers?
→ All counters are negative (black), so they represent negative integers

- c. -4 + (-3) = ?
→ Adding two negative numbers: -4 - 3 = -7

✔ Answer: -7

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#### Problem 2: 4 + (-7)

Wait — this is not adding integers with the same sign!
4 is positive, -7 is negative → different signs.

But the title says "Adding Integers with the Same Sign", so maybe it's a typo or mislabeling?

Let’s look at the actual problems:

Wait — Problem 2 is 4 + (-7) — different signs. But let’s check what the worksheet asks.

Actually, the instructions say: *"Find each sum. Write counters are positive, black counters are negative."*
And the image shows:

> 2. 4 + (-7)

With 4 white counters and 7 black counters.

So:
- a. How many counters are there?
→ 4 + 7 = 11 counters

- b. Do the counters represent positive or negative integers?
→ Mixed: 4 positive (white), 7 negative (black)

- c. 4 + (-7) = ?
→ This is different signs, so we subtract: |7 - 4| = 3, and since negatives are greater in number, result is -3

But wait — the section is titled "Adding Integers with the Same Sign", but this problem has different signs.

Let’s double-check the worksheet.

Looking closely at the worksheet:

The first two problems are:

1. -4 + (-3) → both negative → same sign ✔
2. 4 + (-7) → one positive, one negative → different signs ✘

But the worksheet might be including mixed-sign examples too. Let's proceed carefully.

We'll assume the worksheet includes both types, even if the title is misleading.

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Section 2: Model addition problem on the number line to find each sum

#### Problem 3: -3 + (-2)

- Start at -3
- Add -2 → move 2 units to the left
- End at: -5

✔ Answer: -5

#### Problem 4: -5 + (-4)

- Start at -5
- Move 4 units left → -9

✔ Answer: -9

#### Problem 5: -6 + (-6)

- Start at -6
- Move 6 units left → -12

✔ Answer: -12

#### Problem 6: -7 + (-5)

- Start at -7
- Move 5 units left → -12

✔ Answer: -12

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Section 3: Find each sum

Now we do direct calculations.

#### 7. -7 + (-1) = ?
→ Both negative: -7 -1 = -8

#### 8. 39 + (-17) = ?
→ Different signs: 39 - 17 = 22, positive because 39 > 17 → +22

#### 9. -10 + (-9) = ?
→ Both negative: -10 -9 = -19

#### 10. -303 + (-205) = ?
→ Both negative: -303 - 205 = -508

#### 11. -5 + (-4) = ?
→ Both negative: -5 -4 = -9

#### 12. 51 + (-42) = ?
→ Different signs: 51 - 42 = 9, positive → +9

#### 13. -55 + (-75) = ?
→ Both negative: -55 -75 = -130

#### 14. -170 + (-109) = ?
→ Both negative: -170 -109 = -279

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Bonus Problem:

> A construction crew is digging a hole. On the first day, they dig a hole 3 feet deep. On the second day, they dig 2 more feet. On the third day, they dig 4 more feet. Write a sum of negative numbers to represent this situation. Find the total sum and explain how it related to the problem.

- Each day they go deeper → depth increases in negative direction.
- First day: -3 ft
- Second day: -2 ft
- Third day: -4 ft

Sum: -3 + (-2) + (-4)

→ Combine: -3 -2 -4 = -9

✔ Answer: -9 feet

Explanation: The total depth of the hole is 9 feet below ground level. Since the crew dug deeper each day, the total change in elevation is -9 feet. The negative sign indicates downward direction.

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✔ Final Answers:

#### Section 1:
1. a. 7 counters
b. Negative
c. -7

2. a. 11 counters
b. Mixed (positive and negative)
c. -3

#### Section 2:
3. -5
4. -9
5. -12
6. -12

#### Section 3:
7. -8
8. +22
9. -19
10. -508
11. -9
12. +9
13. -130
14. -279

#### Bonus:
- Sum: -3 + (-2) + (-4) = -9
- Total depth: 9 feet below ground
- The negative sum represents the total downward movement.

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Let me know if you'd like a visual explanation or number line diagrams!