1 lesson 1.1.2 adding and subtracting integers adding and subtracting integers

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Lesson 1.1.2Lesson 1.1.2

Adding andSubtracting Integers

Adding andSubtracting Integers

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Lesson

1.1.2Adding and Subtracting IntegersAdding and Subtracting Integers

California Standard:Number Sense 2.3Solve addition, subtraction, multiplication, and division problems, including those arising in concrete situations, that use positive and negative integers and combinations of these operations.

What it means for you:You’ll learn to add positive and negative numbers to integers.

Key words:• positive• negative• integer

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Adding and Subtracting IntegersAdding and Subtracting Integers

You’ve met positive and negative numbers, and you know how to arrange them on the number line.

Lesson

1.1.2

This Lesson covers addition and subtraction of integers, including negative numbers.

0 1 2 3 4–1–2–3–4

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Adding and Subtracting IntegersAdding and Subtracting Integers

Adding a Positive Moves Right on the Number Line

In the last Lesson, you saw that numbers on the number line are greater the farther to the right they are.

Lesson

1.1.2

To add a positive integer, move that number of positions to the right on the number line.

When you add a positive integer to any number, you’re making it greater, so you move to the right.

It doesn’t make any difference whether the original number is positive or negative — you always move to the right.

0 1 2 3 4–1–2–3–4greatersmaller

5

0 1 2 3 4–1–2–3–4 5–5 6 7

Adding and Subtracting IntegersAdding and Subtracting Integers

Example 1

Using the number line, add 9 to –4.

Solution follows…

Lesson

1.1.2

Solution

Counting 9 spaces to the right of –4 on the number line shows that the answer is 5.

+1 +2 +3 +4 +5 +6 +7 +8 +9

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Adding and Subtracting IntegersAdding and Subtracting Integers

Adding a Negative Moves Left on the Number Line

When you add a negative integer, move that number of positions to the left on the number line.

Lesson

1.1.2

When you’re adding a negative number, it doesn’t matter whether you’re adding it to a positive or negative number — you always move to the left.

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Counting 6 spaces to the left of 5 on the number line shows that the answer is –1.

0 1 2 3 4–1–2–3–4 5–5 6 7

Adding and Subtracting IntegersAdding and Subtracting Integers

Example 2

Using the number line, add –6 to 5.

Solution follows…

Lesson

1.1.2

Solution

6 5 4 3 2 1

8

Counting 5 spaces to the left of –1 on the number line shows that the answer is –6.

–1 0 1 2 3–2–3–4–5 4–6 5 6

Adding and Subtracting IntegersAdding and Subtracting Integers

Example 3

Using the number line, add –5 to –1.

Solution follows…

Lesson

1.1.2

Solution

5 4 3 2 1

9

1. 7 + 3

2. –2 + 2

3. –8 + 4

4. 1 + 3

Adding and Subtracting IntegersAdding and Subtracting Integers

Guided Practice

Solution follows…

Lesson

1.1.2

Answer the following Exercises without using a calculator.Use a number line to help.

= 10

= 0

= –4

= 4

8 9 10 11 127654 13 14 15

+1 +2 +3

0 1 2 3 4–1–2–3–4 5 6 7

+1 +2

–6 –5 –4 –3 –2–7–8–9–10 –1 0 1

+1 +2 +3 +4

0 1 2 3 4–1–2–3–4 5 6 7

+1 +2 +3

10

5. –81 + 8

6. –9 + 11

7. 9 + (–2)

8. 35 + (–10)

Adding and Subtracting IntegersAdding and Subtracting Integers

Guided Practice

Solution follows…

Lesson

1.1.2

Answer the following Exercises without using a calculator.Use a number line to help.

= –73

= 2

= 7

= 25

–78 –77 –76 –75 –74–79–80–81–82 –73 –72 –71

+1 +2 +3 +4 +5 +6 +7 +8

–5 –4 –3 –2 –1–6–7–8–9 0 1 2

+1 +2 +3 +4 +5 +6 +7 +8 +9 +10 +11

6 7 8 9 105432 11 12 13

2 1

28 29 30 31 3227262524 33 34 35

2 14 36 58 710 9

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9. –5 + (–1)

10. 0 + (–5)

11. 36 + (–10)

12. –15 + (–7)

Adding and Subtracting IntegersAdding and Subtracting Integers

Guided Practice

Solution follows…

Lesson

1.1.2

Answer the following Exercises without using a calculator.Use a number line to help.

= –6

= –5

= 26

= –22

–3 –2 –1 0 1–4–5–6–7 2 3 4

2 14 35

–6 –5 –4 –3 –2–7–8–9–10 –1 0 1

1

29 30 31 32 3328272625 34 35 36

2 14 357 69 810

–20 –19 –18 –17 –16–21–22–23–24 –15 –14 –13

2 14 357 6

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Adding and Subtracting IntegersAdding and Subtracting Integers

Subtracting a Positive is Like Adding a Negative

You already know that to add a negative integer, you move that number of positions to the left on the number line.

The method for subtracting a positive integer is exactly the same.

Lesson

1.1.2

13

4 5 6 7 83210 9 10

Adding and Subtracting IntegersAdding and Subtracting Integers

Example 4

Using the number line, calculate 8 – 2.

Solution follows…

Lesson

1.1.2

Solution

The 2 tells you that you need to move 2 steps, and the “–” sign tells you that you need to move left.

So the answer is 6.

2 1

14

13. 7 – 3

14. –1 – 10

15. 8 – 8

Adding and Subtracting IntegersAdding and Subtracting Integers

Guided Practice

Solution follows…

Lesson

1.1.2

Answer the following Exercises without using a calculator.Use a number line to help.

= 4

= –11

= 0

–8 –7 –6 –5 –4–9–10–11–12 –3 –2 –1

2 14 357 69 810

3 4 5 6 7210–1 8 9 10

2 14 357 68

3 4 5 6 7210–1 8 9 10

2 13

15

16. 3 – 8

17. –2 – 9

18. 1 – 10

Adding and Subtracting IntegersAdding and Subtracting Integers

Guided Practice

Solution follows…

Lesson

1.1.2

Answer the following Exercises without using a calculator.Use a number line to help.

= –5

= –11

= –9

–6 –5 –4 –3 –2–7–8–9–10 –1 0 1

2 14 357 69 810

–2 –1 0 1 2–3–4–5–6 3 4 5

2 14 357 68

–8 –7 –6 –5 –4–9–10–11–12 –3 –2 –1

2 14 357 69 8

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Adding and Subtracting IntegersAdding and Subtracting Integers

Subtracting a Negative Is Like Adding a Positive

You’ve already seen that adding a negative means you move left on the number line. So subtracting a negative must mean you move right on the number line.

Another way of saying this is that subtracting a negative is the same as adding a positive.

Lesson

1.1.2

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Adding and Subtracting IntegersAdding and Subtracting Integers

Example 5

Calculate 8 – (–3).

Solution follows…

Lesson

1.1.2

Solution

8 – (–3)

This – sign tells you to go left on the number line…

…but this – sign reverses the direction again.

You end up moving 3 steps right on the number line. So you can just write 8 – (–3) as 8 + 3 = 11. 7 8 9 10 11 12

+1 +2 +3

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Adding and Subtracting IntegersAdding and Subtracting Integers

Guided Practice

Solution follows…

Lesson

1.1.2

Write Exercises 19–24 as additions, then find the solutions.

19. 14 – (–9)

20. 23 – (–10)

21. –9 – (–15)

22. 4 – (–4)

23. –4 – (–8)

24. –26 – (–17)

14 + 9 = 23

23 + 10 = 33

–9 + 15 = 6

4 + 4 = 8

–4 + 8 = 4

–26 + 17 = –9

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Adding and Subtracting IntegersAdding and Subtracting Integers

Independent Practice

Solution follows…

Lesson

1.1.2

–7

Write each of Exercises 2–5 as an addition problem.

2. 4 – 3 3. 7 – 8

4. –1 – 26 5. 4 – 5

4 + (–3)

–1 + (–26)

7 + (–8)

4 + (–5)

1. The water level of a lake in early April was 3 inches above normal.

The water level had dropped to –4 inches below normal by early May.

What integer can be added to 3 to get the water level, in inches, in early May?

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Write each of Exercises 6–9 as a subtraction problem.

6. 5 + (–9) 7. 1 + (–3)

8. 2 + (–1) 9. 433 + (–348)

Adding and Subtracting IntegersAdding and Subtracting Integers

Independent Practice

Solution follows…

Lesson

1.1.2

5 – 9

Find the answer to each of Exercises 10–13.

10. 4 + (–15) 11. 18 – 9

12. 23 + 6 13. 15 – (–3)

1 – 3

2 – 1 433 – 348

–11 9

29 18

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Adding and Subtracting IntegersAdding and Subtracting IntegersLesson

1.1.2

Round UpRound Up

Adding to and subtracting from integers is a matter of deciding which direction to move, then moving the correct distance.

When you’re deciding whether to go left or rightyou only need to think about whether you’re adding a positive or negative number — it doesn’t matter what you’re adding it to.