Evaluating Algebraic Expressions

1-5 Subtracting Integers

Holt CA Course 2

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Georgia StandardsGeorgia Standards

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Evaluating Algebraic Expressions

1-5 Subtracting Integers

EQ: What are the rules for subtracting integers?Warm Up: Add the following

1. –7 + 2 4. –6 + (–28)

2. –12 + (–9) 5. 104 + (–87)

3. 32 + (–19) 6. –18 + (–24)

–5 –34

17

–42

–21

13

Evaluating Algebraic Expressions

1-5 Subtracting Integers

M7N1: Add, subtract, multiply, and divide rational numbers (integers, fractions, and terminating decimals) and take positive rational numbers to whole-number powers.

Understand the meaning of the absolute value of a number; interpret the absolute value as the distance of the number from zero on a number line; and determine the absolute value of real numbers.

Georgia Standards

Evaluating Algebraic Expressions

1-5 Subtracting Integers

When you subtract a positive integer, the difference is less than the original number. Therefore, you move to the left on the number line. To subtract a negative integer, you move to the right.

You can also subtract an integer by adding its opposite. We also refer to this as “keep, change, change.” You can then use the rules for addition of integers.

Evaluating Algebraic Expressions

1-5 Subtracting IntegersAdditional Example 1: Subtracting Integers

A. –7 – 4

–7 – 4 = –7 + (–4)

B. 8 – (–5)

8 – (–5) = 8 + 5

C. –6 – (–3)

–6 – (–3) = –6 + 3

= –11

= 13

= –3

Add the opposite of 4. (Keep, change, change)

Keep, change, change.

Keep, change, change.

Same sign; use the sign of the integers.

Same sign; use the sign of the integers.

6 > 3; use the sign of 6.

Subtract.

Evaluating Algebraic Expressions

1-5 Subtracting IntegersCheck It Out! Example 1

A. 3 – (–6)

3 – (–6) = 3 + 6

B. –4 – 1

–4 – 1 = –4 + (–1)

C. –7 – (–8)

–7 – (–8) = –7 + 8

= 9

= –5

= 1

Keep, change, change.

Keep, change, change.

Keep, change, change.

Same signs; use the sign of the integers.

Same sign; use the sign of the integers.

8 > 7; use the sign of 8.

Subtract.

Evaluating Algebraic Expressions

1-5 Subtracting Integers

–9 – y if y = –4

–9 + 4

–5

Evaluate the expression for the given value of the variable.

–9 – y

–9 – (–4) Substitute –4 for y.

Keep, change, change.

9 > 4; use the sign of 9.

Additional Example 2A: Evaluating Expressions with Integers

Evaluating Algebraic Expressions

1-5 Subtracting Integers

n – 6 for n = –2

n – 6

–2 – 6 Substitute –2 for n.

Evaluate the expression for the given value of the variable.

–2 + (–6)

–8

Keep, change, change.

Same sign; use the sign of the integers.

Additional Example 2B: Evaluating Expressions with Integers

Evaluating Algebraic Expressions

1-5 Subtracting Integers

|8 – j | + |–2| for j = –6

|8 – j| + |–2|

|8 – (–6)| + |–2| Substitute –6 for j.

Evaluate the expression for the given value of the variable.

|14| + |–2|

14 + 2

Keep, change, change.

8 + 6 = 14.

Additional Example 2C: Evaluating Expressions with Integers

|8 + 6| + |–2|

The absolute value of 14 is 14, and the absolute value of –2 is 2. Add.16

Evaluating Algebraic Expressions

1-5 Subtracting Integers

–5 – r for r = –2

–5 + 2

–3

Evaluate the expression for the given value of the variable.

–5 – r

–5 – (–2) Substitute –2 for r.

Keep, change, change.

5 > 2; use the sign of 5.

Check It Out! Example 2A

Evaluating Algebraic Expressions

1-5 Subtracting Integers

a – 7 for a = –9

a – 7

–9 – 7 Substitute –9 for a.

Evaluate the expression for the given value of the variable.

–9 + (–7)

–16

Keep, change, change.

Same sign; use the sign of the integers.

Check It Out! Example 2B

Evaluating Algebraic Expressions

1-5 Subtracting Integers

|11 – m | + 7 for m = –3

|11 – m| + 7

|11 – (–3)| + 7 Substitute –3 for m.

Evaluate the expression for the given value of the variable.

|14| + 7

14 + 7

Add the opposite of –3.

11 + 3 = 14.

Check It Out! Example 2C

|11 + 3| + 7

The absolute value of 14 is 14. Add.21

Evaluating Algebraic Expressions

1-5 Subtracting Integers

The top of the Sears Tower, in Chicago, is 1454 feet above street level, while the lowest level is 43 feet below street level. How far is it from the lowest level to the top?

Additional Example 3: Architecture Application

1454 – (–43) Subtract the lowest level from the top.

1454 + 43 Keep, change, change.

1497 Same sign; use the sign of the integers.

It is 1497 feet from the lowest level to the top.

Evaluating Algebraic Expressions

1-5 Subtracting Integers

The distance from the high dive to the swimming pool is 10 feet. The pool is 12 feet deep. What is the total distance from the high dive to the bottom of the pool?

Check It Out! Example 3

10 – (–12) Subtract the depth of the pool from the height of the high dive.

10 + 12 Keep, change, change.

22 Same sign; use the sign of the integers.

It is 22 feet from the diving board to the bottom of the pool.

Evaluating Algebraic Expressions

1-5 Subtracting IntegersLesson Quiz

Subtract.

1. –6 – (–4)

–2 –6 9

2. –3 – 3 3. 4 – (–5)

Evaluate each expression for the given value of the variable.

4. 9 – s if s = –5 14

5. –4 – w + 5 if w = 21 –20

6. Suretta is flying in an airplane and rises an additional 20 feet. Then she descends 190 feet toward the ground. How far below her original height did Suretta go? 170 feet