1-21-2 Adding and Subtracting Real NumbersAdding and ...blog.wsd.net/rejohnson/files/2010/09/5th-A1CH1L2.pdf · 1-21-2Adding and Subtracting Real NumbersAdding and Subtracting Real

1-2 Adding and Subtracting Real Numbers1-2Adding and SubtractingReal Numbers

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Lesson QuizLesson Quiz

1-2 Adding and Subtracting Real Numbers

Bell Quiz 1-2

Give two ways to write each algebra expression in words.

1. 8g

Evaluate each expression for m = 6, n = 3, and

p = 10.

4 pts

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p = 10.

2. p ÷ m

3. np

4. p - n

10 pts

possible

2 pts

2 pts

2 pts

1-2 Adding and Subtracting Real Numbers

Add real numbers.

Subtract real numbers.

Objectives

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1-2 Adding and Subtracting Real Numbers

Vocabulary

absolute value

opposites

additive inverse

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additive inverse

1-2 Adding and Subtracting Real Numbers

All the numbers on a number line are called real

numbers. You can use a number line to modeladdition and subtraction of real numbers.

+ • + = +(+) = +

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– • – =

+ • – =

– • + =

- (-) =

+(-) =

-(+) =

+

―

―

1-2 Adding and Subtracting Real Numbers

Example 1A: Adding and Subtracting Numbers

on a Number line

Add or subtract using a number line.

Start at 0. Move left to –4.

.

–4 + (–7)

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11 10 9 8 7 6 5 4 3 2 1 0

–4+ (–7) = –11

To add –7, move left 7 units.

1-2 Adding and Subtracting Real Numbers

Example 1B: Adding and Subtracting Numberson a Number line

Add or subtract using a number line.

Start at 0. Move right to 3.

To subtract –6, move right 6 units.

3 – (–6)

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To subtract –6, move right 6 units.

-3 -2 -1 0 1 2 3 4 5 6 7 8 9

3 – (–6) = 9

1-2 Adding and Subtracting Real Numbers

Add or subtract using a number line.

1a: –3 + 7

Check It Out! Example 1

-3 -2 -1 0 1 2 3 4 5 6 7 8 9

1b: –3 – 7

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1b: –3 – 7

11 10 9 8 7 6 5 4 3 2 1 0

1c: –5 – (–6.5)

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

1-2 Adding and Subtracting Real Numbers

The absolute value of a number is the distance from zero on a number line. The absolute value of 5 is written as |5|.

5 units 5 units

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210123456 6543- - - - - -

|5| = 5|–5| = 5

1-2 Adding and Subtracting Real Numbers

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1-2 Adding and Subtracting Real Numbers

Example 2A: Adding Real Numbers

Add.

When the signs of numbers are

different, find the difference of the

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Use the sign of the number with the greater absolute value.

The sum is negative.

absolute values:

1-2 Adding and Subtracting Real Numbers

Example 2B: Adding Real Numbers

Add.

y + (–2) for y = –6

First substitute –6 for y.

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When the signs are the same, find the sum of the absolute values: 6 + 2 = 8.

Both numbers are negative, so the sum is negative.

1-2 Adding and Subtracting Real Numbers

Add.

2a: –5 + (–7)

Check It Out! Example 2

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2b: –13.5 + (–22.3)

3b: x + (–68) for x = 52

1-2 Adding and Subtracting Real Numbers

Two numbers are opposites if their sum is 0. A number and its opposite are on opposite sides of zero on a number line, but are the same

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number line, but are the same distance from zero. They have the same absolute value.

1-2 Adding and Subtracting Real Numbers

A number and its opposite are additive inverses.

To subtract signed numbers, you can use additiveinverses.

Additive inverses

Subtracting 6 is the same

as adding the inverse of 6.

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11 – 6 = 5 11 + (–6) = 5

Additive inverses

Subtracting a number is the same as adding the

opposite of the number.

1-2 Adding and Subtracting Real Numbers

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1-2 Adding and Subtracting Real Numbers

Subtract.

–6.7 – 4.1

To subtract 4.1, add –4.1.

Example 3A: Subtracting Real Numbers

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When the signs of the numbers

are the same, find the sum of the

absolute values: 6.7 + 4.1 = 10.8.

Both numbers are negative, so

the sum is negative.

1-2 Adding and Subtracting Real Numbers

Subtract.

5 – (–4)

To subtract –4 add 4.

Example 3B: Subtracting Real Numbers

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To subtract –4 add 4.

Find the sum of the absolute values.

1-2 Adding and Subtracting Real Numbers

Subtract.

3a: 13 – 21

Check It Out! Example 3

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3b: x – (–12) for x = –14

1-2 Adding and Subtracting Real Numbers

Example 4: Oceanography Application

An iceberg extends 75 feet above the sea. The bottom of the iceberg is at an elevation of –247 feet. What is the height of the iceberg?

Find the difference in the elevations of the top of the iceberg and

the bottom of the iceberg.

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elevation at top of iceberg

75

Minus elevation at bottomof iceberg

–247

75 – (–247)

75 – (–247) = 75 + 247

= 322

The height of the iceberg is 322 feet.

–

1-2 Adding and Subtracting Real Numbers

HOMEWORKSec 1-2: (Pg 17) 1-3, 6-11, 13, 14, 17–25, 28–31, 37-40, 65, 66

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