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Holt Algebra 1

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

Holt Algebra 1

Warm Up

Lesson Presentation

Lesson Quiz

Holt Algebra 1

1-2 Adding and Subtracting Real Numbers

Add real numbers.

Subtract real numbers.

Objectives

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Vocabulary

absolute value

opposites

additive inverse

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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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Example 1A: Adding and Subtracting Numbers

on a Number line

Add or subtract using a number line.

Start at 0. Move left to –4.

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

–4+ (–7) = –11

To add –7, move left 7 units.

–4 + (–7)

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Example 1B: Adding and Subtracting Numberson a Number line


Start at 0. Move right to 3.

To subtract –6, move right 6 units.

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

3 – (–6) = 9

3 – (–6)

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1a: –3 + 7

Check It Out! Example 1

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

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

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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

210123456 6543- - - - - -

|5| = 5|–5| = 5

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Holt Algebra 1


Example 2A: Adding Real Numbers

Add.

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

The sum is negative.

When the signs of numbers are

different, find the difference of the

absolute values:

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Example 2B: Adding Real Numbers

Add.

y + (–2) for y = –6

First substitute –6 for y.

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.

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Add.

2a: –5 + (–7)


2b: –13.5 + (–22.3)

2c: x + (–68) for x = 52

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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 distance from zero. They have the same absolute value.

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A number and its opposite are additive inverses.

To subtract signed numbers, you can use additiveinverses.

11 – 6 = 5 11 + (–6) = 5

Additive inverses

Subtracting 6 is the same

as adding the inverse of 6.

Subtracting a number is the same as adding the

opposite of the number.

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Holt Algebra 1


Subtract.

–6.7 – 4.1

To subtract 4.1, add –4.1.

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.

Example 3A: Subtracting Real Numbers

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Subtract.

5 – (–4)

To subtract –4 add 4.

Find the sum of the absolute values.

Example 3B: Subtracting Real Numbers

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Subtract.

3a: 13 – 21


3b: x – (–12) for x = –14

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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.

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.

–

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HOMEWORKSec 1-2: (Pg 17) 1-3, 6, 9, 13, 14, 17–25, 28–31, 37-42, 65, 66

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