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Holt Algebra 1
1-2 Adding and Subtracting Real Numbers1-2&1-3
Holt Algebra 1
Warm Up
Lesson Presentation
Lesson Quiz
Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
Warm UpSimplify.
1.
3 2. –4
Write an improper fraction to represent eachmixed number.
3. 423
143
4. 767
557
Write a mixed number to represent each improper fraction.
5. 125 2
2
56. 24
9 2
2
3
|–3| –|4|
Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
Add real numbers.
Subtract real numbers.
Objectives
Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
All the numbers on a number line are called realnumbers. You can use a number line to modeladdition and subtraction of real numbers.
AdditionTo model addition of a positive number, move right. To model addition of a negative number move left.
Subtraction
To model subtraction of a positive number, move left. To model subtraction of a negative number move right.
Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
Example 1A: Adding and Subtracting Numberson 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
+ (–7)
–4+ (–7) = –11
To add –7, move left 7 units.
–4
–4 + (–7)
Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
Check It Out! Example 1c
Add or subtract using a number line.
–5 – (–6.5) Start at 0. Move left to –5.To subtract negative 6.5 move right 6.5 units.
8 7 6 5 4 3 2 1 0
–5
–5 – (–6.5) = 1.5
1 2
– (–6.5)
Holt Algebra 1
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
210123456 6543- - - - - -
|5| = 5|–5| = 5
Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
Add.
–5 + (–7)
Check It Out! Example 2a
When the signs are the same, find the sum of the absolute values.
Both numbers are negative, so the sum is negative.
–5 + (–7) = 5 + 7
5 + 7 = 12
–12
Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
Check It Out! Example 2b
Add.
–13.5 + (–22.3)
When the signs are the same, find the sum of the absolute values.
–13.5 + (–22.3)
–35.8 Both numbers are negative so,the sum is negative.
13.5 + 22.3
Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
Check It Out! Example 2c
Add.
x + (–68) for x = 52 First substitute 52 for x.
x + (–68) = 52 + (–68)
68 – 52
When the signs of the numbers are different, find the difference of the absolute values.
–16Use the sign of the number with the greater absolute value. The sum is negative.
Holt Algebra 1
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 distance from zero. They have the same absolute value.
Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
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 sameas adding the inverse of 6.
Subtracting a number is the same as adding theopposite of the number.
Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
Subtract.
13 – 21
Check It Out! Example 3a
13 – 21 To subtract 21 add –21.
When the signs of the numbers are different, find the difference of the absolute values: 21 – 13 = 8.
Use the sign of the number with the greater absolute value.
–8
= 13 + (–21)
Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
Check It Out! Example 3b
Subtract.
Both numbers are positive so, the sum is positive.
To subtract add .–3 12 3 1
2
When the signs of the numbers are the same, find the sum of the absolute values: = 4.3 1
212
+
4
Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
x – (–12) for x = –14
Check It Out! Example 3c
Subtract.
x – (–12) = –14 – (–12) First substitute –14 for x.
–14 + (12) To subtract –12, add 12.
When the signs of the numbers are different, find the difference of the absolute values: 14 – 12 = 2.
Use the sign of the number with the greater absolute value.
–2
Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
Add or subtract using a number line.
1. –2 + 9 7 2. –5 – (–3) –2
Add or subtract.
3. –23 + 42 19 4. 4.5 – (–3.7) 8.2
5.
Lesson Quiz
6. The temperature at 6:00 A.M. was –23°F.At 3:00 P.M. it was 18°F. Find the differencein the temperatures.41°F
Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
Multiply real numbers. Divide real numbers.
Objectives
Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
WORDS
Multiplying and Dividing Numbers with the Same Sign
If two numbers have the same sign, their product or quotient is positive.
NUMBERS 4 5 = 20
–15 ÷ (–3) = 5
Multiplying and Dividing Signed Numbers
Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
WORDS
Multiplying and Dividing Numbers with Different Signs
If two numbers have different signs, their product or quotient is negative.
NUMBERS6(–3) = –18
Multiplying and Dividing Signed Numbers
–18 ÷ 2 = –9
Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
Find the value of each expression.
–7The quotient of two numberswith different signs is negative.
Check It Out! Example 1a and 1b
1a. 35 (–5)
44 The product of two numberswith the same sign is positive.
1b. –11(–4)
Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
Find the value of each expression.
–6x = –6(7) First substitute 7 for x.
Check It Out! Example 1c
1c. –6x for x = 7
= –42 The product of two numbers with different signs is negative.
Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
Two numbers are reciprocals if their product is 1.A number and its reciprocal are called multiplicative inverses. To divide by a number, you can multiply by its multiplicative inverse.
Dividing by a nonzero number is the same as Multiplying by the reciprocal of the number.
Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
10 ÷ 5 = 2 10 ∙ = = 215
105
Multiplicative inverses
Dividing by 5 is the same as multiplying by thereciprocal of 5, .
Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
You can write the reciprocal of a number by switching the numerator and denominator. A whole number has a denominator of 1.
Helpful Hint
Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
Check It Out! Example 2a
Divide.
Write as an improper fraction.
To divide by , multiply by .
and have the same signs,
so the quotient is positive.
Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
Check It Out! Example 2b
Divide.
Write the reciprocal of .
To divide by , multiply by .
and have different signs,
so the quotient is negative.
Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
Check It Out! Example 2c
Divide.
Write as an improper fraction.
To divide by multiply by .
The signs are different so the quotient is negative.
Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
No number can be multiplied by 0 to give a product of 1, so 0 has no reciprocal. Because 0 has no reciprocal, division by 0 is not possible. We say that division by zero is undefined.
Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
Properties of Zero
WORDS
NUMBERS
ALGEBRA
Multiplication by ZeroThe product of any numberand 0 is 0.
13 · 0 = 0 0(–17) = 0
a · 0 = 0 0 · a = 0
Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
Properties of Zero
WORDS
NUMBERS
ALGEBRA
Zero Divided by a NumberThe quotient of 0 and any nonzero number is 0.
06 = 0
0 ÷ a = 0
0 ÷ 23 = 0
0a = 0
Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
Properties of Zero
WORDS
NUMBERS
ALGEBRA
Division by Zero
Division by 0 is undefined.
a ÷ 0 a0
12 ÷ 0Undefined
–5 0
Undefined
Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
Check It Out! Example 3a
Divide:
Multiply by the reciprocal.
Any number multiplied by0 equals 0.
Turn into an improperfraction.
Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
Check It Out! Example 3b and 3c
Divide:
3b. 0 ÷ 0
0 ÷ 0 = undefined Any number divided by 0 is undefined.
3c. (–12.350)(0)
(–12.350)(0) = 0 The product of any number and 0 is 0.
Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
Find the value of each expression.
1. 35–7 –5 2. 2x for x = –6 – 12
Lesson Quiz
Multiply or divide if possible.
3. –3 1 34 (0)4. –21
3 5. – 034
– 12 7
0 undefined
15 miles
6. A cyclist traveled on a straight road for 1 hours at a speed of 12 mi/h. How many miles did the cyclist travel?
14
Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
Homework:
Vocabulary for Sections 1-2 and 1-3
p. 17-18, #’s 17-43 Odd, 53, 55
p. 23-24, 13-61 Odd
This is a lot of problems!!! Don’t put it off!!!