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Pg. 67-70 # 14-50 e, 59, 61- 62

Pg. 67-70 # 14-50 e, 59, 61-62. 61. D 62. A

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Page 1: Pg. 67-70 # 14-50 e, 59, 61-62. 61. D 62. A

Pg. 67-70 # 14-50 e, 59, 61-62

Page 2: Pg. 67-70 # 14-50 e, 59, 61-62. 61. D 62. A
Page 3: Pg. 67-70 # 14-50 e, 59, 61-62. 61. D 62. A
Page 4: Pg. 67-70 # 14-50 e, 59, 61-62. 61. D 62. A

61. D62. A

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Page 7: Pg. 67-70 # 14-50 e, 59, 61-62. 61. D 62. A

Modeling Addition of Integers

+ – + –

+ –

To model addition problems involving positive and negative integers, you can

use tiles labeled and . Each represents positive 1, and each

represents negative 1. Combining a with a gives 0. You can use

algebra tiles to find the sum of –8 and 3.

1 Model negative 8 and positive 3 using algebra tiles.

+– – – – – – – – + +

2 Group pairs of positive and negative tiles. Count the remaining tiles. +

– – – – – – – –

+ +

3 The remaining tiles show the sum of –8 and 3.

–8 + 3 = –5

3

Each pair has a sum of 0.Each pair has a sum of 0.

– – – – –

–80

Page 8: Pg. 67-70 # 14-50 e, 59, 61-62. 61. D 62. A

The sum can be written as –2 + 5 = 3.

Addition can be modeled with movements on a number line.

You add a positive number by moving to the right.Model –2 + 5.

1–3 –2 –1 0 32– 4 4

Move 5 units to the right.Start at –2. End at 3.

• •

Adding Real Numbers

Page 9: Pg. 67-70 # 14-50 e, 59, 61-62. 61. D 62. A

The sum can be written as –2 + 5 = 3.

Addition can be modeled with movements on a number line.

You add a positive number by moving to the right.

You add a negative number by moving to the left.

Model –2 + 5.

1–3 –2 –1 0 32– 4 4

0– 4 –3 –2 –1 21–5 3

Move 5 units to the right.

Move 6 units to the left.

Model 2 + (–6).

Start at –2. End at 3.

• •

Start at 2.End at – 4.

••

Adding Real Numbers

The sum can be written as 2 + (–6) = – 4.

Page 10: Pg. 67-70 # 14-50 e, 59, 61-62. 61. D 62. A

The rules of addition show how to add two real numbers without a number line.

Adding Real Numbers

RULES OF ADDITION

TO ADD TWO NUMBERS WITH THE SAME SIGN:

1 Add their absolute values.

2 Attach the common sign.

Example: – 4 + (–5) – 4 –5+ = 9 –9

Page 11: Pg. 67-70 # 14-50 e, 59, 61-62. 61. D 62. A

The rules of addition show how to add two real numbers without a number line.

Adding Real Numbers

RULES OF ADDITION

TO ADD TWO NUMBERS WITH THE SAME SIGN:

1 Add their absolute values.

2 Attach the common sign.

Example: – 4 + (–5) – 4 –5+ = 9 –9

TO ADD TWO NUMBERS WITH OPPOSITE SIGNS:

1 Subtract the smaller absolute value from the larger absolute value.

2 Attach the sign of the number with the larger absolute value.

Example: 3 + (–9) –9 3– = 6 –6

Page 12: Pg. 67-70 # 14-50 e, 59, 61-62. 61. D 62. A

The rules of addition on the previous slide will help you find sums of positive and negative numbers. It can be shown that these rules are a consequence of the following Properties of Addition.

Adding Real Numbers

PROPERTIES OF ADDITION

COMMUTATIVE PROPERTY

The order in which two numbers are added does not change the sum.

a + b = b + a Example: 3 + (–2) = –2 + 3

ASSOCIATIVE PROPERTY

The way you group three numbers when adding does not change the sum.

(a + b) + c = a + (b + c) Example: (–5 + 6) + 2 = –5 + (6 + 2)

Page 13: Pg. 67-70 # 14-50 e, 59, 61-62. 61. D 62. A

The rules of addition on the previous slide will help you find sums of positive and negative numbers. It can be shown that these rules are a consequence of the following Properties of Addition.

Adding Real Numbers

PROPERTIES OF ADDITION

IDENTITY PROPERTY

The sum of a number and 0 is the number.

a + 0 = a Example: – 4 + 0 = – 4

PROPERTY OF ZERO (INVERSE PROPERTY)

The sum of a number and its opposite is 0.

a + (–a) = 0 Example: 5 + (–5) = 0

Page 14: Pg. 67-70 # 14-50 e, 59, 61-62. 61. D 62. A

Adding Three Real Numbers

Use a number line to find the following sum.

–3 + 5 + (– 6)

SOLUTION

0– 4 –3 –2 –1 21–5 3

Move 6 units to the left.

–3 + 5 = 2

End at – 4.

••Start at –3. Move 5 units to the right.

The sum can be written as –3 + 5 + (–6) = – 4.

Page 15: Pg. 67-70 # 14-50 e, 59, 61-62. 61. D 62. A

Finding a Sum

Find the following sums.

1.4 + (–2.6) + 3.1 Use associative property.= 1.4 + (–2.6 + 3.1)

Simplify.= 1.4 + 0.5

= 1.9

Page 16: Pg. 67-70 # 14-50 e, 59, 61-62. 61. D 62. A

Finding a Sum

Find the following sums.

1.4 + (–2.6) + 3.1 Use associative property.= 1.4 + (–2.6 + 3.1)

Simplify.= 1.4 + 0.5

= 1.9

– + 3 + 12

12

= – + + 312

12

– + + 312

12( ) =

= 0 + 3 = 3

Use commutative property.

Use associative property.

Use identity property and property of zero.

Page 17: Pg. 67-70 # 14-50 e, 59, 61-62. 61. D 62. A

Using Addition in Real Life

SCIENCE CONNECTION Atoms are composed of electrons, neutrons, and protons. Each electron has a charge of –1, each neutron has a charge of 0, and each proton has a charge of +1. The total charge of an atom is the sum of all the charges of its electrons, neutrons, and protons. An atom is an ion if it has a positive or a negative charge. If an atom has a charge of zero, it is not an ion. Are the following atoms ions?

Aluminum: 13 electrons, 13 neutrons, 13 protons

SOLUTION The total charge is –13 + 0 + 13 = 0, so the atom is not an ion. In chemistry, this aluminum atom is written as Al.

Page 18: Pg. 67-70 # 14-50 e, 59, 61-62. 61. D 62. A

Using Addition in Real Life

SCIENCE CONNECTION Atoms are composed of electrons, neutrons, and protons. Each electron has a charge of –1, each neutron has a charge of 0, and each proton has a charge of +1. The total charge of an atom is the sum of all the charges of its electrons, neutrons, and protons. An atom is an ion if it has a positive or a negative charge. If an atom has a charge of zero, it is not an ion. Are the following atoms ions?

Aluminum: 13 electrons, 13 neutrons, 13 protons

Aluminum: 10 electrons, 13 neutrons, 13 protons

SOLUTION The total charge is –10 + 0 + 13 = 3, so the atom is an ion. In chemistry, this aluminum atom is written as Al

3 +.

SOLUTION The total charge is –13 + 0 + 13 = 0, so the atom is not an ion. In chemistry, this aluminum atom is written as Al.

Page 19: Pg. 67-70 # 14-50 e, 59, 61-62. 61. D 62. A

Finding the Total Profit

A consulting company had the following monthly results after comparing income and expenses. Add the monthly profits and losses to find the overall profit or loss during the six-month period.

$12,932.54$7613.17$3825.01

JuneMayApril

–$4734.86–$6783.16–$13,142.50

MarchFebruaryJanuary

SOLUTION With this many large numbers, you may want to use a calculator.

13142.50 6783.16 4734.86

3825.01 7613.17 12932.54

+/– +

=

+/– + +/–

+ + + –289.8

The display is –298.8. This means the company had a loss of $289.80.

Page 20: Pg. 67-70 # 14-50 e, 59, 61-62. 61. D 62. A
Page 21: Pg. 67-70 # 14-50 e, 59, 61-62. 61. D 62. A

Check Yourself

Pg. 77-79 #12-50 e, 60-61