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Seatwork:Evaluate each expression for a = 3 and b = 6.

September 17, 2013

63=2

4 (3 )=12

6+11=173 (6 )−3=18−3=15

Add real numbers.

Subtract real numbers.

Objectives

Vocabulary

real numbersnumber linenegative numbersabsolute value

All the numbers on a number line are called real numbers.

Number lines can be used to model addition and subtraction of real numbers.

A negative number is any real number whose value is less than zero. They are represented using a negative (-) symbol.

Real and Negative Numbers

Negative numbers are always represented by a minus (-), or negative sign.

Sometimes the negative sign will be inside or outside of a parenthesis.◦ Ex: Negative Eight

-8 -(8) (-8)

Positive numbers will either have a plus (+) sign or no sign.◦ Ex: Positive Four

4 +(4) +4

Representing a Negative or Positive Number

Temperature◦ -15℉

Money◦ Debt: Owing money; Negative bank account

balance◦ - $20

Distance below sea level◦ -67 ft

Examples of Negative Numbers

Reduce the following:

Solve the following:

Examples

+10𝑜𝑟 10−57

−4+63𝑜𝑟 63

7−3=44+4=8

Ex. 1:On one particularly cold winter day, your thermometer shows that it is 5℉ outside. According to the meteorologist, it will be 10 degrees colder tomorrow. What temperature will it be tomorrow?

Number Line Practice

Ex. 2:Before going to the movies with a friend, you check your bank account and see that you have a balance of $10. At the movies you end up spending $25 in tickets and food. How much money do you have in your account?

Number Line Practice

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)

Example 1B: Adding and Subtracting Numbers

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

+ 3

3 – (–6) = 9

3 – (–6)

–6

Add or subtract using a number line.

–3 + 7

Check It Out! Example 1a

Start at 0. Move left to –3.

To add 7, move right 7 units.

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

–3

+7

–3 + 7 = 4

Check It Out! Example 1b

Add or subtract using a number line.

–3 – 7 Start at 0. Move left to –3.

To subtract 7 move left 7 units.

–3–7

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

–3 – 7 = –10

We can also represent numerical expressions using colored counters.◦ Red counters are negative numbers.◦ Yellow counters are positive numbers.◦ One yellow counter (+1) plus one red counter (-1)

equals zero. 1+(-1)=0

Ex.1.

Subtraction with Counters

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

Absolute Value

Find the absolute value of the following numbers:

1. 12|12|=12

2. -6|-6|=6

3. 42|42|=42

4. -42|-42|=42

Absolute Value Practice

Adding/Subtracting Real #’s

Steps:

1. Simplify the signs2. If the signs are the same, add their

absolute values and keep the same sign.3. If the signs are different, subtract their

absolute values and keep the sign of the number with the greater absolute value.

Adding/Subtracting Negative/Positive Numbers

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:

Additional Example 2: Adding Real Numbers

Add.

B. –6 + (–2)

(6 + 2 = 8)

–8 Both numbers are negative, so the sum is negative.

When the signs of numbers are the same, add the absolute values:

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

Check It Out! Example 2c

c. 52 + (–68)

(68 – 52 = 16)

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

Different signs: subtract the absolute values.

Add.

Solve the following expressions:

Calculator Practice

Section 1.2 Practice Worksheet Section 1.2 Questions:

◦ #3, 11, 15, 19-25 odd◦ #29, 33-37 odd

◦ Use your answer key & selected answers in your student handbook (online) to check your answers!

◦ If you’re having trouble, watch the example lesson tutorial videos.

Homework

Solve the following expressions:

Exit Questions