1) Evaluate 7 cubed2) Solve: 2 •12 ÷ 3 + 2

3) Solve: (5 +3) + 8 ÷ 2

INTEGERS

Real Numbers

Negative

Positive

Zero

-

+

21/3

427

3

Rational

5,600

0

zero

-1

Integers

What model can be used to show positive and negative rational

numbers?How can I use models to prove

that opposites combine to 0?What is absolute value? How can

I show it on a number line?

integers- the set of whole numbers and their opposites (positive or negative)

additive inverse- the sum of a number and its opposite

absolute value- the distance of a number from zero on a number line; shown by l l

Integers are positive and negative numbers.

…, -6, -5, -4, -3, -2, -1, 0, +1, +2, +3, +4, +5, +6, …

Each negative number is paired with a positive number the same distance from 0 on a number line. These numbers are called opposites.

-3 -2 -1 20 1 3

Numbers to the left of zeroare less than zero.

Numbers to the right of zero are more than

zero.

The numbers –1, -2, -3 are called negative integers. The number negative 3 is written –3.

The numbers 1, 2, 3 are called positive integers. The number positive 4 is written +4 or 4.Zero is neither

negative nor positive.

0102030

-10-20-30-40-50

Let’s say your parents bought a car buthad to get a loan from the bank for $5,000.When counting all their money they add in -$5.000 to show they still owe the bank.

If you don’t see a negative or positive sign in front of a number it is positive.

9 = 9+

•The opposite of a number is the same distance from 0 on a number line as the original number, but on the other side of 0; zero is its own opposite.•When you find the additive inverse, you take the opposites and add them together; the sum will ALWAYS be ZERO.

1 2 3 4 5 • •

–5–4–3–2–1 0

–4 and 4 are opposites; when you find the additive inverse you add (-4)+4=0

–4 4

Opposites and Additive Inverses

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

1 2 3 4 5 6 7 8 –8 –7–6–5–4 –3–2 –1 0

The integer (-9) and 6 are graphed on the number line along with its

opposites; What would be the additive inverses? How?

The symbol is read as “the absolute value of.” For example -3 is the absolute value of -3.

Reading Math

Use a number line to find each absolute value.

Absolute Value Example 1

|8|

1 2 3 4 5 6 7 8 –8 –7–6–5–4 –3–2 –1 0

8 units

8 is 8 units from 0, so |8| = 8.

Absolute Value Example 2

Use a number line to find each absolute value.

|–12|

–12 –11 –10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2

–12 is 12 units from 0, so |–12| = 12.

12 units

1 2 3 4 5 6 7 8 –8 –7–6–5–4 –3–2 –1 0

2

1 2 3 4 5 6 7 8 –8 –7–6–5–4 –3–2 –1 0

7

Absolute Value Examples 3 & 4

Being in class<<<<<<talking on the phone

Playing X-Box>>>>>>Doing chores

What does the symbol “>” and “<“ mean?

•Integers increase in value as you move to the right along a number line.

•They decrease in value as you move to the left.

The symbol < means “is less than,” and the symbol > means “is greater than.”

Remember!

You can compare and order integers by graphing them on a number line.

Compare the integers. Use < or >.

Comparing Example 1

-4 is farther to the right than -11, so -4 > -11.

-4 -11>

-15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1

Use a number line to order the integers from least to greatest.

Comparing Example 2

–3, 6, –5, 2, 0, –8

The numbers in order from least to greatest are –8, –5, –3, 0, 2, and 6.

1 2 3 4 5 6 7 8 –8 –7–6 –5–4 –3 –2 –1 0

What are integers? When would you use negative numbers in the real world?

Do the numbers increase or decrease as you move to the left of zero? What happens when you move to the right of zero?

< means:

> means:

Place homework in a safe place within your binder; remember to

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