Transcript Integers Comparing and Ordering

Integers:
Comparing and
Ordering
EQ
• How do we compare and order
rational numbers?
Rational Numbers
Rational Numbers
Integers
Whole Numbers
(Positive Integers)
Fractions/Decimals
Negative Integers
Rational numbers
•Numbers that can be written as a fraction.
Example: 2 = 2 = 2 ÷ 1 = 2
1
Whole Numbers
• Positive numbers that are not
fractions or decimals.
1
2
3
4
5
6
Integers
• The set of whole numbers and their
opposites.
-7 -6 -5 -4 -3 -2 -1 0
1
2
3
4
5
Positive Integers
• Integers greater than zero.
0
1
2
3
4
5
6
Negative Integers
• Integers less than zero.
-6 -5 -4 -3 -2 -1
0
Comparing Integers
• The further a number is to the right
on the number line, the greater it’s
value.
< -1
Ex: -3 ___
-5 -4 -3 -2 -1
.
.
0
1
2
3
4
5
-1 is on the right of -3, so it is the greatest.
Comparing Integers
• The farther a number is to the right
on the number line, the greater it’s
value.
> -5
Ex: 2 ___
-5 -4 -3 -2 -1
.
0
1
2
.
3
4
5
2 is on the right of -5, so it is the greatest.
Comparing Integers
• The farther a number is to the right
on the number line, the greater it’s
value.
> -2
Ex: 0 ___
-5 -4 -3 -2 -1
.
0
.
1
2
3
4
5
0 is on the right of -2, so it is the greatest.
Ordering Integers
When ordering integers from least to
greatest follow the order on the
number line from left to right.
Ex: 4, -5, 0, 2
-5 -4 -3 -2 -1
.
0
.
1
2
.
3
Least to greatest: -5, 0, 2, 4
4
.
5
Ordering Integers
When ordering integers from greatest
to least follow the order on the
number line from right to left.
Ex: -4, 3, 0, -1
-5 -4 -3 -2 -1
.
0
..
1
2
3
.
Greatest to least: 3, 0, -1, -4
4
5
Try This:
< 4
a. -13 ___
b. -4 ___ -7
<
< 32
c. -156 ___
d. Order from least to greatest:
-9, -3, 5, 15
15, -9, -3, 5 _______________
e. Order from greatest to least:
2, -7, -8, -16
-16, -7, -8, 2 _______________
EQ
• How do we find the absolute value of
a number?
Absolute Value
• The distance a number is from zero
on the number line.
Symbols: |2| = the absolute value of 2
Start at 0, count the jumps to 2.
-5 -4 -3 -2 -1
0
1
2
It takes two jumps from 0 to 2.
|2| = 2
3
4
5
Absolute Value
• The distance a number is from zero
on the number line.
Ex: |-4| =
Start at 0, count the jumps to -4.
-5 -4 -3 -2 -1
0
1
2
3
It takes four jumps from 0 to -4.
|-4| = 4
4
5
Solving Problems with
Absolute Value
When there is an operation inside the
absolute value symbols; solve the
problem first, then take the absolute
value of the answer.
Ex: |3+4| =|7| =7
Ex: |3|- 2 = 3-2 = 1
Hint: They are kind of like
parentheses – do them first!
Try This:
a. |15| = _____
15
b. |-12| = _____
12
13
c. |-9| + 4 = _____
d. |13 - 5| = _____
8