Download Name Date Period ______ Study Guide for Absolute Value

Name _____________________________________________
Date _____________________
Period ________
Study Guide for Absolute Value, Operations with Integers, Exponents, Order of Operations, Square Roots
INTEGERS – the set of positive whole numbers, negative whole numbers and zero
…, -4, -3, -2, -1, 0, 1, 2, 3, 4, …
OPPOSITES two numbers that are the same distance from zero on a number line
Example: 6 and -6
ADDITIVE INVERSES: 6 + -6 = 0
ABSOLUTE VALUE – the distance a number is from zero on the number line, represented by the symbol
-13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
1 2 3
4 5 6 7
8
x
9 10 11 12 13 14
Notice how the arrows start at different numbers (-9 and 9), but both move the same amount of space to get to zero!
Examples:
1)
|7| = 7 (spaces to get to zero)
2)
|-10| = 10 (spaces to get to zero)
3)
-|-9| = -9 (take the abs. value of -9, which is 9, and then the outside negative stays with the answer)
4) |-12| + |5| = 12 + 5 = 17
Your Turn to Practice:
1) |-18| = _____
2) |3| = _____
3) -|4| = _____
4) |9| - |-3| = ____
5) |-10| + |8| = ____
6) |-6|
|-2|
COMPARE/ORDER INTEGERS
-13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
1 2 3
Remember that as negative numbers start to move to the left (
4 5 6 7
8
9 10 11 12 13 14
) they will become smaller in value.
Example:
Directions: Compare the integers.
-9
-5
can be compared as
-9 < -5
Ordering the Integers: Put the integers in order from least (small) to greatest (big):
-9, 3, 0, -2, 1, -12, 5, 8, -8, -6
Least to Greatest: -12, -9, -8, -6, -2, 0, 1, 3, 5, 8
Your Turn to Practice:
Order the Integers from Least to Greatest:
-10, 3, 9, 2, -8, 8, -4, -5, 0, -1
(Smallest)______________________________________________________________ (Greatest)
Compare the integers using <, >, or =.
-5
8
4
0
-3
-6
- 10
-4
5+4 = 9 because
signs are the same
RULES FOR ADDING INTEGERS
Same signs  add the numbers, keep the sign
Example: - 5 + - 4 = - 9
Different signs  subtract the numbers, take the sign of the larger number
Example: - 5 + 3 = - 2
5 – 3 = 2 because
signs are different,
used a negative
sign because the 5
is larger
STEPS FOR SUBTRACTING INTEGERS
Step 1: Use Keep (1st integer), Change (subtraction to addition), Change (to opposite sign)
Step 2: Solve the problem using the addition of integer rules
Example:
-4 – (-6)
Keep the -4, Change - to +, Change -6 to +6
-4 + 6
Now use addition rules to solve, different signs  subtract (6 - 4)
+2
Take the sign of the larger number, which is the positive 6
Your Turn to Practice:
1) -7 + -8 = ____
2) -10 + 5 = ____
3) 9 + - 7 = ____
5) -20 + 14 = ____
6) 8 - -5 = _____
7) 10 - 13 = ______
4) 6 + - 11 = ____
8) - 5 - 7 = _____
RULES FOR MULTIPLYING/ DIVIDING INTEGERS
____ X or ÷____ ___________
+
+
 + answer
­
­
 + answer
­
+
 ­ answer
+
­
 ­ answer
Examples
10 ÷ 2 = 5
-4 x -3 = 12
-15 ÷ 5 = -3
5 x -4 = -20
Your Turn to Practice:
1)
-9 x 3 = ____
5) 30 ÷ -10 = ____
2) -5 x -4 = ____
3)
6 x -10 = ____
4) -3 x -7 = ____
6) -25 ÷ 5 = ____
7)
-24 ÷ -6 = ____
8)
18 ÷ 6 = ____
EXPONENTS
Example:
24
Exponent (tells you how many times to multiply the base by itself)
Base
Evaluate the expression: 24 = 2 · 2 · 2 · 2 = 16
*Important Fact – any number to the zero power equals one.
Your Turn to Practice:
X0 = 1
Evaluate the expression or write the product in exponential form.
1) 9 · 9 · 9 · 9 · 9 · 9 = ______
2) 7 squared = ___________= ______
3) 43 = ___________ = ______
4) 2 · 2 · 2 · 2 · 2 · 2 · 2 = _____
SQUARES AND SQUARE ROOTS
When squaring a number – multiply the number by itself.
Example: Find the square of 8.  8 x 8 or 82 = 64
Your Turn to Practice:
1)
Find the square of each number.
12 = ________ = _____
2)
15 = ________ = _____
3) 4 = ________ = _____
When finding the square root of a number – break down the number inside the square root symbol to find a number
that multiplies by itself
Example: Find the square root of 121 
121 =
11x11 = 11
** For every pair of the same number inside the square root symbol, one of the pair comes outside of the square root
symbol in the answer.
Your Turn to Practice:
1)
81 = _______
2)
100 = ________
3)
25 = _______
ORDER OF OPERATIONS – tells how to solve a mathematical sentence
Parentheses (Please)
Exponents (Excuse)
Multiplication (My)
Division (Dear)
solve left to right as they come up
Addition (Aunt)
Subtraction (Sally)
solve left to right as they come up
Example:
(60 ÷ 6) – 42 + 12
10 – 42 + 12
Solve the parenthesis: (60 ÷ 6) =10
10 – 16 + 12
Solve the exponent: 42 = 16
-6 + 12
6
Your Turn to Practice:
Solve the subtraction of integers: 10 – 16 = 10 + (-16) = -6
Solve the addition of integers: -6 + 12 = +6
Evaluate the expression.
1)
(6 - 2)2 · 3 + 4
2)
52 + 4(7 + 3)
3)
6 x 2 + (8 – 7) + 24
4)
11 + 24 ÷ 4 - 8