1. Math notes and tips

2. Adding and subtracting decimals
Line up your decimals a

3. Multiplying decimals 4.376 X2.1 ----------------
Don’t worry about lining up the decimals.
However many numbers are behind the decimals then that is how many are in your answer!

4. Dividing decimals 6.625 ÷ 0.53 0 53 /6 625 ------------------------
Move the decimal so that the outside number is a whole number
What ever you do with the decimal on the out side you need to do to the decimal on the inside

5. M.A.D
M – multiply
A – add
D – denominator stays the same

6. You have to make the bottom number (the denominator) the same in the fractions
Subtracting
Adding
1 ¼ - 1/3= The smallest common multiple for 4 and 3 is 12 So 1 ¼ = 1 3/12 and 1/3 = 4/12 You also need to make 1 3/12 in to an improper fraction(use MAD) so it is 15/12 You can now subtract them and you get 11/12
1 + 1 3
The smallest common multiple for 2 and 3 is 6
So: 1 = 3
2 = 6
1 = 2
3 = 6
You can now add them and you get 5/6

7. Multiplying fractions
Regular
Mixed numbers
2/4 x 1/3 = Multiply the top number (numerator) and the bottom number (denominator) So multiply 2 and 1 and also 4 and 3 to get 2/12
1 2/4 x 1/3 = You must get rid of the whole number by multiplying the 1 by the 4 and adding 2 then you keep the denominator (use MAD) 4x Then multiply like regular 6/4 x 1/3 = 6/12
= =
Use order of operations

8. Dividing fractions Keep Change Flip 1÷2 3 4 1 X 4 3 2
3 4
Keep Change Flip
Keep 1st fraction the same change the ÷ to x flip the 2nd fraction X
Now you multiply it like regular
Answer: 4 2
6 reduced 3

9. Adding & Subtracting Integers
Same sign – find the “sum” Add #’s keep the sign Ex: -6 + (-2) = -8 Ex: -6 – (+2) = -8 + (-2)
Different signs – find the difference
Subtract the #’s and keep the sign of the # with the higher value.
Ex: -8 + (2) = -6
Ex: = 3
Ex: -6 – (-2) = -4
+ (+2)
Remember: when it shows subtraction – change to addition and flip the sign behind the sign

10. Multiplying and Dividing Integers
Same sign – ALWAYS POSITIVE Ex: -5 x -4 = 20 Ex: -36 ÷ -6 = 6
Different signs – ALWAYS NEGATIVE
Ex: -3 x 4 = -12
Ex: 30 ÷ -5 = -6

11. Order of Operations Order of operations () X2 x / + - P E M D A S
L X Y E U A
E C A N L
A U R T L
S S Y
E E
Multiplication and division are equal and opposite operations. Work left to right!
Addition and subtraction are equal and opposite operations. Work left to right!
Multiply
Divide
Add
Subtract
Parentheses
Exponents

12. Converting Fractions/Decimals/Percents

13. Number Line -4 -3 -2 -1 0 1 2 3 4 Moving to the left
Moving to the left
#’s decrease in value
Negative # look like they get larger, but they are really getting smaller in value.
Moving to the right
#’s increasing in value
Positive # get larger,

14. 0.6 = 2/3 = 66.6% = 33 2/3% (0.66666) Repeating Decimals
0.3 = 1/3 = 33.3% = 33 1/3% ( )
0.6 = 2/3 = 66.6% = 33 2/3%
( )

15. Fractions to remember Fraction Decimal Percent ½ .50 50% ¼ .25 25% 1/8
.125
12.5%
1/16
.0625
6.25%
1/3
.3333
33.3%
2/3
.6666
66.6%
1/12
.08333
8.3%
1/24
.04166
4.16%
1/5
.20
20%