Download Addition with regrouping (carrying)

Addition with regrouping (carrying)
tens
10's
ones
1's
Put the tens guy up in the tens column.....
Put the ones guy in the ones answer spot
Subtraction with regrouping (borrowing)
Place Value Chart
Place Value - Template
For 0,1,2,3, or 4 we round down (leave alone)
For 5,6,7,8, or 9 we round up (up by 1)
Rounding Poem
Find your number
Look next door
4 or less just ignore
5 or more, add 1 more
• Everything to the left of your number leaves alone
• Everything to the right your number turns to zeros
Multiplying Whole Numbers
Example 1:
Example 2:
Multiplying Multi-Digits - Whole Numbers
+
3 84
Dividing Whole Numbers
top
785 ÷ 5 or 785
5
both mean the same
first
Step 1: First or top number goes in the house
1) ÷
5
785
house
2) X
3) -
4)
Top dog in the house rules!
"Long Division"
Operation Expressions
Scientific Notation and Standard Form
Standard Form to Scientific Notation
Positive Exponent
1,960,000 1.96 x106
Negative Exponent
1.96 x 10­3
.00196
Start at the decimal and scoop to the right
No decimal always start at the back of the number and scoop to the left. *You must have one number in front of the decimal.
*You must have one number in front of the decimal.
Scientific Notation to Standard Form
Positive Exponent
Negative Exponent
scoop 6 to the right
1.96 x106
1.96 0 0 0 0
1,960,000 scoop 3 to the left
1.96 x 10
0 0 1.96
­3
.00196
Add/Subtract/Multiply/Divide
Decimals
Add or Subtract Decimals:
Step 1: Line up your decimals
Step 2: Add zeros where you have empty spots
Step 3: Add or Subtract like normal
Step 4: Make sure you bring down your decimal into your answer.
1.1 0
+ 2.24
3.34
Multiplying Decimals:
Step 1: Take out the decimals
Step 2: Multiply
Step 3: Put the decimal back in....how do I do this? Add all the
decimal places....start at the back of your answer and use the scoops
to move the decimal back.
2 decimal places
1.20 x .4
1 decimal place
x
120
4
480
=
.480
All together 3 decimal places ­­ three scoops from the back
Dividing with Decimals:
Step 1: If dividing a decimal by a whole number....remember top dog
goes in the house (this should be your number with a decimal).
Step 2: Line up your decimal into your answer
Step 3: Divide using your dividing rules.
Dividing with Decimals:
Step 1: If dividing inside and outside of the dog house with decimals.
Take out the decimals from outside the house.
Step 2: How many ever scoops you make to the outside make to the
inside and move the decimal to the top of the house.
Step 3: Divide using your dividing rules.
Order of Operations - PEMDAS
P - Parenthesis First
E - Exponent next
M - Multiplication and Division
D - from left to right
A - Addition and Subtraction
S - from lest to right
Adding Integers
(Positive and negative #'s)
Subtracting Integers
(positive and negative numbers)
Multiplying and Dividing Integers
When the signs are the same
Multiplying
(+) (+) = +
Positive
(-) (-) = +
Positive
Dividing
(+)/(+) = +
(-)/(-) = +
Positive
Positive
When the signs are different
Multiplying
Negative
(+) (-) = Negative
(-) (+) = -
Dividing
(+)/(-) = (-)/(+) = -
Negative
Negative
Integers and Number Lines
Absolute Values
Number Properties
Associative, Commutative, and Distributive
For addition or multiplication
Step 1: JUST ADDING You can change the grouping or numbers to make solving the problem easier Step 1: JUST MULTIPLYING You can change the grouping or numbers to make solving the problem easier For addition or multiplication
Step 1: JUST ADDING Step 1: JUST MULTIPLYING You can add in any ORDER. No grouping involved
You can add in any ORDER. No grouping involved
Multiply the outside of the
parentheses to everything on the
inside of the parentheses.
example:
3(2+4) = 3(2) + 3(4)
Prime and Composite Numbers
2 =2x1
3 =3x1
6=2x3
12 = 3 x 4
Prime Factorization w/Factor Trees
Factors: The two numbers that are multiplied together before getting the
final answer.
To find all the factors of a specific number make a factor tree
36
6
6
2 3 2 3
How to write Prime Factorization:
2 x 3 x 2 x 3 = 22 x 32
If a number can be broken
down --- It is a composite
number (no circle)
If a number cannot be broken
down (no you cannot use 1) --- It
is a prime number (circle)
Factors:
Multiples:
(12 x 1)
(12 x 2)
(12 x 3)
Factors are two numbers that multiply
together to find the product.
Multiple is a product (answer) of a number.
When you multiply two whole numbers
together you get a multiple.
Factors: are two numbers that multiply together found on the outside of the multiplication chart
Multiples: can be found inside the multiplication chart. Equivalent Fractions
Step 1: Multiply the top and
bottom by the same number.
*You get a equivalent
fraction
Adding/Subtracting Fractions
w/ like denominator
1 + 3 = 4 5 5 5
Step 1: When the denominators
(bottom) are the same they stay
the same.
Step 2: Add or Subtract the top
4 ­ 3 = 1 9 9 9
Comparing Fractions:
The denominators (bottoms)
have to be the same in order to
compare
Note: "Whatever I do
to the bottom I have to
do to the top"
<
less than
>
greater than
=
equal to
When the bottoms are the same compare the numerators.
Add and Subtract Fractions with Unlike Denominators
STOP! Are the bottoms the same? NO
How do I make the bottoms the same?
4x
x3
=
x
4
=
x3
SAME RULE FOR SUBTRACTION
Final Step SIMPLIFY: Proper fractions "Reduce" Improper
Fractions "Divide" (use top dog)
Adding with unlike denominators
Adding /Subtracting Mixed
Numbers
Step 1: Pull out the whole numbers
3+4=7
Step 2: Add the fractions "remember to look at the denominators"
denominators are the same they stay
the same and add the top.
If the denominators are not the same you have to make them the same­­­look at your strategy
Step 3: Now put your WHOLE # and FRACTION together!!
Whole # This was the fraction Subtracting Mixed Numbers
+
+
x
x
Step 1: Turn into improper fractions
Are the bottoms the same?
Step 2: Subtract your fractions
- are the denominators the same or different
- find the strategy
What kind of
fraction?
Step 3: Turn your improper fraction back into a mixed number
- find that strategy (you can use your calculators)
Multiplying Fractions
=
1 x 4 =
2 x 5
4
10
2
=
2
2
5
Proper Fraction - "REDUCE"
Rule: Multiply across.
Proper Fractions "REDUCE"
Improper Fractions "DIVIDE" top dog
All whole numbers ­ put a 1 under them then multiply across. 2 x x
=
=1
Dividing Fractions
Changing Mixed Numbers to Improper Fractions
+
=
x
=
Proper Fractions - "REDUCE"
Proper fractions try to simplify by reducing
Small #
Large #
top dog goes in the house
Large #
Small #
2
numerator
6
denominator
4
14
4√ 6
⇒ -4
Step 1: Top dog goes in the house
2
Step 2: How many times does the outside
number go into the inside number without
going over
numerator
left over
Step 3: Write the remainder as a fraction
mixed number
whole number and a fraction together
Change Mixed #'s to Improper Fractions
Find a common denominator: What
you do to the bottom you got to do
to the top.
Change Improper Fractions to Mixed Numbers - Divide "top dog in
the house" or use the calculator If you get a proper fraction - "Reduce"
use the calculator Finding Unit Rate
Ratio:
Converting between
fractions, decimals and percents
Percent to decimal: two scoops to the left
75%
.75
Decimal to percent: two scoops to the right
.375
37.5%
Percent to fraction: change to decimal then fraction - need to
know your place values.
Reduce by 25
75%
.75
75
100
3
4
what place value?
Fraction to percent: Use your percent formula
3 x =
4 100
3x = 400
3
3
is = %
of 100
cross multiply
isolate the variable - divide each side by the number on the same side of the letter
x = 75%
Fraction to decimal: Find the percent then change percent into
decimal.
Solving Proportions
Remember: your units have to match
Solving Word Problems
with percent's
Solving Percent Problems
Mean
Median
Mode
Range