6th grade math notes

1. 6
th
Grade Math Notes




























*One Step Equations*
The goal of an equation is to isolate (get it by
itself) the variable (the unknown
value..usually is represented by an “x”).
In order to do that you must do the inverse
(opposite operation) which means instead of
adding you subtract and instead of
multiplying you divide.


*Example #1*

*Check*
Instead of x put your
answer (4). 4 + 3 does
equal 7 so your answer is
correct!


*Example #2*

*Check*
Instead of x put your
answer (13). 13 - 8 does
equal 5 so your answer is
correct!


*Example #3*

*Check*
Instead of x put your
answer (7). -7 x -8 does
equal 56 so your answer
is correct!


*Example #4*

*Check*
Instead of x put your
answer (24). 24 ÷ 8 does
equal 3 so your answer is
correct!


*Two Step Equations*
The goal of an equation is to isolate (get it by
itself) the variable (the unknown value is
always represented by a letter)
In order to do that you must do the inverse
(opposite operation) which means instead of
adding you subtract and instead of
multiplying you divide.


*Example #1*







*Check*
Instead of x put your answer (9). (3 x 9) + 7
does equal 34 so your answer is correct.


*Rules*
1) Perform the inverse operation
2) Check your answer (in order to check you
must put your answer in place of the variable
to see if the equation holds true)


One Step Equations
Two Step Equations
*Rules*
1) Perform the inverse operation (undo addition
or subtraction first)
2) Then undo multiplication or division
3) Check your answer (in order to check you
must put your answer in place of the variable
to see if the equation holds true)


Rule 1 (undo +/-)

Rule 2 (undo x/÷)

*Example #2*

*Check*
Instead of x put your answer (3). (7 x 3) + 1
does equal 22 so your answer is correct.

2. *Expressions*
There are four types of expressions
Addition: x + 5, or 5 + x
Subtraction: x – 3, or 3 – x
Multiplication: 6x
Division: x/7, or 7/x






























Expressions
*Rules*
1) Instead of the variable put the number that
the problem tells you it equals.
2) Solve the expression

*Example #2*
X - 2
Instead of x put 8
8 - 2 = 6
Answer = 6


*Example #1*
X + 5
Instead of x put 8
8 + 5 = 13
Answer = 13


*Example #3*
5x + 2
Instead of x put 8
(5 x 8) + 2 = 42
Answer = 42


*Example #4*
x/2 - 1
Instead of x put 8
(8/2) - 1 = 3
Answer = 3


*Rules*
1) Underline the place value
2) Circle the # on the right
3) Round up the circled # is 5 or greater. When
you round up the underlined # goes up one #
higher
4) Round down if the circled # is 4 or less.
When you round down the underlined # stays
the same
5) Everything after the underlined # then
becomes zeros.
Rounding
*Example #1* (round to nearest thousand)
5,678

5, 6 78 (round up since 6 is 5 or higher)

6,000 (5 becomes a 6 and everything else zeros)

*Example #2* (round to nearest hundredth)
.562

.5 6 2 (round down since 2 is 4or lower)

.560 (the 6 stays the same and everything else zeros)

Place Value

Directions: Solve the expression when x = 8

3. Multiplication
*2 digit multiplication (34 x 23 or 345 x 56)*
With 2 digit multiplication use Only Pizza
Tastes Astonishing or OPTA.
O = (Ones place) First multiply the # in the
ones place
P = (Place Holder) Put one place holder
T = (Tens Place) Next multiply the # in the
tens place
A = (Add) Then add all of the numbers up
*3 digit multiplication (342 x 823)*
With 3 digit multiplication use Only Pirates
Tickle Parrots Hairy Ankles or OPTPHA.
O = (Ones place) First multiply the # in the
ones place
P = (Place Holder) Put one place holder
T = (Tens Place) Next multiply the # in the
tens place
P = (Place Holder) Put two place holders
H = (Hundreds Place) Then multiply the # in
the hundreds place
A = (Add) Finally add all of the numbers up
*Multiplying with Decimals
Do not line up decimals!!!
Multiply
Add all of the numbers
Count the decimals


*Example #1*



*Dividing w/ a decimal in the dividend
Bring the decimal up in the dividend
Divide
You cannot have a remainder..if there is a
remainder you must add a zero, drop it, and
continue dividing
*Dividing w/ a decimal in the dividend and divisor
Move the decimals over first
Bring up the decimal in the dividend
Divide
You cannot have a remainder..if there is a
remainder you must add a zero, drop it, and
continue dividing

*Example #1*


*Example #1*


Division

4. *example* what is the unit rate if 8 apples cost $16
To find your answer divide (16/8). The unit rate
ends up being $2/apple.





























*Rules*
1) Line up the decimals!!!
2) Add or Subtract

If you have a whole # you must turn it
into a decimal first (5 = 5.00, 7 = 7.00)

Adding & Subtraction Decimals
*Ratios*
Ratios explain how for every x units of one
item there are x units of another.
For example a ratio of 3 to 5 would mean for
every 3 apples there are 5 oranges.
A ratio of 2:6 would mean for every 2 girls
there are 6 boys.
Rations can be expressed three different
ways: 1 to 3, 1:3, and 1/3.

*Unit Rates*
Unit rates compare unlike units to 1 unit.
For example how much one item costs, how
many miles a car travels in 1 hour, or how
many laps a person runs in 1 day.

Unit Rates
*Rules*
Change all mixed #’s and whole #’s into
improper fractions
The denominators do not have to be the same
Simply multiply across (numerator x
numerator…denominator x denominator)
Make sure your answer is a proper fraction
and in simplest form..

*Rules*
If there are mixed #’s or whole #’s you must
first change them into improper fractions
Change the division sign into a multiplication
sign
Use the reciprocal or flip the second fraction
upside down
Multiply
Make sure your answer is a proper fraction
and in simplest form


Ratios
*Rules*
If the denominators are not the same then
you must first make them the same
Add or subtract (borrow if you have do)
Make sure your answer is a proper fraction
and in simplest form.

Multiplying Fractions
Dividing Fractions
Adding & Subtracting Fractions
*Prime Numbers*
Prime #’s are those that have only 2 factors
like 5, 7, 3, 11.
*Composite Numbers*
Composite #’s are those that have more than
2 factors like 4, 6, 8, 10.


Prime and Composite Numbers

5. Subtracting Fractions w/ borrowing

There is not fraction on top to subtract 1/3
You must borrow from the 6 which makes the
whole # a 5. When you borrow you are
borrowing a whole #. Since the denominator in
1/3 is a 3 you are borrowing 3/3.
Now you can subtract & make sure you answer is
in simplest form

In this case you can’t subtract 3/12 from 5/12 so you
have to borrow which makes the whole # 10 a 9. Again
look at the denominator which is a 12 so you are
borrowing 12/12. Add 12/12 to 3/12 and you get 15/12.
Now you can subtract and make sure your answer is in
simplest form

Prime Factorization
1) List all of the factors for each #
2) Find the greatest factor that the #’s both have

Example: 12 = 12, 1, 2, 6, 3, 4
16 = 1, 16, 2, 8, 4
GCF = 4


1) List all of the multiples for each #
2) Find the smallest multiple that the #’s
both have

Example: 3 = 3, 6, 9, 12, 15, 18, 21, 24
5 = 5, 10, 15, 20, 25, 30, 35
LCM = 15


Factors: the 2 #’s you multiply to get the
product. In 2 x 3 = 6, 2 & 3 are the factors.
Factors of 8 = 8, 1, 4, 2

Multiples:
Multiples of 8 = 8, 16, 24, 32, 40, 48 etc..
Multiples of 3 = 3, 6, 9, 12, 15, 18, 21 etc..

Prime #’s: Have only 2 factors
Composite #’s: Have more than 2 factors

1) In the box out of the box (numerator in,
denominator out)
2) Whole #: Quotient
Numerator: Remainder
Denominator: Divisor

3) Make sure your answer is in simplest form


Greatest Common Factor (GCF)
Least Common Multiple (LCM)
Factors, Multiples, Prime #’s, & Composite #’s
Improper fractions into mixed #’s

6. 1) Multiply the denominator and the whole #
together
2) Add the answer from step one to the
numerator
3) The denominator from the mixed # will
be the denominator in your improper
fraction


1) A proper fraction is one where the numerator is
smaller than the denominator: 1/3, 3/5, or 6/8
2) An improper fraction is one where the numerator is
larger than the denominator: 5/3, 8/2, or 13/4
3) A mixed # will have a whole # and a fraction: 3 2/4,
5 1/6, or 7 4/9.


Ordered Pairs (x,y)
1) Probability is always a fraction
2) Numerator: what you want to get
3) Denominator: Total possible outcomes


Example: Probability of landing on a 3
Answer: 1/8

Example: Probability of landing on an even #
Answer: 4/8 = 1/2



Mode: The # that occurs the most often (there can
be no mode or several modes)
Example: 5,6,2,6,3,4,9 mode = 6
Example: 4,5,2,1,4,6,5 mode = 4, 5

Mean:
1) add all of the 3’s
2) divide by how many #’s there are
3) no remainders you must add a decimal and bring
it up
4) round your answer to the nearest tenth




Median:
1) Put the #’s in order from least to greatest
2) Cross the #’s out two at a time from the outside
3) If there r 2 #’s left, add them together and
divide by 2 (no remainders and round to nearest
tenth)

Range: Subtract the largest # from the tiniest #

Outlier: The # in a set of #’s that does not belong,
it either way larger or smaller than the rest of the
#’s. ex: 2,4,5,6,22…outlier would be 22.



Median, Range, Outlier Mode & Mean
Probability
Proper Fractions, Improper Fractions, Mixed #’s
Mixed #’s into Improper Fractions
1) To find the probability of 2 or more events u must
add the probabilities of each event together & then
simplify

Example: Probability of landing on a 3 then a 4. P(3,4)
Answer: 1/8 + 1/8 = 2/8 = 1/4

Example: Probability of landing on an even # then 3.
P(even#,3)
Answer: 4/8 + 1/8 = 5/8


Adding Probabilities

7. 1) If the integers have the same sign (either both
positive or negative) then you just add
Example: (+5) + (+4) = +9
Example: (-4) + (-3) = -7

2) If the signs of the integers are different (one is
positive and one negative) then you must subtract.
The larger # goes on top and use the sign of the
larger #.
Example: (-10) + (+3) = -7
Example: (+15) + (-6) = +9







1) Change the subtraction sign into a plus sign
2) Change the sign of the 2
nd
integer
3) use addition rules to add
Example: (-10) - (+3) =
(-10) + (-3) = -13

Example: (+7) – (+2) =
(+7) + (-2) = +5






1) If the signs of the integers are the same then
your answer is always positive (+)
Example: (+5) x (+4) = +20
Example: (-12) ÷ (-3) = +4

2) If the signs of the integers are different then
your answer is always negative (-)
Example: (-10) x (+3) = -30
Example: (+54) ÷ (-6) = -9







Area = Length x Width (A=lw)
(area is always squared)
Example:





Area = Length x Width
Area = 14 x 7
Area = 98cm²


Area = 1/2 x base x height (A= 1/2bh)
(area is always squared)







Example:






Area = 1/2 x base x height
Area = 1/2 x 12 x 15
Area = 180/2
Area = 90m²



Adding Integers Subtracting Integers
Area of a rectangle or square
Multiply & Dividing Integers
Area = base x height (A= bh)
(area is always squared)







Example:






Area = base x height
Area = 15 x 5
Area = 75cm²




Area of a triangle Area of a parallelogram

8. Area = TTr² (TT = 3.14)
(area is always squared)

Example:







Area = TTr²
Area = 3.14 x 6²(6 x 6)
Area = 3.14 x 36
Area = 113.04m²



D=12m
m
Area = TTr² (TT = 3.14)
(area is always squared)

Example:







Area = TTr²
Area = 3.14 x 4²(4 x 4)
Area = 3.14 x 16
Area = 50.24m²



C = TT x Diameter (TTd)
(TT = 3.14)
(area is always squared)

Example:







C = TTd
C = 3.14 x 12
C = 37.68m



D=12m
m
C = TT x Diameter (TTd)
(TT = 3.14)
(area is always squared)

Example:







C = TTd
C = 3.14 x 8
C = 25.12m



Circles Area of a Circle Area of a Circle
Volume = (area of the base) x height
(volume is always cubed)

Example:







Volume = (area of the base) x height
Volume = (length x width) x height
Volume = (8 x 3) x 12
Volume = 288in³



Volume = (area of the base) x height (connects the bases)
(volume is always cubed)

Example:








Volume = (area of the base) x height
Volume = (1/2 x base x height) x height
Volume = (1/2 x 6 x 3) x 12
Volume = 9 x 12
Volume = 108cm³
Volume of a rectangular prism Circumference of a Circle Circumference of a Circle
Volume of a triangular prism

9. Volume of a cylinder
Volume = (area of the base) x height
(volume is always cubed)

Example:







Volume = (area of the base) x height
Volume = (TTr²) x height
Volume = (3.14 x 4²) x 12
Volume = 50.24 x 12
Volume = 602.88in³



Volume of a cylinder
Volume = (area of the base) x height
(volume is always cubed)

Example:







Volume = (area of the base) x height
Volume = (TTr²) x height
Volume = (3.14 x 4²) x 12
Volume = 50.24 x 12
Volume = 602.88in³



1)Brackets + Parenthesis first
2) exponents
3) multiply or divide from left to right
4) add or subtract from left to right

Example:
(48 ÷ 8) x 5 + 3²
6 x 5 + 3²
6 x 5 + 9
30 + 9
Answer: 39






Order of operations
1) Change the percent into a decimal
(add a decimal to the end of the number
and then move the decimal to the left
twice)
2) Larger # goes on top, multiply, count
decimals

Example: 25% of 35 = .25 x 35 = 8.75

Example: 34% of 125 = 125 x .34 = 42.5





Percent (%) of a # (of = multiply)
1) Change the tax from a percent into a decimal
(add a decimal to the end of the # and then move
the decimal to the left twice)
7% = .07
2) then multiply the tax by the subtotal (amount you
are spending). This gives you the tax amount.
25 x .07 = $1.75

3) To find the total cost you must then add the tax
amount to your subtotal
25.00 + 1.75 = $26.75




Tax & Total Cost
Example:
Subtotal: $25

Tax : 7%
Tax Amount: $1.75
Total Cost: $26.75

10. 4m x
8m 6m
8x = 24
X = 24/8
X = 3 meters




























1) Change the discount from a percent into a
decimal (add a decimal to the end of the # and then
move the decimal to the left twice)
25% = .25
2) then multiply the discount by the subtotal
(amount you are spending). This gives you the
discount amount.
52 x .25 = $13.00

3) To find the total cost you must then subtract
the discount amount from your subtotal
52.00 - 13.00 = $39.00







Discount & Sale Price
Example:
Subtotal: $52

Discount : 25%
Discount Amount: $13.00
Sale Price: $39.00

1) Change the tip from a percent into a decimal (add
a decimal to the end of the # and then move the
decimal to the left twice)
15% = .15
2) then multiply the tip by the subtotal (amount you
are spending). This gives you the tip amount.
85 x .15 = $12.75

3) To find the total cost you must then add the tip
amount to your subtotal
85.00 + 12.75 = $97.75







Tip & total Cost
Example:
Subtotal: $85

Tip : 15%
Tip Amount: $12.75
Total Cost: $97.75

If Alex ran 12 miles in 3 hours then how many did
he run in 1 hour?

*in order to solve this problem you must use a
proportion.
*When using a proportion the labels in the
numerators must be the same as well as the label in
the numerators.
*Once your proportion is set up you must then cross
multiply (always start with the variable) and solve
accordingly.

With Shapes
*When doing proportions with shapes…each side of
the proportion corresponds with the exact same
side on each shape.
*Same shape has to be on top and bottom of the
proportion then cross multiply and then solve





Proportions
X miles 12 miles
1 hour 3 hours
3x = 12
X = 12/3
X = 4 miles
=

=
x

11. The 3 angles of a triangle add up to
180°

Example:





1) add the 2 angles together
36 + 57 = 93
2) Then subtract your answer from 180
180 – 93 = 87
3) angle a = 87
4) If your answer is correct then all 3
angles should add up to 180



Missing Angles: Triangles
The 3 angles of a triangle add up to 180°

Example:





1) Subtract 180 - 40
180 - 40 = 140
2) 140 is how many degrees both missing angles
add up to. To find each individual angle’s degrees
you must divide by 2
140 ÷ 2 = 70
3) So each missing angle (x) is 70°
4) If your answer is correct then all 3 angles
should add up to 180



Missing Angles: Triangles
40°
x
x
The 4 angles of a quadrilateral add
up to 360°

Example:



1) add the 3 angles together
50 + 50 + 130 = 230
2) Then subtract your answer from 360
360 – 230 = 130
3) missing angle = 130
4) If your answer is correct then all 4
angles should add up to 360



Missing Angles: Quadrilaterals
The 4 angles of a quadrilateral add up to
360°

Example:




1) add the 2 angles together
48 + 64 = 112
2) Then subtract your answer from 360
360 – 112 = 248
3) 248 is the total of both missing angles
together
4) To find each angle you must divide by 2
248 ÷ 2 = 124
5) See each missing angle is 124°
6) If your answer is correct then all 4
angles should add up to 360


Missing Angles: Quadrilaterals
48° 64°
x x
1) add all of the sides
2) line up the decimals if there are any

Example:





Perimeter = add all sides
Perimeter = 1 + 5 + 4 + 2 + 7
Perimeter = 19

Perimeter

12. 1) In the box out of the box (numerator in,
denominator out)
2) Add a decimal to the end of the # (dividend)
and bring it up
3) There are NO remainders, if you have a
remainder then you must add a zero, drop it, and
continue dividing
*To change a fraction into a % you must
change it to a decimal then to a %







Fractions into Decimals

Example: 1.25
1) the # before the decimal is always the whole #
2) look at the last #..the 5 is in the hundredths
place so the fraction would be:
1 25/100 = 1 1/4

Example: .8
1) the 8 is in the tenths place so the fraction
would be:
8/10 = 4/5

Example: .05
1) the 5 is in the hundredths place so the fraction
is: 5/100 = 1/20






Decimals into fractions (always simplify)
1) If there is no decimal in the percent
then you must add a decimal at the end
of the percent 45% = 45.%
2) Move the decimal twice to the left
45.% = .45

Example: 4.5%
4.5% = .045

Example: 125%
125.% = 1.25






Percents into Decimals
1) Move the decimal twice to the right
.38 = 38%

Example: .8
.8 = 80%

Example: 9
9.00 = 900%






Decimals into Percents
1) Two angles that add up to 180°







Supplementary Angles
1) Two angles that add
up to 90°







Complementary Angles
es



1) Angles that are
opposite to each other
(are always congruent)






Vertical Angles











Types of Triangles

13. Quadrilaterals





















Polygons
1) List all of the factors of the numerator
2) Start w/ the largest factor and see which
one you can divide the denominator by
3) Once u find the factor you must divide
both the numerator and denominator by it
4) Repeat until u can no longer simplify
anymore




















Simplifying Fractions
Comparing Fractions
Number Lines
Least Greatest
1) U can only compare fractions when the
denominators are the same
2) If the denominators are different then
make them the same
3) Compare the fractions




















1) Plug in known values into the
formula then solve the equation.

Ex: Erik ran 24 miles at a rate
of 4 miles per hour. How long
did it take him to run 24 miles?

D = R x T

24 = 4T

24/4 = T

6 hours = T




Distance = Rate x Time
Least to Greatest
1) If there r fractions u must change them all to decimals
first.
2) Line up your decimals and compare your #’s (be very
careful if there are negative integers)
3) Remember that the # furthest left on the # line is
always the smaller #.
4) Write down the original #’s for your answer.

Example (least – Greatest) 1/2, .67, 2, 3/4
1/2, .67, 3/4 = .50, .67, 2.00, .75
Put in order= .50, .67, .75, 2.00
Answer = 1/2, .67, 3/4, 2

14. Example 2: how many 4 letter codes can u make from
the letters a,b,c,d,e (repeat letters can be used)?
Since there r repeat letters…once a letter is
chosen it can be used again (so a code of aaaa
would be allowed)
For the 1
st
letter in the code u can choose from 5
letters
For the 2
nd
u can choose from 5 letters
The 3
rd
5 letters and the 4
th
5 letters
So your permutation would look like this:
5 x 5 x 5 x 5 = 625 possible codes



















Example 2: how many ways can u give 3 cans to 8
kids?
The order of the cans does not matter so we
have a combination
Since there r 8 kids….u can choose 8 different
kids for the 1
st
can, 7 kids for the 2
nd
can, & 6
kids for the 3rd
So far your combination looks like this 8 x 7 x 6..
Since we r using 3 cans we must divide by 3! (3
factorial)
So we now have 8 x 7 x 6 divided by 3! = 336/6 =
56 ways to give 3 cans.
























































Permutations
If a problem is a permutation then the order
of the items matters.
For example if you were to make a 4 letter
code from the letters a, b, c, d, e……then the
code abcde is totally different than the code
abced.
Therefore in this case order matters and the
problem would be a permutation.

Example 1: how many 4 letter codes can u make
from the letters a,b,c,d,e (no repeat letters can
be used)?
Since there r no repeat letters…once a letter
is chosen it cannot be used again (so a code
of aaaa would not be allowed)
For the 1
st
letter in the code u can choose
from 5 letters
For the 2
nd
u can choose from 4 letters
The 3
rd
3 letters and the 4
th
2 letters
So your permutation would look like this:
5 x 4 x 3 x 2 = 80 possible codes



















Combinations
If a problem is a combintation then the order of
the items does not matter.
For example if you were to make teams of 2 from
matt, sara, tim, rob, and ally……then the team of
tim & rob is the same as rob & tim
Therefore in this case order does not matter and
the problem would be a combination.
To solve combinations you must use factorials…..4
factorial (4!) = 4 x 3 x 2 x 1 and 5 factorial (5!) = 5
x 4 x 3 x 2 x 1
In combinations u must divide by the factorial of
the # in each team or group to get rid of
duplicate groups like team rob/tim & team tim/rob
Example 1: how many teams of 2 can u make from
sara, tim, rob, and ally?
Since there r 4 kids….u can choose 4 different
kids for the 1
st
spot on the team and then 3 kids
for the 2
nd
spot on the team….
So far your combination looks like this 4 x 3..
Now we r choosing teams of 2 so we must divide
by 2! (2 factorial)
So we now have 4 x 3 divided by 2! = 12/2 = 6
teams of 2.

15. Probability w/replacement
Probability with replacement means that once
an item is picked it is then put back into the
sample space so that it can be picked again

Example 1: What the probability of picking a black
marble and then a stripped marble (p)
black,strpiped w/ replacement
The probability of getting a black marble = 1/6
The probability of getting a stripped marble =
3/6
Add the probabilities for each event
1/6 + 3/6 = 4/6 = 2/3






































Probability w/o replacement
Probability without replacement means that
once an item is picked it is not put back into
the sample space so that it cannot be picked
again

Example 1: What the probability of picking a black
marble and then a stripped marble (p)
black,strpiped w/o replacement
The probability of getting a black marble = 1/6
The probability of getting a stripped marble =
3/5 (remember there is one less marble now)
Add the probabilities for each event
1/6 + 3/5 = 5/30 + 18/30 = 23/30






































Figuring out percents (out of)
1) Change to a fraction
2) Change the fraction into a decimal
3) Change the decimal into a percent

Example 1: Find the % for 1 out of 4
1) change to a fraction = 1/4
2) change to a decimal = .25
3) change to a percent = 25%

16. Shirts Sizes
Red Small
Blue Medium
White Large
X-Large





















Probability (Finding all Possible Combinations): List, Tree Diagram, Counting Principal
Counting Principal
1) Multiply the total # of choices from each category
2) 3(shirts) x 4 (sizes) = 12 possible combinations

List
1) In a list you do just that make a list of all of the
possible combinations..this is also usually done at the
end of a tree diagram.

Ex.
Red, small blue, small white, small
Red,medium blue,medium white,medium
Red,large blue, large white,large
Red,xlarge blue,xlarge white,xlarge


















Tree Diagram















Graphing Equations
Ex: Graph the equation y = 2x

1) Make a table…in place of x pick 3 #’s usually
pick 3’s that r easy to calculate…in this case we
will pick 1, 2, -2
X Y
1
2
-2
2) Fill out the table by solving the equation with
each value u have for x (y = 2 x 1…so y = 2)
X Y
1 2
2 2
-2 -4
3) Plot each set of points on a graph…connect your
dots and then label your equation on the line.




y = 2x

17. Words and their operation
Addition Subtraction Multiplication Division
Sum Difference Of Each
Deposit Withdraw
Above Below
Forward Backward
Increase Decrease
Gain Loss
Altogether

Hidden Integers

You can divide any number by…
1) 2 if the number is even
2) 3 if the individual numbers in the number add up to a multiple of 3
3) 5 if the number ends in a 5 or 0
4) 10 if the number ends in a 0
5) if you can divide by 2 then always try a 4 and an 8
6) if you can divide by 3 three then always try a 6 and a 9


















1) Change the rate from a percent into a decimal
(add a decimal to the end of the # and then move
the decimal to the left twice)
4% = .04
2) then multiply the principal by the rate.
52 x .05 = 2.08

3) Now multiply that answer by the time.
2.08 x 3 = $6.24







Calculating Interest…..Interest = Principal x rate x time
Example:
Principal (amount u have in bank): $52

Rate (interest rate): 4%
Time (amount of time interest is
accruing): 3 years
Interest (amount gained over x
amount of time): ?