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Divisibility Rules
A number is divisible by:
2 if the number ends in 2,4,6,8,0
3 if the sum of the digits is divisible by 3
4 if the last to digits of the number is divisible by 4
5 if the number ends in 0 or 5
6 if the number is divisible by 2 AND 3
9 if the sum of the digits is divisible by 9
10 if the number ends in 0
PRIME, COMPOSITE or Neither
Prime numbers have exactly two factors 1 and itself
2x1=2
13 x 1 = 13
19 x 1 = 19
Composite numbers have many factors
1x6=6, 2x3=6 or 1x12=12, 2x6=12, 3x4=12
The number 1 is NEITHER prime nor composite!
1x1=1 it only has ONE factor!
Exponents
3
8
8 is the base & the number you multiply
3 is the exponent and tells you how many times
to multiply the base (or how many time to
write the big number)
8x8x8= 512
Decimal Rule for Adding and Subtracting
LINE UP THE DECIMAL and ADD or SUBTRACT
3.34
+2.333
5.673
Add a zero
To fill in
blanks
7.990
- 1. 23
6.760
Add a zero
To fill in blanks
Multiply Decimals Rule
Multiply and forget the decimal.
After you get the answer count the number of
digits after the decimal in the problem and
that will BE the number of digits after the
decimal in the problem
2.01 2 digits after the decimal
X 3.8 1 digit after the decimal
1608 Total of 3 digits after the decimal
+603
7.638 Count 3 digits and add the decimal point
Count 3,2,1
Dividing Decimals Rule
You CANNOT divide by a DECIMAL!
MOVE the Decimal to the Right UNTIL the
number you are dividing by is a WHOLE #
THEN do the same thing to the other
NUMBER & DIVIDE!
.8 6.4 change to 8 64
COMPARE FRACTIONS!
CROSS MULTIPLY
3/4 < > = 2/3
3 2
4 3
3x3 2x4
9> 8
3/4 > 2/3
CROSS MULTIPLY
Compare the numbers
Compare Similar Figures
SET UP A Proportion
Height of 1 = length of 1
Height of 2 = length of 2
Divide the top by the bottom and compare.
RATE
Rate = $ divide top by bottom to get rate
unit
Units are – gallons, meters, miles, hours,
minutes, inches, feet, yards, etc
Rate + $60 =
20 gallons = $3 per gallon
RATIO
Write and READ fraction as:
___ : ___ or ___to___
2/3
2:3
or 2 to 3
A proportion is an equation that shows two
equivalent ratios.
2
4
__
= __
1
2
4
8
__
= __
2
4
2
6
__
= __
1
3
Reading Math
2
4
__
__
Read the proportion
=
as “two is to
1
2
one as four is to two.”
Additional Example 1: Modeling Proportions
Write a proportion for the model.
First write the ratio of hearts to stars.
4
number of hearts = __
number of stars
8
Next separate the hearts and stars into two
equal groups.
Metric conversion Rules
King Henry Died
Kilo Hecto Deka
Over Drinking Chocolate Milk
Origin Deci
Centi
Milli
RIGHT
The direction and how many times the frog has to jump is the direction and number of
times You move the decimal point.
Change 3.888 kilometers to decimeters 38880. decimeters
Origin = 1 liter, 1 meter, 1 gram
• 60 seconds = 1 minute
• 60 minutes = 1 hour
• 24 hours = 1 day
• 7 days = 1 week
• About 4 weeks = 1 month
• 12 months = 1 year
• 365 days = 1 year
•
•
•
•
Percent = per 100… place the percent over 100 and simplify.
45% = 45/100 = 9/20
2 % = 2/100 = 1/50
2 ½ % = 2.50 % = .025 = 25/1000 = 1/40 (you must change to a
decimal then to a fraction and then simplify)
• Decimal to percent – is in the correct alphabetic order D to P so you
move to the Right ---- move the decimal 2 places to the right…
• .35 = 35 %
• .08 = 8 %
• .8 = 80 %
• Percent to Decimal – is not in the correct alphabetic order P to D so
you move to the Left ---- move the decimal 2 places to the left…
• 5 % = .05
• 30 % = .30 or .3
• 2.5 % = .025
•Decimals to fractions – use place values and simplify .03 OR .03
3
put a 0 for each number and a 1 where the decimal is
100 100
•Fractions to decimals – divide bottom number into top number ¾
.75
4 3.00
-2 8
20
20
0
•You will have a terminating decimal – with no remainder, or
a repeating decimal – use a repeating bar…. 6
SIMPLIFY ALL FRACTIONS EVERY TIME!!!!
¼ = .25
1/8 = .125
1/5 = .2
½ = .5
3/8 = .375
2/5 = .4
¾ = .7
5/8 = .625
3/5 = .6
1/6 = .6
SQUARED2
when a number is squared it is
multiplied times itself
Memorize these squared numbers:
22 = 4
82 = 64
142 = 196
32 = 9
92 = 81
152 = 225
42 = 16
102 = 100
52 = 25
112 = 121
62 = 36
122 = 144
72 = 49
132 = 169
Variable
letter that stands for a number
To solve for a variable
DO THE OPPOSITE OPERATION
TO BOTH SIDES
multiply
2x = 12
divide is opposite 2x/2 = 12/2
X=6
A translation is the movement of a figure along a
straight line.
Only the location of the figure changes with a
translation.
A rotation is the movement of a figure around a
point. A point of rotation can be on or outside a
figure.
The location and position of a figure can change
with a rotation.
When a figure flips over a line, creating a mirror
image, it is called a reflection. The line the figure
is flipped over is called line of reflection.
The location and position of a figure change with a
reflection.
Additional Example 1A: Identifying
Transformations
Tell whether each is a translation, rotation,
or reflection.
The figure is flipped over a
line.
It is a reflection.
30 days hath September, April,
June and November.
All the rest have 31 days except
February which have 28
or 29 on leap year.
How do you know which months have 30 or 31 days? Look at your
knuckles! The peaks are 31 days the valleys are 30….except for Feb!
A O
D
M
J
J
M
u
c
e
a
u
a
a
g
t
c
y
l
n
r
3
3
3
3
3
3
1
No
1
1
1
1
3
1
Peak or
S
1
J
valley
A
N
e
F
u
p
o
p
e
n
r
v
t
b
3
3
3
0
0
3
0
2
0
8
Time and Date
60 seconds in a minute
60 minutes in an hour
24 hours in a day
7 days a week
52 weeks in a year
365 days in a year
3
4 +
1
3 =
3 x3= 9
4 x3= 12
LCM factor both numbers- all the couples and the ugly
people go to the party
3= 3,1
4= 2,2
LCM = 3X2X2
LCM = 12 (use 12 as the common denominator)
1 x4= 4
+3 x4= +12
13
12
Simplify to 1 112
Simplify all fraction
answers as
the last step!
3
4 x
1
3
3 = 12
3
12 divide top and bottom by 3 =
1
4
!! HINT !!
HINT!has mixed
If the problem
Ifnumbers
the problem
has to
mixed
change
an
numbers change
an mixed
improper
fractionto
then
follow
number
multiply!
the
rules then
for multiplying
fractions!
Simplify all fraction
answers as
the last step!
3
4 ÷
1
3 =
3
4 X
3
1 =
9
2
4 = (simplify)
1
!! HINT !!
If the problem has mixed
numbers change to an
improper fraction then follow
the rules for dividing fractions!
2
Simplify all fraction
answers as
the last step!