| 0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
| 1 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
| 2 |
2 |
4 |
6 |
8 |
10 |
12 |
14 |
16 |
18 |
20 |
22 |
24 |
| 3 |
3 |
6 |
9 |
12 |
15 |
18 |
21 |
24 |
27 |
30 |
33 |
36 |
| 4 |
4 |
8 |
12 |
16 |
20 |
24 |
28 |
32 |
36 |
40 |
44 |
48 |
| 5 |
5 |
10 |
15 |
20 |
25 |
30 |
35 |
40 |
45 |
50 |
55 |
60 |
| 6 |
6 |
12 |
18 |
24 |
30 |
36 |
42 |
48 |
54 |
60 |
66 |
72 |
| 7 |
7 |
14 |
21 |
28 |
35 |
42 |
49 |
56 |
63 |
70 |
77 |
84 |
| 8 |
8 |
16 |
24 |
32 |
40 |
48 |
56 |
64 |
72 |
80 |
88 |
96 |
| 9 |
9 |
18 |
27 |
36 |
45 |
54 |
63 |
72 |
81 |
90 |
99 |
108 |
| 10 |
10 |
20 |
30 |
40 |
50 |
60 |
70 |
80 |
90 |
100 |
110 |
120 |
| 11 |
11 |
22 |
33 |
44 |
55 |
66 |
77 |
88 |
99 |
110 |
121 |
132 |
| 12 |
12 |
24 |
36 |
48 |
60 |
72 |
84 |
96 |
108 |
120 |
132 |
144 |
Handy Formulas:
Area of a triangle
:
A=1/2 base X
height Written as A = 1/2 b h
Volume of a
cube:
V=
length x width x
height
Written as V = lwh
Area
of a square:
A=length x
width Written as A=lw
Circumference
of a circle:
C= Diameter Pi or
C=Pi 2 radius
Area
of a Circle:
Pi Radius
squared
Here are some ways to help with the conversion of fractions,
decimals, and percents:
A percent to a fraction:
Put
the number over 100 and reduce. Then, drop the percent sign.
25%
= 25/100 = ¼
A decimal to a percent:
Move the
decimal point two places to the right. Then, attach a percent sign.
0.25 = 25%
A percent to a decimal:
Move the
decimal point two places to the left. Then, drop the percent sign.
25% = 0.25
A fraction to a decimal:
Divide the
denominator (the bottom part) into the numerator (the top part):
¼ = 1 ÷ 4.00 = 0.25
A fraction to a percent:
Multiply the
fraction by 100 and reduce it. Then, attach a percent sign.
¼ x 100/1 = 100/4 = 25/1
= 25%
A decimal to a fraction:
Starting from the
decimal point, count the decimal places. If there is one decimal place,
put the number over 10 and reduce. If there are two places, put the
number over 100 and reduce. If there are three places, put it over 1000
and reduce, and so on.
0.25 = 25/100 = ¼
Back
to Top
Order
of Operations:
The
Meaning of the Letters:
P
= Parentheses
E
= Exponents
M
& D = Multiplication & Division (from left to right)
A
& S = Addition & Subtraction (from left to right)
Keep in mind when solving a problem
using "PEMDAS" you have to follow the steps in order
Example: 4+3x5
4 + 15 first multiply 3 and 5
19 add 4 and 15
Addition, Subtraction and
Multiplication:
Example:
4+ 5 x 3 - 2 x 4 + 6 x 3=
4 + 15 - 8 + 18 Multiply 5 and 3, then multiply
6 and 3
19 - 8 + 18
add 4 and 15
11 +
18
subtract 8 from 19
29
add 11 and 18
Division in Order of Operations
Example: 5
+ 12 / 2 + 3 x 4 - 2 ( 5 - 2 )
5 + 12 / 2 + 3 x 4 - 2
(3)
First simplify the parentheses
5 + 6 + 3 x 4 - 2
(3)
Divide the 12 by 2
5 + 6 + 12 - 2
(3)
*Multiply the 3 and the 4
5 + 6 + 12 -
6
*Multiply the 2 and the 3
11 + 12 -
6
*Add and subtract from left to right. Add 5 and 6
23 -
6
Add 11 and 12
17
To get your final answer subtract 6 from 23
* This can be done in less
steps, but watch the signs.
Back
to Top
Multiplication of fractions:
When multiplying 2 fractions, multiply
the two numerators together and the two denominators together.
Multiply a whole number
by a fraction,
multiply the whole number by the numerator of the fraction. The denominator
stays the same.
Another example of
Multiplication of whole numbers:
Multiplication of Mixed fractions:
Let’s change these
into improper fractions
Next multiply across the
tops (numerators), then across the bottom (denominators).
Back to Top
Division of fractions:
When we divide a whole
number by a fraction, we multiply the whole number with the inverse
(or reciprocal) of the fraction. In
this example, the inverse (or reciprocal) of 1/3 is 3/1.
Another way to look at
it is to:
Change the sign and flip!
Let’s
put it all together:
Dividing
Fractions with Whole:
Place
the whole number over 1, change the sign and flip. Now it is the same as Multiplication of fractions.
Division with mixed and whole numbers
Change the mixed fraction into and improper fraction; place the
whole number over 1. Change
sign, flip number (use the reciprocal) and multiply:
Back to Top
Calculating
the Area of a Triangle
How
to find the area of a triangle:
·
The area of
a triangle can be found by multiplying the base times the one-half the
height.
·
If a
triangle has a base of length 6 inches and a height of 4 inches, its
area is 6*2=12 square inches
|
