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Multiplication Chart~ Handy Formulas~ Fraction Conversion~ Order of Operation ~ 

Multiplying Fractions~Division of Fractions

Feel free to cut and  paste this chart into word for future reference.

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

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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  

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  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.

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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).

 

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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.

 

9/17 divided by 3

 

 

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:

1 2/7 divided by 5

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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

 

                        

                   

 

 

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