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Math notes and tips

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**Adding and subtracting decimals**

Line up your decimals a

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**Multiplying decimals 4.376 X2.1 ----------------**

Don’t worry about lining up the decimals. However many numbers are behind the decimals then that is how many are in your answer!

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**Dividing decimals 6.625 ÷ 0.53 0 53 /6 625 ------------------------**

Move the decimal so that the outside number is a whole number What ever you do with the decimal on the out side you need to do to the decimal on the inside

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M.A.D M – multiply A – add D – denominator stays the same

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**You have to make the bottom number (the denominator) the same in the fractions**

Subtracting Adding 1 ¼ - 1/3= The smallest common multiple for 4 and 3 is 12 So 1 ¼ = 1 3/12 and 1/3 = 4/12 You also need to make 1 3/12 in to an improper fraction(use MAD) so it is 15/12 You can now subtract them and you get 11/12 1 + 1 3 The smallest common multiple for 2 and 3 is 6 So: 1 = 3 2 = 6 1 = 2 3 = 6 You can now add them and you get 5/6

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**Multiplying fractions**

Regular Mixed numbers 2/4 x 1/3 = Multiply the top number (numerator) and the bottom number (denominator) So multiply 2 and 1 and also 4 and 3 to get 2/12 1 2/4 x 1/3 = You must get rid of the whole number by multiplying the 1 by the 4 and adding 2 then you keep the denominator (use MAD) 4x Then multiply like regular 6/4 x 1/3 = 6/12 = = Use order of operations

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**Dividing fractions Keep Change Flip 1÷2 3 4 1 X 4 3 2**

3 4 Keep Change Flip Keep 1st fraction the same change the ÷ to x flip the 2nd fraction X Now you multiply it like regular Answer: 4 2 6 reduced 3

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**Adding & Subtracting Integers**

Same sign – find the “sum” Add #’s keep the sign Ex: -6 + (-2) = -8 Ex: -6 – (+2) = -8 + (-2) Different signs – find the difference Subtract the #’s and keep the sign of the # with the higher value. Ex: -8 + (2) = -6 Ex: = 3 Ex: -6 – (-2) = -4 + (+2) Remember: when it shows subtraction – change to addition and flip the sign behind the sign

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**Multiplying and Dividing Integers**

Same sign – ALWAYS POSITIVE Ex: -5 x -4 = 20 Ex: -36 ÷ -6 = 6 Different signs – ALWAYS NEGATIVE Ex: -3 x 4 = -12 Ex: 30 ÷ -5 = -6

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**Order of Operations Order of operations () X2 x / + - P E M D A S**

L X Y E U A E C A N L A U R T L S S Y E E Multiplication and division are equal and opposite operations. Work left to right! Addition and subtraction are equal and opposite operations. Work left to right! Multiply Divide Add Subtract Parentheses Exponents

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**Converting Fractions/Decimals/Percents**

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**Number Line -4 -3 -2 -1 0 1 2 3 4 Moving to the left**

Moving to the left #’s decrease in value Negative # look like they get larger, but they are really getting smaller in value. Moving to the right #’s increasing in value Positive # get larger,

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**0.6 = 2/3 = 66.6% = 33 2/3% (0.66666) Repeating Decimals**

0.3 = 1/3 = 33.3% = 33 1/3% ( ) 0.6 = 2/3 = 66.6% = 33 2/3% ( )

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**Fractions to remember Fraction Decimal Percent ½ .50 50% ¼ .25 25% 1/8**

.125 12.5% 1/16 .0625 6.25% 1/3 .3333 33.3% 2/3 .6666 66.6% 1/12 .08333 8.3% 1/24 .04166 4.16% 1/5 .20 20%

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