Math notes and tips

Adding and subtracting decimals 4.3 0.7 6.2 +5.0 +3.0 ------------ ----------- Line up your decimals a

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!

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

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

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

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) 4x1+2 4+2 6 4 4 4 Then multiply like regular 6/4 x 1/3 = 6/12 ------------ = --------- = -------- Use order of operations

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 1 X 4 3 2 Now you multiply it like regular Answer: 4 2 6 reduced 3

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: -4 + 7 = 3 Ex: -6 – (-2) = -4 + (+2) Remember: when it shows subtraction – change to addition and flip the sign behind the sign

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

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

Converting Fractions/Decimals/Percents

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

0.6 = 2/3 = 66.6% = 33 2/3% (0.66666) Repeating Decimals 0.3 = 1/3 = 33.3% = 33 1/3% (0.333333) 0.6 = 2/3 = 66.6% = 33 2/3% (0.66666)

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%