PAX - MATH tips/helps

dividing decimals

1. multiply the divisor by the appropriate power of 10 to make it a whole # 2. multiply the dividend by the same power of 10 3. bring the decimal point up to the top of the box, and place it directly over the decimal in the dividend ex: 0.25)0.625, multiply the divisor by 100 25)0.625 multiply the dividend by 100 25)62.5 now divide normally. remember to bring the decimal point up to the top of the box: directly over other decimal point 2.5 25)62.5

converting decimals to fractions

1. write down decimal divided by 1 ex: 0.75 0.75/1 2. multiply both top/bottom by 10 for every # after the decimal 0.75 x 100/ 1 x 100 = 75/100 3. simplify the fraction 75/100 = 3/4

% Increase & Decrease

1. write the amount of increase or decrease as the numerator 2. write the original amount as the denominator 3. change the fraction to %

improper fraction A/B

A is greater than or equal to B

proper fraction A/B

A is less than B

unit fraction

a fraction A/B, where A = 1 ex: 1/5

complex fraction

a fraction A/B, where A and/or B are fractions ex: 1/4 / 4/5

adding/subtracting fractions

all fractions must have the same denominator, find LCD if they do not, multiply to get same denominator. do not add/sub the denominators

MULTIPLYING INTEGERS

an even # of - #'s gives you a + product ex: 2 x -5 x -3 x 4 = 120 an odd # of - #'s gives you a - product ex: -2 x -5 x -3 x 4 = -120

multiplying mixed #'s

convert them to improper fractions and then multiply ex: 1 2/3 x 3 1/2 converted to 5/3 x 7/2 = 35/6. then convert to mixed # again = 5 5/6 *always remember to reduce final answer

multiplying decimals

do not have to line up decimal points, don't worry about them until the end. 1. multiply as normal 2. count the # of decimal places in each # & add them 3. starting from the right end in your product, count from right to left the same # of places as your answer

SUBTRACTING INTEGERS

easiest way is to turn subtraction into addition *subtracting a + is the same as adding a - ex: +15 - +5 = +15 + -5 = 10 -20 - +5 = -20 + -5 = -25 *subtracting a - is the same as adding a + ex: +15 - -5 = +15 ++5 = 20 -20 - -5 = -20 + +5 = -15

equivalent fractions

equal fractions ex: 1/5 = 10/50 = 100/500

converting a mixed # into an improper fraction

ex: 1 4/5 = 9/5 1. multiply the denominator by the whole #, and add the result to the numerator: (5 x 1) +4 2. the answer becomes the numerator of the improper fraction: 9 3. the denominator of the original mixed number becomes the denominator of the improper fraction: 5

converting fractions to decimals

ex: 2/5 1. find a # you can multiply the denominator to make it 10, 100, or 1000 2. multiply both numerator & denominator by that # 2 x 2 / 5 x 2 = 4/10 3. then write down the numerator, putting a decimal point in the correct spot 0.4 (one space from the right hand side for every zero in the bottom #)

converting improper fractions to mixed #'s

ex: 9/5 = 1 4/5 1. divide the denominator into the numerator 9 / 5 2. the result is the whole # part of the mixed number: 1 3. the remainder becomes the numerator part of the mixed #: 4 4. the original denominator becomes the denominator part of the mixed #: 5

lowest terms

in a fraction A/B, where A & B are relatively prime ex: 4/6 = 2/3

Dividing Fractions

invert the second fraction, then multiply ex: 1/5 / 2/3 = 1/5 x 3/2 = 3/10

adding/subtracting decimals

line up decimal points, add any zeros if needed, ex: 23.8 - 7.09 23.80 - 7.09 16.71

dividing decimals by powers of 10

move the decimal point to the left in the dividend by the same # of places as there are zeros in the power of 10 ex: 45.67 / 100 = 0.4567

multiplying decimals by power of 10

move the decimal point to the right the same # of places as there are zeros in the power of 10 ex: 45.67 x 100, two points to the right, = 4,567

multiplying fractions

multiply the numerators, and multiply the denominators ex: 4/5 x 2/3 = 8/15

relatively prime

term used to describe two or more #'s whose greatest common factor is 1

greatest common factor

the largest # that divides evenly into two or more #'s

reciprocal

the resulting fraction when you switch the numerator and denominator. A/B is B/A

least common denominator

the smallest denominator that two or more fractions have in common

mixed number

the sum of a whole # and a fraction, or just another way of writing an improper fraction, ex: 1 4/5 really means 1 + 4/5

converting between decimals, fractions, & percentages

to convert a decimal to a % multiply by 100 to convert a % to a decimal, divide by 100 to convert a fraction to a %: 1. change fraction to a decimal 2. change decimal to a percentage to convert a % to a fraction: 1. change the % to a fraction 2. reduce the fraction

% Discount & Tax Increase

to find the amount of discount or increase when % is known: 1. change the % to a decimal (or fraction) 2. multiply by the original cost 3. add/subtract accordingly ex: a $250 stereo is discounted 18%. find new sale price. convert 18% to a decimal by dividing by 100, multiply the decimal by $250. 18% / 100 = 0.18 0.18 x $250 = $45 then subtract $45 (the 18% decrease) from $250 (original cost) to find the new cost. $250 - $45 = $205