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### rational #'s

any # that can be written as a fraction, terminating (ending) decimal (0.25), or repeating decimal (0.212121....)

### calculation of percents

step 1. change the written statement into a mathematical equation. Keep in mind:

- the word of translates into multiply

- the word is translates into equals

- the decimal form of the percent should be used in the equation

step 2. solve for the unknown quantity

step 3. rewrite the statement & make sure that the answer is reasonable (example: 15% of 500 is what #?= 0.15 x 500= 75 )

### solving for percent decrease

percent decrease = original value minus new value

divided by original value

then multiply by 100

### solving for percent increase

percent increase = new value minus original value

divided by original value

then multiply by 100

### converting from decimals to fractions

the decimal # expressed becomes the numerator of the fraction & the # of decimal places to the right of the decimal determines the value of the denominator

### converting from fractions to percents

1st, convert the fraction to a decimal - convert the decimal to a percent by multiplying by 100 & adding the % symbol

5/8= 0.625 = 62.5%

### converting from percents to fractions

step 1. remove the % sign

step 2. write the number from step 1 in the numerator of the fraction & write 100 in the denominator

step 3. simplify the fraction

### converting from percents to decimals

remove the % symbol & move the decimal point left 2 places

(example: 0.045= 4.5 %)

### determining which fraction is greatest

find a common denominator for the fractions- the fraction with the greater numerator is the greater fraction

### estimation

the approximate value= the 1st digit in the # will not be zero but all the other digits will be zeros

### to balance a checking or savings

1st group the deposits & add them together -then group the checks & add them together- next add the deposits to the previous balance & subtract the checks from the result- then subtract the service charge & add interest

### proportion

this states that 2 ratios are equal- when setting up this, the numerators must be in the same units & the denominators of both ratios must be in the same units- use this formula to solve for this:

units of an item = units of an item

divided by units of a different # Divided by units of a different #

### rate of change problems

use proportions to determine the difference in completion times for a given task

example: 10 pages / 1 hour = 288 pages / A hours

use the method of cross products to solve:

10 x A= 288 x 1 - 10A / 10 = 288 / 10 A= 28.8 hrs

### calipers

this is used to measure very small lengths, usually 6 inches or fewer with greater precision than a ruler

### independent variable

the variable that is put into the set of data, or the input, (statistics) a variable whose values are independent of changes in the values of other variables

### dependent variable

is the output based on the input, (statistics) a variable in a logical or mathematical expression whose value depends in the independent variable

### line graphs

these graphs show changes over a period of time or compares the relationship between 2 quantities (compare time of day to temperature)

### pie (circle) graphs

a circular graph divided into sectors representing the frequency of an event- percentage of a whole, where the whole circle or pie equals 100%- shows how much of the whole each part represents

### bar graphs

this graph is used to compare the frequencies of an event

(the number of inches of rain that fell in a certain city in the each month)

### adding integers

positive + positive = positive

negative + negative = negative

when signs are different = subtract the smaller # from larger & give the sign of the larger #

### subtracting integers

- subtracting a positive is the same as adding a negative

- subtracting a negative is the same as adding a positive

### multiplying integers

positive x positive = positive

negative x negative = positive

positive x negative = negative

### percentage discount & tax increase

to find the amount of discount or increase when the % is known

1. change the percentage to a decimal (or fraction)

2. multiply by the original cost

3. add or subtract accordingly

### percentage increase & decrease

often the problem asks you to determine the percentage of increase or decrease. This type of problem is easily solved by making a fraction out of the information provided

1. write the amount of increase or decrease as the numerator

2. write the original amount as the denominator

3. change fraction to percent

### ratio

a comparison of 2 #'s, usually by division

(ex: in a class of 15 people, there are 7 boys & 8 girls. The ratio pf boys to girls is 7 to 8 or 7:8 or 7/8)

### rate

a ratio made up of 2 different units of measurement or amounts

(ex: I can drive my car 250 mi on 10 gal of gas. This relationship can be expressed as a ratio of miles to gallons: 250 to 10, 250:10, or 250 mi/ 10 gal = 25/ 1 or 25 miles per gal)

### proportion

an equation of 2 equal ratios. All proportions equations have have a special property: cross products are equal. When you multiply the numerator on the left side of the equation by the denominator on the other side & then multiply the left-side denominator by the right-side numerator, the are products equal to each other

(ex: if a car gets 25 miles to the gallon, then how many gallons do I need to drive 125 miles?

set up a proportion to solve this problem. Make sure you align your units correctly on both sides of the equation: in this case, miles across from miles & gallons across from gallons

25 mi / 1 gal = 125 mi / x gal

now cross multiply: 25x = 125

now divide both sides by 25 to solve for x. x = 5

this is your answer- you need 5 gal to go 125 mi

### exponent rules

1. when multiplying similar bases, add the exponents

2. when dividing similar bases, subtract the exponents

3. when raising a power to another power, multiply the exponents

(ex:(s^2)^3 = s^ 6

4. when the exponent is negative, move its base to the denominator & make the exponent positive

5. any base (except zero) to the 0 power equals 1