average formula

8/13/2019 Average Formula

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Average formula:

Let a1,a2,a3,......,an be a set of numbers, average = (a1 + a2 + a3,+......+ an)/n

Fractions formulas:

Converting a mixed number to an improper fraction:

Converting an improper fraction to a mixed number:

Formula for a proportion:

In a proportion, the product of the extremes (ad) equal the product of the means(bc),

Thus, ad = bc

Percent:

Percent to fraction: x% = x/100

Percentage formula: Rate/100 = Percentage/base

Rate: The percent.Base: The amount you are taking the percent of.Percentage: The answer obtained by multiplying the base by the rate



Consumer math formulas:

Discount = list price × discount rate Sale price = list price − discount

Discount rate = discount ÷ list price Sales tax = price of item × tax rate

Interest = principal × rate of interest × time Tips = cost of meals × tip rate

Commission = cost of service × commission rate

Geometry formulas:

Perimeter :

Perimeter of a square: s + s + s + ss:length of one side

Perimeter of a triangle: a + b + ca, b, and c: lengths of the 3 sides

Area:

Area of a square: s × ss: length of one side

Area of a rectangle: l × wl: lengthw: width

Area of a triangle: (b × h)/2b: length of baseh: length of height

Area of a trapezoid: (b1 + b2) × h/2

b1 and b2: parallel sides or the bases

h: length of height

volume:

Volume of a cube: s × s × ss: length of one side

Volume of a box: l × w × hl: lengthw: widthh: height

Volume of a sphere: (4/3) × pi × r 3

pi: 3.14r: radius of sphere

Volume of a triangular prism: area of triangle × Height = (1/2base × height) × Heightbase: length of the base of the triangleheight: height of the triangleHeight: height of the triangular prism

Volume of a cylinder:pi × r 2 × Height

pi: 3.14r: radius of the circle of the baseHeight: height of the cylinder

Formula for percentage

The formula for percentage is the following and it should be easy to use:

We will take examples to illustrate.Let us start with the formula on the left An important thing to remember: Cross multiplyIt means to multiply the numerator of one fraction by the denominator of the other fraction

Examples #1:

25 % of 200 is____In this problem, of = 200, is = ?, and % = 25

We get:

is/200 = 25/100Since is in an unknown, you can replace it by y to make the problem more familiary/200 = 25/100



Cross multiply to get y × 100 = 200 × 25

y × 100 = 5000Divide 5000 by 100 to get ySince 5000/100 = 50, y = 50So, 25 % of 200 is 50

Examples #2:

What number is 2% of 50 ?

This is just another way of saying 2% of 50 is___So, set up the proportion as example #1:

is/50 = 2/100

Replace is by y and cross multiply to get:

y × 100 = 50 × 2y × 100 = 100

Since 1 × 100 = 100, y = 1

Therefore, 1 is 2 % of 50

Examples #3:

24% of___ is 36

This time, notice that is = 36, but of is missing After you set up the formula, you get:

36/of = 24/100

Replace of by y and cross multiply to get:

36/y = 24/100y × 24 = 36 × 100y × 24 = 3600

Divide 3600 by 24 to get y

3600/24 = 150, y = 1500

Therefore, 24 % of 150 is 36

Now, we will take examples to illustrate how to use the formula for percentage on the right

Examples #4:

To use the other formula that says part and whole, just remember the following:The number after of is always the wholeThe number after is is always the part

If I say 25 % of___ is 60, we know that the whole is missing and part = 60

Your proportion will will like this:

60/whole = 25/100

After cross multiplying, we get:

whole × 25 = 60 × 100whole × 25 = 6000

Divide 6000 by 25 to get whole

6000/25 = 240, so whole = 240Therefore, 25 % of 240 is 60



Examples #5:

___% of 45 is 9

Here whole = 45 and part = 9, but % is missing

We get:

9/45 = %/100

Replacing % by x and cross multiplying gives:

9 × 100 = 45 × x900 = 45 × x

Divide 900 by 45 to get x

900/45 = 20, so x = 20

average formula

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