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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
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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
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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
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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