denbeigh

Decimal to Percent: 2 ie 0.75

Percent to Fraction: 3 ie 75% or 75,000%

Percent to decimal: 4 ie 75%=

Decimal to Fraction: 5 ie 0.7534= 7534/10000

Fraction to percent: 6 ie 3/4= 0.75

Look at the factors of each number: find greatest common factor of both numerator and denominator

(12 in this case)

divide both the numerator and the denominator by that GCF

=9/12

=7/2 -3/4

=7x2/2x2 -3/4

=14/4 - 3/4

=11/4

Method:

1- convert any mixed fractions to improper fractions (multiply the denominator by the whole number, add product onto numerator)

2- convert fractions so that they are both over a common denominator. Remember: what you to the top of a fraction, you must also do to the bottom :)

3- add or subtract the numerators, write the sum/difference over the denominator

4- simplify, and/or turn back into mixed fraction if asked in the question

Difference- the answer to a subtraction

Product- answer to a multiplication

Quotient- answer to a division

Operation- a multiplication, division, subtraction, addition, etc.

=2/3 x 79/18

=(2)(79) x (3)(18) (cancel out)

=(1)(79) x (3)(9)

=79/27

1) Method:

1-convert any mixed fractions to improper fractions (multiply the denominator by the whole number, add product onto numerator)

2- Simplify the multiplication by cancelling out terms (terms that have a common factor with another term on the opposite side of the fraction line)

3- multiply the numerators by each other, and the denominators by each other

4- simplify if possible

=4/5 / 72/20

=4/5 x 20/72

=(4)(20) x (5)(72)

=(1)(4) x (1)(18)

=(2) x (9)

=18

Method:

1- convert any mixed fractions to improper fractions (multiply the denominator by the whole number, add product onto numerator)

2- flip the second fraction (so that denominator becomes the numerator and vice versa), and multiply (see other note)

-two of the same sign together means "add" i.e. (-3)(-5)=(+15) 

or (-4)-(-3)= (-4)+3= (-1)

-two opposite signs together mean "subtract" i.e. (+5)+(-6)=(-1)

or (-6/+2)= (-3)

-similar to fractions, except to get the number of pieces in your "whole pie", you have to add all the numbers of pieces together i.e. 3:2:1, there are 3+2+1=6 pieces ("parts") total

-"parts" don't have to be the same, i.e. it could be 3 carrots: 2 radishes: 1 celery stick

Example Question:

The ratio of nitrogen to potassium to phosphorus in a bag of fertilizer is 4:5:2. If there are 33 kg of fertilizer, how much of that is phosphorus?

-> here, our "whole pie" is the 33kg

-> the number of "parts" in our pie is 4+5+2=11 parts

-> we want to know what ONE part is worth, (so we can figure out how much the TWO parts of phosphorus are worth):

33kg/11 parts = 3 kg per part

-> now we know that one part is worth 3kg, so 2 parts is worth:

(3kg)(2)=6kg

Therefore, the amount of phosphorus in the bag is 6kg.

-> note: 30/100 =30% (this is a ratio of 30 to 100)

->i.e. if you had 30% of an hour, how many minutes it that?

-> to solve, let x represent what you're trying to find (here, the number of minutes)

-> look at whatever number is across from "x" (here, the 100)

-> take the other two number, and multiply them

-> divide that answer by 100 (the last number)

-> that will be the value of x

x= (30)(60) / (100)

x= 18

That means 30% of one hour is 18 min.

-> if we had 2.5kg of cereal that is worth $6.30, what is the unit price?

->here, the "whole" is the 2.5 kg, and the "parts" is $6.30

-> to find the price of ONE kg, we divide the 2.5kg by $6.30:

2.5kg/$6.30 = $o.40/kg

^unit price

If you had $10, how many kg could you buy?

$10/$0.40 per kg = 25k

X= Base

X^n = Power

When Bases are the same:

Product Law: (X^m)(X^n) = X^(n+m) -> if you have two powers being multiplied, add the exponents

Quotient Law: (X^m) / (X^n) = X^(m - n) -> if you have two powers that are being divided, subtract the exponents

Zero Exponents: X^0 = 1
-> Anything to an exponent of zero is equal to one (except if the base is zero)

Negative Exponents: X^(-n) = 1/(X^n) -> if you have a negative exponent, to make it positive, use the reciprocal (flip the fraction (if it's a whole number, remember it's an imaginary fraction over 1), and write the base and a positive version of the exponent on the bottom)

Flip the number so that the numerator is on the bottom, and the denominator is on the top. Remember that if a number doesn't appear to have a denominator, it actually has an imaginary denominator of 1.

ie 3 -> 1/3

or 3/2 -> 2/3

(3x+2)(3+x)= (3x)(3)+(2)(3)+(3x)(x)+(2)(x)

=9x + 6 +3x^2 + 2x

=3x^2 + 11x +6

or

3(4x-5) = (3)(4x) + (3)(-5)

= (12x) + (-15)

= 12x - 15

3x^2 + 4x^3 + 5x^2 +7 -3x -7x^2 + 4x^3

= 8x^3 +x^2 -3x +7

-> remember that most teachers want you to write the final answer in descending, alphabetical order (descending exponents, NOT coefficients)

-> 3 = Numerical Coefficient

-> X = Variable/ Literal  
Coefficient

Degree of the expression: 2nd

(Degree is the number of the highest exponent in the expression)

-> 3X = term

Remember: terms are usually separated by addition/subtraction

-> if there are variables in the expression, the question will probably give you the values of those variables.

Method:
1) sub in the given number (replace the variable with its number)

2) solve (follow bedmas)

ie 3x + 2x^2 +1

Given: x= -3

Hint: put -3 in brackets when you sub it in!

= 3(-3) + 2(-3)^2 +1

= -9 + 2(9) +1

= -9 + 18 +1

= 10

2) collect like terms