Math

Links

             


               

PEMDAS

Order of Operations: PEMDAS

Perform operations inside Parenthesis
Perform Exponentials.
Perform Multiplication and Division in order, from left to right.
Perform Addition and Subtraction in order, from left to right.
 
 
CLICK HERE for a more in-depth review of Order of Operations!

Like Terms

Add or Subtract Like Terms:

Like terms have the same “variable part”.
To combine the terms, just add or subtract their coefficients (the number in front of the variable part).

Example: 5x + 6x – 3x is the same as (5 + 6 – 3) x or 8x.

Signs

Addition of Signed Number:

When adding two negative numbers, ignore the signs of the numbers, add the numbers, and give your answer a negative sign.
Example: (-2) + (-7) = -9
 
When adding two positive numbers, add the numbers and give the answer a positive sign.
 
When adding a positive number and a negative number, ignore the signs and subtract the smaller number from the larger number. Give your answer the same sign as the number with the larger absolute value.
Example: (-2) + (7) = 5

 

Subtraction of Signed Numbers:

When subtracting signed numbers, change the sign of the subtrahend (2nd number) and proceed as in addition.
Example: (-2) – (-7) is the same as (-2) + (7) = 5

Distributive Property

Factors & Divisibility

Rules for Factoring Numbers:

If a number ends in 0, 2, 4, 6, or 8 it is divisible by 2.
If a number ends in 5 or 0 it is divisible by 5.
If the sum of the digits in a number is divisible by 3, then the number is divisible by 3.
If the sum of the digits in a number is divisible by 9, then the number is divisible by 9.
 
Divisible by 2
  All even numbers
 
Divisible by 3
  Sum of all digits is divisible by 3
  ex – 741, 7+4+1 = 12, 1+2 = 3
 
Divisible by 4
  Last two digits are divisible by 4
  ex – 1020, last two digits are 20, 20 = 5*4
 
Divisible by 5
  Last digit is 5 or 0
 
Divisible by 6
  Divisible by both 2 and 3
 
Divisible by 7
  Double last digit
  Subtract sum of remaining digits
  Product is divisible by 7
  ex – 756, 6*2=12, 75-12 = 63, 63/7 = 9
 
Divisible by 8
  Last three digits are divisible by 8
  ex – 8,153,256, 256/8 = 32
 
Divisible by 9
  Sum of all digits is divisible by 9
  ex – 13,536,  1+3+5+3+6 = 18, 1+8 = 9
 
 

Fractions

Click HERE for a more in-depth review on Fractions!

 

Reduce a Fraction:

Factor the numerator and denominator.
Cancel out like factors.
Example: 15/35 = (3*5)/ (7*5) = 3/7
 

Equivalent Fractions:

If two fractions are equivalent, then the product of the means equals the product of the extremes. (ie) The cross products are equal.
Example: 4/5 = 8/10 because 4 * 10 = 5 * 8
 

Addition and Subtraction of Two Fractions:

Find a common denominator, a number that is a multiple of both denominators. (You can use the product of both denominators for the common denominator, although this may not be the lowest common denominator.)
Express each fraction as an equivalent faction with the new denominator.
Add or subtract the numerators of the equivalent fractions and put that over the common denominator.
Reduce the fraction by factoring the numerator and the denominator and then canceling out like factors.
 

Multiplication of Two Fractions:

If possible, cancel out like factors of the numerators and denominators.
Multiply the numerators and put that product over the product of the denominators.
 

Division of Two Fractions:

Invert the divisor (second fraction) and proceed as in multiplication.
 

Express a Fraction with a New Denominator:

Divide the denominator of the faction into a new denominator.
Multiply the result by the numerator of the fraction and put the product over the new denominator.
Example: Write 2/3 as an equivalent fraction with the denominator of 12. 
12/3 = 4. Multiply 4 by 2, the numerator of the fraction. Put the product, 8, over the new denominator to get 8/12.

Decimals & Percentages

Click Here for a more in-depth review on decimals!

 

 

Multiply Two Decimal Numbers:

Multiply the numbers, ignoring the decimal point.
Count the number of decimal places in both numbers. Give your answer the same number of decimal places.
 

Divide Two Decimal Numbers:

Move the decimal point in the divisor to the right as many places as it takes to make the divisor a whole number.
Move the decimal point in the dividend an equal number of places to the right.
Put the decimal point in the answer directly above the decimal point in the dividend.
Proceed as dividing whole numbers.
 

Converting a Decimal to a Percent:

Move the decimal point two places to the right. This is equivalent to multiplying by 100.
.01 = 1% or 1/100.

Convert a Percent to a Decimal:

Move the decimal point two places to the left. This is equivalent to dividing by 100.
5% = .05 or 5/100.
 
 

10 is What Percent of 50?

In this problem, “of” means “to multiply” and “is” means “equals”.
Mathematically the statement is equivalent to the equation 10 = N/100 * 50, where * means multiply.
To solve this equation, divide both sides by 50 to get
     10/50 = N/100

Reduce the fraction on the left to get  
     1/5 = N/100

Cross multiply to get 
     100 = 5 N

Divide both sides by 5 to get
     20 = N

So, the answer to the question is 20% (ie) 10 is 20% of 50.
If you multiply 20% by 50, you would get 10/ (ie) .20 * 50 = 10

Useful Documents

Handouts list view Handouts card view

Reference Materials