Find the third angle of a triangle.
- 180 - (the sum of the two other angles)
- 180 - 58 - 33 = 89
- The sum of the angles in a triangle always equals 180 degrees
What is the Order of Operations?
- - Multiplication & Division go together (can be switched)
- - Same with Addition and Subtraction
Percent = Part / Whole
Part = Percent x Whole
Percent Increase =
(Amount of Inrease / Original Whole) x 100
Ex: The price goes up from $80 to $100. What is the percent increase?
% Inc. = (20/80) x 100 = 25%
Percent Decrease =
(Amount of Decrease / Original Whole) x 100
How can you redict whether a sum, difference, or product will be ODD or EVEN?
Don't bother memorizing. Just take simple numbers, like 2 & 3, and see what happens.
Ex: If m
is even and n
is odd, is the product mn
odd or even?
- Say m = 2 and n = 3.
- 2 x 3 is even.
- Thus, mn is even.
How to recognize MULTIPLES of 2, 3, 4, 5, 6, 9, and 12.
- 2: Last digit is even (Ex: 24)
- 3: Sum of digits is a multiple of 3 (Ex: 108)
- 4: Last two digits are a multiple of 4 (Ex: 148)
- 5: Last digit is a 5 or 0 (Ex: 85)
- 6: Sum of digits is a multiple of 3, and last digit is even (Ex: 144)
- 9: Sum of digits is a multiple of 9 (Ex: 216)
- 10: Last digit is a 0 (Ex: 180)
- 12: Sum of digits is a multiple of 3, and last two digits are a multiple of 4 (Ex: 168)
How to find a COMMON FACTOR of two numbers.
Break both numbers down to their prime factors to see what they have in common. Then multiply the shared prime factors to find all common factors.
Ex: What factors greater than 1 do 135 and 225 have in common?
- Prime factors of 135 = 3 x 3 x 3 x 5
- Prime factors of 225: 3 x 3 x 5 x 5
The two numbers share the common factors 3, 3, and 5. By multiplying these in every possible combination, you get the common factors 3, 5, 9, 15, and 45.
How to find a COMMON MULTIPLE of two numbers.
The product of two numbers is the easiest common multiple to find, but it is not always the least common multiple.
Ex: What is the least common multile of 28 and 42?
- 28 = 2 x 2 x 7
- 42 = 2 x 3 x 7
The LCM can be found by finding the prime factorization of each number, then seeing the greatest number of times each factor is used. Multiply each prime fctor the greatest number of times it appears.
In 28, 2 is used twice. In 42, 2 is used once. In 28, 7 is used once. In 42, seven is used once, and 3 is used once.
Thus, multiply each factor the greatest number of times it appears in a prime factorization:
LCM = 2 x 2 x 3 x 7 = 84