Download Math Fundamentals

Math Fundamentals
Number Concepts and Definitions
Integer: Any number that does not have a fraction or decimal part. { … -3, -2, -1, 0, 1, 2, 3 …}
Factor: An integer that can be divided into another integer without a remainder. For
example, 3 is a factor of 12 because 12/3 = 4. We say that the larger number “is divisible by”
the smaller number, so her 12 is divisible by 3.
Multiple: An integer that is part of another integers times table. For example, 12 is a multiple
of 3 because 3 x 4 = 12.
Prime Number: A number that is divisible by only 1 AND itself.
List the first 10 Prime Numbers:
What is the only even prime number? Why??
Remainder: The integer that is left over when an integer is divided by another integer that is
not its factor. For Example 13/5 = 2 with a remainder of 3. (Please note: if you punch 13 / 5
into the calculator the answer is 3.6. The remainder is NOT 6.)
Properties of Odd and Even Integers:
(Even) x (Even) = Even
(Even) x (Odd) = Even
(Odd) x (Odd) = Odd
Even / Even = Even
Even / Odd = Odd
Odd / Odd = Even
Decimal Places:
In the number 25.97
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2 is the “tens digit” and is in the “tens place”
5 is the “units digit” and is in the “units place”
9 is the “tenths digit” and is in the “tenths place”
7 is the “hundredths digit” and is in the “hundredths place”
Scientific Notation: 43,500 would be 4.35 x 104 and 0.00524 would be 5.24 x 10-3. SAT
questions may ask you to manipulate numbers in this form, but usually that’s easy to do on
your calculator.
Prime Factors
breaking a number down into factors of Prime numbers, meaning they can’t be factored
anymore.
For Example:
What are the prime factors of 12 and 420?
Examples:
1) In the number 379.045 , what digit is in the units place?
2) If x is an odd positive integer, which of the following expressions must be even?
a. 2x
b. x + 2
c. 3x + 1
3) If x has a remainder of 5 when divided by 6 and x>10, what is the smallest possible value
of x?
4) If j is the largest prime factor of 42, and k is the largest prime factor of 36, what is the
value of j + k?
5) If x and y are integers such that xy=-12 and x>0, what is the greatest possible value of y?