Unit 1
How do you solve a math problem with multiple operatons?
Use:
Parenthesis
Exponents
Multiplication and Division
Addition and Subtraction
Whole Numbers
All natural numbers and 0.
Rational Numbers
The set of all numbers that can be written as a fraction of 2 integers.
Divisibility Rules
2 - Any even number.
3 - All digits add up to a multiple of 3.
4 - Last 2 digits have to be a number divisible by 4.
5 - Any number that ends in 5 or 0.
6 - All digits add up to a multiple of 3 and the number is even.
8 - Last 3 digits have to be a number divisible by 8.
9 - All digits add up to a multiple of 9.
10 - Ends in 0.
Numerical Expression
Math sentence with numbers and operations.
Why are multiplication and division along with adding and subtracting in the same order?
You have to do those two operations at the same time left to right.
Natural Numbers
1, 2, 3, 4, 5, ..., ∞
Repeating Decimal
A decimal that goes on forever.
Prime Numbers
Any number with only 2 factors (1 and 0 are neither).
Algebraic Expression1 and Variable2
Math sentence wth numbers, operations, and variables.1 A symbol (usually a letter) tht represents an unknown quantity.2
a + b = b + a
a x b = b x a
Commutative Property
Integers and Multiplication
+ +, + -, - -, and - +
Whole numbers and their opposities.
+, -, +, and -
Terminating Decimal
A decimal that ends.
Composite Number
Any number with more than 2 factors (1 and 0 are neither).
Distributive Property
Distributing one number with the other ones in parenthesis with multiplication.
a + (b + c) = (a + b) + c
a x (b x c) = (a x b) x c
Associative Property
Opposites
2 numbers that add up to 0.
1/2, 1/3, 1/4, 1/5, 1/6, 1/8, 1/9, 1/10, and 1/16
0.5, 0.333..., 0.25, 0.16666..., 0.125, 0.111..., 0.1, and 0.0625
Factor
A number that divides evenly into a given number.
GCF and LCM
GCF - The greatest of all the factors a number has.
LCM - The least common multiple of two numbers.
a + 0 = a
a x 1 = a
Identity Property
Absolute Value
The distance from 0 (the two bars, also think of it like parenthesis).
Best way to multiply/divide fractions AND decimals.
Fractions - Multiply by reciprocal (multiplicative inverse) and cross simplfy.
Decimals - Larger number at top for multiplying, and dividend has to be an integer in division.
How to write the prime factorization for a number.
Use exponents, and smallest number as the base goes first, second smallest is next, and so forth.
Steps to a one (or more) step equation.
Identify Variable, Isolate Variable (Combine like terms and/or use inverse operations), See-Saw (Balance - "Whatever you do to one side, you must do to the other," -Mr. See-Saw), and Check!