HARD WORK CAFÉ : MATH

GED Math Formula Sheet 2014

Division of Fractions

Why do you "flip" the second number when you divide fractions?

Let's look at this in terms of whole numbers first. To make this a little easier to read, I'll use "d" for "divided by":

6 d 2 = 6 * (1/2) = 3

9 d 3 = 9 * (1/3) = 3

15 d 8 = 15 * (1/8) = 15/8 = 1 7/8

Do you see a pattern here? Multiplication and division are "opposite" operations (it's been too long, I don't remember the correct term; "reciprocal", maybe?). Dividing by a number is the same as multiplying by the inverse of the number. When you "flip" a fraction (or a whole number), you've created its inverse. Since 6 = 6/1 and 3 = 3/1, we can rewrite the first example as

6/1 d 3/1 = 6/1 * 1/3 = (6*1) / (3*1) = 2

So,

15/2 d 5/8 = 15/2 * 8/5 = (15*8) / (2*5) = 120/10 = 12

Integers Review Feb. 2014

Integers (Positive and Negative numbers)
Numbers can indicate a positive (+) amount or a negative (-) amount of a quantity.

For example, it is 85°in North Carolina, but somewhere in Antarctica, it is -6°

Explanation: Introduction to Integers by Sal Khan
WHY DO TWO NEGATIVES EQUAL A POSITIVE VIDEO

Try these: Comparing Integers

Ordering Integers

3 Integer Rules

# 1 Double Signs (Clean-up): IMPORTANT! A number must have only one sign in front of it before you begin the problem. Here is how to "clean -up" before you begin.

a) IF Signs are the same, make the number positive.

Examples: – (-5) = +5 and + (+5) = +5

b) IF Signs are different, make the number negative.

Examples: + (-5) = -5 and - +5 = -5

# 2 Addition/Subtraction
a) If signs are the same, add and keep the sign.

Examples: -5 -5 = -10 and +5 +5 = +10

b) If signs are different, subtract and take the sign of the larger number.

Examples: -6 +5 = -1 and +6 -5 = +1

Try These:
Adding and Subtracting Integers

# 3 Multiplication/Division (this one is too easy)

a) If signs are the same, the answer if positive.

Examples: - 25 ÷ - 5 = +5 and +25 ÷ +5 = +5

-5(-5) = 25 or 5(5) = 25

b) If signs are different, the answer is negative

Examples: - 36 ÷ -6 = -6 and -36 ÷ 6 =-6 -

-8(7) = -56 or 8(-7) = -56

REMEMBER: Integers without signs are positive

Try These:

Multiplying Integers

Dividing Integers

Number Patterns

1. Inductive vs Deductive Reasoning

2. Deductive Reasoning

3. Inductive Reasoning

4. Sal Khan discusses Number Patterns

Input Output Homework

More Input Output Practice

Input Output

X = 0 Y = 1

X = 1 Y = 4

X = 2 Y = ?

Properties of Numbers:

A. Commutative Property of Addition and Multiplication: If you change the order of the numbers, the answer will not change.

B. Associative Property of Addition and Multiplication: If you change the way you group the numbers the answer will not change.

C. Distributive Property: You can add first and then multiply, or you can multiply first and then add and you will get the same answer.

Video Commutative and Associative Properties

Inverse Operations: Inverses are Opposites. Addition and Subtraction are inverse operations. You can use one to undo the other. Multiplication and Division are also inverse operations.

SEE: Achieving TABE Success in Mathematics page 102

FUNCTION - A rule that changes one value to another value is called a function. Applying the rule to a starting number is input the result is the output.

Algebra

Elementary algebra introduces the basic concepts of algebra. It is one of the main branches of mathematics. It builds on students' understanding of arithmetic. Whereas arithmetic deals with specified numbers, algebra introduces quantities without fixed values, known as variables. This use of variables requires the use of algebraic notation and an understanding of the general rules of the order of operations introduced in arithmetic.

The use of variables to denote quantities allows general relationships between quantities to be formally expressed, and thus enables a wide scope of problems. Most quantitative results in science and mathematics are expressed as algebraic equations.