__-__

**Order of Operation***"Operations"*means things like add, subtract, multiply, divide, squaring, etc. If it isn't a number it is probably an operation. But, when you see something like ...

7 + (6 × 52 + 3)

... what part should you calculate first?

Start at the left and go to the right?

Or go from right to left?

*Warning: Calculate them in the wrong order, and you will get a wrong answer !*

So, long ago people agreed to follow rules when doing calculations, and they are:

**Order of Operations**

**Do things in Parentheses First.**Example:

6 × (5 + 3)

6 × 8

48

**Exponents (Powers, Roots) before Multiply, Divide, Add or Subtract**. Example:

5 × 22

5 × 4

**20**

**Multiply or Divide before you Add or Subtract**. Example:

2 + 5 × 3

2 + 15

**17**

**Otherwise just go left to right**.

**How Do I Remember It All ... ? PEMDAS !**

**P**=

**P**arentheses first

**E**=

**E**xponents (ie Powers and Square Roots, etc.)

**MD**=

**M**ultiplication and

**D**ivision (left-to-right)

**AS**=

**A**ddition and

**S**ubtraction (left-to-right)

http://www.mathsisfun.com/operation-order-pemdas.html (see this web page for more explanation - information used from site)

**more ...**

__Factor__Factors are the numbers you multiply together to get another number:

Example: 3 and 4 are factors of 12, because 3x4=12.

Also 2x6=12 so 2 and 6 are also factors of 12, and 1x12=12 so 1 and 12 are factors of 12 as well.

So ALL the factors of 12 are 1,2,3,4,6 and 12

(and also -1,-2,-3,-4,-6 and -12).

http://www.mathsisfun.com/definitions/factor.html (see this web page for more explanation - information used from site)

**- A number that only has one and itself as a factor**

__Prime Numbers__Examples: 1, 2, 3, 5, 7, 11

**- A number that has more than one and itself as a factor**

__Composite Numbers__Examples: 4, 6, 8, 9

http://www.mathsisfun.com/prime-composite-number.html (see this web page for more explanation)

**- numbers that you count by...**

__Multiples__Examples: The first five multiples of 2 are = 2, 4, 6, 8, 10 The first five multiples of 8 are= 8, 16, 24, 32, 40

http://www.mathsisfun.com/definitions/multiple.html (see this web page for more explanation)

**- finding**

__Prime Factorization__**which prime numbers**multiply together to make the original number.

Here are some examples:Example 1: What are the prime factors of 12 ?It is best to start working from the smallest prime number, which is 2, so let's check: 12 ÷ 2 = 6

Yes, it divided evenly by 2. We have taken the first step!

But 6 is not a prime number, so we need to go further. Let's try 2 again:

6 ÷ 2 = 3

Yes, that worked also. And 3

**is**a prime number, so we have the answer:

**12 = 2 × 2 × 3**

As you can see,

**every factor**is a

**prime number**, so the answer must be right.

Note:

**12 = 2 × 2 × 3**can also be written using exponents as

**12 = 22 × 3**

http://www.mathsisfun.com/prime-factorization.html (see this web page for more explanation- information used from this site)

**- The**

__Exponent__**exponent**of a number says

**how many times**

**to use the number in a multiplication.**

In

**8 2nd power**the "2" says to use 8 twice in a multiplication,

so

**8**

**2nd power**

**= 8 × 8 = 64**

Exponents are also called Powers or Indices.

In words: 82 could be called "8 to the power 2" or "8 to the second power", or simply "8 squared"

http://www.mathsisfun.com/exponent.html (see this web page for more explanation- information used from this site)

__- a number that has a whole number and a fraction.__

**Mixed Numbers****- a fraction that has a larger number for the numerator than denominator.**

__Improper Fraction__**- fractions that are equal to each other.**

__Equivalent Fractions__

__Dividing Fractions-__*Turn the second fraction upside down, then just multiply.*

There are 3 Simple Steps to Divide Fractions:Step 1. Turn the second fraction

*(the one you want to divide by)*upside-down

(this is now a reciprocal).Step 2. Multiply the first fraction by that reciprocal

Step 3. Simplify the fraction (if needed)