# Tuesday, Nov. 7 - Introduction to Fractions

Slice a pizza, and we get fractions:

1/2 **(One-Half)**

1/4 **(One-Quarter)**

3/8 **(Three-Eighths)**

The top number says how many slices we **have.**

The bottom number says how many equal slices the whole pizza was **cut into**.

**Equivalent Fractions**

Some fractions may look different, but are really the same, for example:

4/8 = 2/4 =1/2

It is usually best to show an answer using the simplest fraction ( 1/2 in this case ). That is called ** Simplifying**, or

**the Fraction**

*Reducing*

**Numerator / Denominator**

We call the top number the **Numerator**, it is the number of parts we **have**.

We call the bottom number the **Denominator**, it is the number of parts the whole is **divided into**.

*Numerator*

*(over)*

**Denominator**

You just have to remember those names! (If you forget just think "Down"-ominator)

*To simplify a fraction, divide the top and bottom by the highest number that
can divide into both numbers exactly.*

**Kinds of Fractions**

**Proper Fraction** - A Proper Fraction has a top number less than its bottom number

I**mproper Fraction **- An Improper Fraction has a top number larger than (or equal to) the bottom number.

**M****ixed Fraction or Mixed Number** - A Mixed Fraction is a whole number and a proper fraction combined such as 1 ¾

**Simplifying Fractions**

Simplifying (or *reducing*) fractions means to make the fraction as simple as possible.

Why say four-eighths (*4/***8**) when we really mean half (*1/***2**) ?

*4/***8 **=*2/***4 **=*1/***2**

**Method 1**

Try to **exactly divide** (only whole number answers) both the top and bottom of the fraction by 2, 3, 5, 7 ,... etc, until we can't go any further.

**Method 2**

Divide both the top and bottom of the fraction by the Greatest Common Factor (you have to work it out first!).

**Comparing Fractions**

Sometimes we need to compare two fractions to discover which is larger or smaller.

There are two main ways to compare fractions: using **decimals**, or using the** same denominator**.

**The Decimal Method of Comparing Fractions**

Convert each fraction to decimals, and then compare the decimals.

**The Same Denominator Method**

*The denominator is the bottom number in a fraction.*

*It shows how many equal parts the item is divided into*

When two fractions have the **same denominator** they are easy to compare.

**Remember**

*"Multiplying fractions no big problem,
Top times top over bottom times bottom,*

*"Dividing fractions, easy as pie,
Flip the second fraction, then multiply,*

*"If adding or subtracting is your aim,
The bottom numbers must be the same!*

*"Change the bottom using multiply or divide,
But the same to the top must be applied,*

*"And don't forget to simplify,
Before it's time to say goodbye" *