Wednesday, Oct 23 - 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 Reducing the Fraction

 

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

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

Mixed 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"