Lesson 2: Equivalent Fractions.

1. What EQUIVALENT Means.
2. When Fractions Are Equivalent.
3. Simplifying Fractions.
4. Practice Game.

WHAT EQUIVALENT MEANS

The word EQUIVALENT means the same as EQUAL or, more precisely, of equal value.

For example, you can see that the colored part of each of the circles below is exactly the same.
 
 
 

 
It must follow that = = 
  

 WHEN FRACTIONS ARE EQUIVALENT.

Equivalent fractions are obtained by multiplying or dividing both the numerator and the denominator by the same number.

 
In the example above, we see that = =     

(Both numerator and denominator are multiplied by 2)     
 

 
Going in the opposite direction, we see that = =  

(Both numerator and denominator are divided by 2)
 

Example:

Complete the following equivalent fractions:

 = 

SOLUTION:

 = =  

   (Both numerator and denominator are multiplied by 2)
 

 SIMPLIFYING FRACTIONS

Many fractions can be reduced down and written in a simpler form.
For example, if your mum cut a big, creamy cake into 8 pieces and you ate 4 of them, she will say to a doctor that you got sick from  eating half of the cake.

To simplify a fraction, both the numerator and denominator must be divided by the same number. This method is also called canceling down or reducing the fraction.

The fraction is in the SIMPLEST FORM when it cannot be any more simplified.

When you are asked to simplify or reduce down a fraction, you should always try to simplify as much as you can to achieve the simplest form. You will do it by dividing both numerator and denominator by their  Highest Common Factor( or H.C.F.). Do not worry too much about H.C.F. now. Just  keep simplifying the fraction until it cannot be simplified.
 

Example:

Simplify 

SOLUTION:

=  =      

(Both sides are divided by 8, so the fraction is canceled by 8)

But the result is not in the Simplest form. It still can be simplified:

= =      

(Both sides are divided by 2, so the fraction is reduced by 2)

Now the result is in the Simplest Form.
You could get this result by reducing the fraction once only by 16. (The Highest Common Factor).
Or by reducing it 4 times by 2. Could you think of any other ways?