Lesson with Fractions
  
    What are and how to do improper fractions?        Have you ever asked yourself, what are improper fractions?  Well, the answer is easy.  Improper fractions are fractions that the numerator is larger in value than the denominator.  for example 13/5.  If you already knew that, did you know how to get it to an improper fraction?  Well, here are a few steps to show you how:

1.  You have to have an mixed number.  Such as 2 4/9.

2.  Multiply  9 × 2 = 18

3.  Add  18 + 4 = 22

4.  Since, when you add and subtract fractions you keep the  same denominator, you do the same thing here.  So, the answer would be 22/9.
 
 

 
    Here are a few steps to show you how to add fractions.
The one thing to remember is if different denominators, such as 2/3 + 1/4 , change both fractions so they each have the same denominator, but still equal 2/3 or  1/4 when reduced.  Here's how.

1.  2/3 + 1/4 , ask yourself what can 3 and 4 both go into evenly.

2.  You should have gotten 12.

3.  So now you make 2/3 and 1/4 into 12ths --- ?/12 + ?/12.
                              1.        2/3 = ?/12
   3 goes  into 12 how many times - 4 times - 4 × 2 = 8 ---
2/3 = 8/12.
                              2.        1/4 = ?/12
   4 goes into 12 how many times - 3 times - 3 × 1 = 3 ---
1/4 = 3/12.

4.  8/12 + 3/12 = 11/12 --- When adding or subtracting fractions always, always, always, keep the same denominator.

5.  Final Answer :  11/12.
 
 

 
 
    How to subtract fractions.        If you know how to add fractions, this is the same.  Except you're subtracting instead of adding.  If different denominators, such as 4/5 - 2/3 , change the denominators so they are the same number.  Like this.

1.  4/5 - 2/3 , ask yourself what can 5 and 3 both go into evenly.

2.  You should have gotten 15.

3.  So now you make 4/5 and 2/3 into 15ths --- ?/15 - ?/15.
                              1.        4/5 = ?/15
   5 goes into 15 how many times - 3 times - 3 × 4 = 12 ---
4/5 = 12/15.
                              2.        2/3 = ?/15
   3 goes into 15 how many times - 5 times - 5 × 2 = 10 ---
2/3 = 10/15.

4.  2/15 - 10/15 = 2/15 --- When subtracting or adding fractions always, always, always, keep the same denominator.

5.  Final Answer :  2/15
 
 


 

    Multiplying fractions.
Multiplying fractions is really quite easy.  The next few steps will show you how in two different ways.

1.  Example: 3/4  ×  8/9

2.  Multiply straight across - 3 × 8 then multiply 4 × 9.

3.  24/36 would be your answer.  But you need to reduce.  Your final answer would be 2/3.

4.  But, there is an easier way to get 2/3.  This way you don't have to reduce big numbers.
 
5.  3/4  ×  8/9 , you can cancel out the 8 and 4 by seeing what numbers can both go into 8 and 4 evenly.  So, it would make the 8 - 2 , and the 4 - 1.  You do the same thing with the 3 and the 9.

6.  It would now look like this :  1/1  ×  2/3.    Then just multiply straight across.

7.  Answer :  2/3  ( Same answer as on number 3, but a faster way to get it. )
 
 

          

    How to divide fractions.

1.    If a mixed number, always make it into an improper     fraction.  If you don't how to do that, check back in this lesson.  If just a fraction, always exchange the numerator and the denominator.

2.  Example : 1 3/5  ÷  2/3

3.  After doing step 1, it should look like this :  8/5  ×  3/2.
When dividing fractions you never really divide, you multiply instead.

4.  Then just multiply straight across.  8  ×  3 , and  5  ×  2.

5.  This should be your answer : 24/10.  Since you wind up with an improper fraction, make it into a mixed number,
2  4/10.  Since your fraction part of the mixed number are both even numbers, reduce it.  So, your final answer would be : 2  2/5.
 

Home