Fractions representing proportions

Question

John, Mike, and Dillon are painting a fence. John paints 1/4 of the fence and Mike paints 2/5 of the fence. How much of the fence is left to paint for Dillion? Please break the common numerator part down for me...thank you

Answer 1

John, Mike, and Dillon are going to paint the entire fence which, mathematically, we can represent as 1 fence.

 

So, the John's part + Mike's part + Dillon's part = 1

 

Substituting what you are given, you see that

 

1/4 + 2/5 + Dillon's part = 1

 

You remember that when you add fractions, the denominators must be the same.  The denominators in the fractions we are given are 4 and 5.  So, we need a number that can be divided evenly by both 4 and 5.   One way to find this number is to simply multiply the denominators together (4 times 5 is 20).  So, let's rewrite both fractions in a way so they have a denominator of 20.

 

CHANGING THE 1/4

Since I have to multiply 4 by a 5 to get 20, I can multiply the 1/4 by 5/5 to rewrite the fraction.  This means that 1/4 is equal to 5/20.

 

CHANGING THE 2/5

Since I have to multiply 5 by a 4 to get 20, I can multiply the 2/5 by 4/4 to rewrite the fraction.  This means that 2/5 is equal to 8/20.

 

So I can now rewrite the equation as

 

5/20 + 8/20 + Dillon's part = 1 (or 20/20)

13/20 + Dillon's part = 20/20

 

So, how many 20th's are left for Dillon to complete?

 

If 13/20 has been painted, this leave 7/20 for Dillon to paint.  

 

Hope this helps!!  :)