Thursday, February 28, 2013

Answer to adding fractions when LCD is not obvious


THIS WAS THE QUESTION AND HINT:

Adding fractions when the LCD is not obvious.

Question:

What is 13/40+12/45?

A hint on finding the Least Common Denominator: 

In order to add these fractions you need a least common denominator.  The LCD is not obvious.  One way to get the LCD is to list all multiples of 45 and determine whether it is divisible by 40.  The smallest such number is the LCD.

This process is somewhat tedious for this problem because the list is sort of long.    It is much better to use the prime factorization method.

Any common denominator of 45 and 40 must have all prime numbers of 40 and 45 as factors.  The LCD will not include extra copies of the prime factors.  If 40 is divisible by prime k and 45 is divisible by prime k then the LCD only includes one copy of k.  If 40 is divisible by prime k and 45 is divisible by k2 then include k twice.

So 40 is 2x2x2x5

45 is 3x3x5

The LCD is 3x3x2x2x2x5

We only included one copy of 5.

Now find the numerators and add.

Will post the answer this afternoon.

THIS IS THE ANSWER:

So the LCD is 360.

We multiplied 40 by 9 so we must multiply 13 by 9 and we get 117.

We multiplied 45 by so we must multiply 12 by 8 and we get 96.

We add 117/360 and 96/360 and get 213/360

Both 213 and 117 are divisible by 3.

The fraction simplifies to 71/120.

This is the simplest form because 71 is prime.

For an interesting web site on prime numbers go to

http://www.mathsisfun.com/prime_numbers.html

I will add more information on how to identify prime numbers at www.fractiontips.blogspot.com soon.



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