Math 6High ( Period 3)

Using a Least Common Denominator 3.2 

In chapter 2 we learned to find the LCM of two or more whole numbers. When you add or subtract fractions with different denominators,  a convenient denominator is the least common denominator… which is really  the Least Common Multiple of the Denominators… but it is simply called the LCD

Add:
3/8 + 5/ 12

Using the method we talked about yesterday, a common denominator is the product of 8 and 12

8(12) = 96

so we would do the following:

3(12) + 5(40)
96

36+ 40
96

76/96 

but we can simplify this. 

Using the GCF  ( OMG- we use both LCM and the GCF  to simplify fractions!!)

76/96 = 19/24

Using the LCM of 8 and 12 (now—how do we find that ?... Oh yeah.. use the BOX method or inverted division to get the prime factorization of each) So the LCM(8.12) = 24

Now rewrite the fractions

I taught you to stack them ( STACK ‘EM}

3/8 ·3/3= 9/24

5/12∙2/2 = 10/24

No you can add the numerators

9 +10
24

Wow—We arrived at the same solution!

Using the LCD reduces the amount of simplifying you need to do!

But what happens when you need to add three fractions with three different denominators? You can’t use the BOX method of finding the LCM… You need to find the LCM by… using

ALL THE FACTORS TO THEIR GREATEST POWERS… 

ALL THE FACTORS TO THEIR GREATEST POWERS!

1/3 + ¼ + 1/8  Yikes… what to do?

First try to see if one of the denominators is a multiple of the other… you now only need to find the LCD of the that fraction and the one that isn’t a multiply or factor . 

In this case,  8 is a MULTIPLY of 4 so I don’t need to worry about 4

I need to find the LCM  of 3 and 8.. Now that’s easy

LCM(3,8) is their product 24

So change all of the denominators to 24

1/3 = 8/24

¼ = 6/24

1/8 = 3/24

And add

23/24

Evaluating a Variable expression

Evaluate x – y + z  when  x = 9/10  y = 3/4 and z = 1/3

x- y + z = 9/10 – 3/4  + 1/3

Rewrite using the LCD

9/10 ·6/6 = 54/60

3/4·15/15 = 45/60

1/3·20/20 = 20/60

54 – 45 + 20
60

29/60