mathy folks...help needed...again! (algebra LCD problem)

[4kids4me]

This is SO simple, but I'm missing *something* so I need someone to explain what I don't understand. ;)

 

This is from Teaching Textbooks Algebra 1, lesson 62.

 

I'm not exactly sure how to type out the problem, so I'll do my best...

 

2x/15 + x/6 = 1/4

 

 

He explains to factor it (and we NEED to learn it this way), the LCD must have all the factors that appear in each denominator, but no extra factors at all.

 

15 factors: (3)(5)

6 factors: (2)(3)

4 factors: (2)(2)

 

So he says you take for LCD: 3, 5, 2, (not the second 3), (not the 3rd 2), but you do take the fourth 2.

 

Ok, so you want all the factors but no extra. Why do we need to add that extra 2, since we've already got 2 in there? Does that make sense? I should know this as I taught it in gr. 5, but this way is NOT making sense to me. I can't even explain it properly.

 

IF you've got a special gift of understanding what I don't get, could you please explain it to me!?!?!?

 

THANKS!!!!!! :001_smile:

[Perry]

Here's an explanation:

 

To elaborate how these steps are done, let's work through these steps with two fractions. Let's find the LCD for 10/24 and 22/45:

 

 

 

1. Write the prime factorization for the denominator of each fraction.
   
   • Prime factors of 24 are: 2, 2, 2, and 3.
     
   • Prime factors of 45 are: 3, 3 and 5.
     

 

 

[*]Note all prime factors that occur. For each prime factor that occurs, determine in which denominator it occurs the most. Write down the prime factor the number of times it occurs in that one denominator.

 

• The prime factors that occur are 2, 2, 2, 3, 3, and 5.
  

 

NOTE: The prime factor 2 occurred most often in 24, so we write that three times. The prime factor 3 occurred most often in 45, so we write that two times, the 5 occurred only once in 45, so we write that once.

[*]Calculate the LCD of your fractions. To do this, multiply the factors written down in step 2. 2 x 2 x 2 x 3 x 3 x 5 = 360 The LCD for these two fractions is 360.

 

 

Let's look at another example of this.

Example

 

Find the LCD for the following group of fractions: 9/12, 14/18, 66/100.

The answer to this is 900.

Let's work through the solution to this example.

 

 

1. Write the prime factorization for the denominator of each fraction.
   We must write the prime factors of 12, 18, and 100.
   
   • Prime factors of 12 are: 2, 2, and 3
     
   • Prime factors of 18 are: 2, 3, and 3
     
   • Prime factors of 100 are: 2, 2, 5, and 5
     

 

 

[*]Note all prime factors that occur. For each prime factor that occurs, determine in which denominator it occurs the most. Write down the prime factor the number of times it occurs in that one denominator.

In this case, the 2 is a prime factor for all three of the denominators. We must take 2 the number of times it occurs most in any one denominator. It occurs twice. This is also the case for both 3 and 5.

This leaves us with the following prime factors for our LCD:

 

• The prime factors that occur are 2, 2, 3, 3, 5, and 5.
  

 

 

[*]Calculate the LCD of your fractions. To do this, multiply the factors selected in step 2. The LCD for our fractions is 2 x 2 x 3 x 3 x 5 x 5 = 900.

 

 

Finding the LCD for a group of fractions is an important step to comparing fractions that have different denominators.

Does that help?

[TXBeth]

Slightly simpler explanation: because your LCD needs to be divisible by 4, not just by 2. So 30 will not work, because you couldn't convert the 1/4 into 30ths. Make sense?

[4kids4me]

Here's an explanation:

 

Does that help?

 

Beth...thanks for your explanation...I knew how to do it that way, but the way it's explained in TT (the way Perry explained it), I'm thinking it's important to know why and how to break it down because as we get further into algebra, I'm assuming it'll bite us in the butt if we don't get it! :)

 

Perry...we slowly went through your examples and it makes perfect sense. The thing that made it click was realizing we needed what prime factor occurred most in each of the denominators. Now that we understand that we can continue on!

 

I'm so grateful to have this board. I'm not great at math, and knowing I can come here and get the help I need is SO reassuring!!!!

 

Thanks, Ladies. :D

[Dana]

Beth...thanks for your explanation...I knew how to do it that way, but the way it's explained in TT (the way Perry explained it), I'm thinking it's important to know why and how to break it down because as we get further into algebra, I'm assuming it'll bite us in the butt if we don't get it! :)

 

It'll bite you in the butt because this is setting you up for rational equations where the numerator and denominator are polynomials. You can look ahead (or look at purplemath) to see examples of this.

 

The technique you're learning now for LCD is what'll work for rationals. You can't find the LCD by counting multiples with polynomials.