Question

i was using the prime number to find the lcd on 2 fractions and im lost, who can help me?

Answer 1

i

Answer 2

the fractions are 3/15 - 2/25 need to find the lcd

Answer 3

What do the numbers 15 and 25 have in common? Well, they're both odd numbers and, in fact, divisible by the prime number 5.

Answer 4

To find the least common denominator using this method, factor each of the denominators into primes. Then for each different prime number in all of the factorizations, do the following...

Count the number of times each prime number appears in each of the factorizations.

For each prime number, take the largest of these counts.

Write down that prime number as many times as you counted for it in step #2.

The least common denominator is the product of all the prime numbers written down.

Example: We'll use the same fractions as above: 1/5, 1/6 and 1/15.

Factor into primes (Click here to see our table of prime numbers.)

Prime factorization of 5 is 5 (5is a prime number)

Prime factorization of 6 is 2 x 3

Prime factorization of 15 is 3 x 5

Notice that the different primes are 2, 3 and 5.

Now, we do Step #1 - Count the number of times each prime number appears in each of the factorizations...

The count of primes in 5 is one 5

The count of primes in 6 is one 2 and one 3

The count of primes in 15 is one 3 and one 5



Step #2 - For each prime number, take the largest of these counts. So we have...

The largest count of 2s is one

The largest count of 3s is one

The largest count of 5s is one



Step #3 - Since we now know the count of each prime number, you simply - write down that prime number as many times as you counted for it in step #2.

Here are the numbers...

2, 3, 5

Step #4 - The least common denominator is the product of all the prime numbers written down.

2 x 3 x 5 = 30

Therefore, the least common denominator of 1/5, 1/6 and 1/15 is 30.

Now I want to apply this concept to this fractions 3/15-2/25 :(( who can help me?

Answer 5

Well, having what I just said in mind, 3/15 can be simplified to 1/5 whereas 2/25 cannot be further simplified. Since 5 is a prime number, it cannot be factored. However, 25 can be factored to 5^2. For the first fraction, our factor was 5^1 and 5^2 for the second. We take the largest prime-factoring, in this case 5^2, and obtain, again, 25. This is our lowest common denominator:

\[3/15-2/25\]
\[1/5-2/25\]
\[5/25-2/25\]

Answer 6

so do i have to simplify the fraction first? 3/15? why not doing it like the instruction says: 3x5=15
5X5=25
what confuses me is that the 5 appears 2 times on the second multiplication so I cant grab the largest:( so I should have both? :(

Answer 7

or maybe if the prime number appears 2 times on the multiplication you just take it one time for example: if we take the larges number on the first is 5, the largest number on the second one is 5, so 5X5= 25 and that will be our LCD. right?

Answer 8

If you don't want to simplify, then you can just find the prime factors of 15: 3 and 5, and the prime factors of 25: 5 and 5. You take the 5s from the second fraction, take the 3 from the first fraction and multiply them: 5*5*3=75. That's your new LCD:
\[3/15-2/25\]\[15/75-6/75\]\[9/75\]\[3/25\]Which is the same thing.

Answer 9

so if the number is equal means that I cant take the larger, so then I have to take the two 5 out of the second fraction.how come im not taking the 5 out the first one?

Answer 10

You're not taking the 5 out of the first one because it is to the power of 1, whilst in the second one, it is to the power of 2. You always take the greatest one out of those two.

Answer 11

that is the part that I don't understand:(

Answer 12

how come in 3X5 I'm taking just the 3 and on 5X5 im taking both five's?

Answer 13

Because you want to take all the primes you can. 25 can't be divided by 3, but 15 can, so we take it.

Take, as an example, the numbers 130 and 15. What's the lowest multiple of these two numbers?

Well, 130 has the following factors: 2, 5 and 13, whilst 125 has the following factors: 5, 5 and 5.

In the first number, 2 repeats itself 1 time and 0 times in the second number. So we take 2.

In the first number, 5 repeats itself 1 time and 3 times in the second number, so we take 5^3 and not 5^1.

In the first number, 13 repeats itself 1 time and 0 times in the second number. So we take 13.

We then multiply everything we got: 2 * 5^3 * 13 = 3250 and that's the lowest multiple of 130 and 125.

Answer 14

I meant 130 and 125 in the first sentence, not 130 and 15.

Answer 15

you wrote: In the first number, 5 repeats itself 1 time and 3 times in the second number, so we take 5^3 and not 5^1.
Me: that is why we don't take 5^4 times, because we are going to go to the fraction that has it more times and use that number that amount of times only...right;(

Answer 16

Let's use across's example 130 and 15
what we want is a number that both divide into.
130 = 2*5*13 (prime factors)
15= 3*5
now what number is would both divide into?

Answer 17

5

Answer 18

You confused me! I mean x/130 and x/15

Answer 19

if x= 2*5*13*more_stuff
then x/130 = 2*5*13*more_stuff/(2*5*13)
This means 2*5*13 must be part of x.

Answer 20

The answer is x= 2*3*5*13
Is this totally confusing?

Answer 21

can you guys can do it with my example: 3x5=15 so I take? then 5x5=25 so I take?
im looking at my book that the LCD is 25 but I want to know how do it get there applying the steps from here: http://www.helpwithfractions.com/least-common-denominator.html

Answer 22

OK,
15= 3*5
25= 5*5

Answer 23

we want x that 15 divides into: x/15
and x that 25 divides into: x/25

Answer 24

Can you find x?

Answer 25

if x is evenly divisible by 15 the 3*5 goes into x.
also, if x is divisible by 25 then 5*5 goes into x
so x=3*5*5 is the answer. check it:
3*5*5/15= 3*5*5/(3*5)= 5. yep it works
3*5*5?25= 3*5*5/(5*5)= 3. yes. it works

Answer 26

To get the answer in your book you must first simplify 3/15 to 1/5. Then your problem becomes 1/5- 2/25.
then we want x/5 and x/25.
x= 5*5 works.

Answer 27

If we use your instructions,

Count the number of times each prime number appears in each of the factorizations.

we have 5 (for the 5) and 5^2 (for the 25). that is 5 is used once in 5 and twice in 25

now take the largest of these counts.
which is 2. We used 5 twice.

The least common denominator is the product of all the prime numbers written down.
we only have 5 used twice. so lcd =5*5= 25