Clearing fractions to solve equations. LCD help

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Rustymamma

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Hello
struggling helping my son with math. Problem is to clear fractions using lcd and use distributive property. Easy enough, but I can’t seem to find the lcd for 8,10&14 in a manner which I can explain and make simple to him, or at all honestly. I feel foolish.
prob is
5/8=1/10+5/14m
Thanks smart people for helping a rusty mom.
 
If you can say "LCD" or "LCM", you should also understand "Prime Factorization".

Identify your denominators: 8, 10, 14 (or is that 14m? Typo?)

Prime Factors:
8 = 2*2*2 <= This is 8 expressed as a product of prime numbers.
10 = 2*5 <= This is 10 expressed as a product of prime numbers.
14 = 2*7 <== This is 14 expressed as a product of prime numbers.

Now, just meet everyone's needs! This will tell you not only the LCD, but how to get every denominator on the same page.

Let's see what you get.

Note: This Prime Factorization is also a useful tool for GCF. A chat for another time, perhaps.
 
Rustymamma said:
Hello
struggling helping my son with math. Problem is to clear fractions using lcd and use distributive property. Easy enough, but I can’t seem to find the lcd for 8,10&14 in a manner which I can explain and make simple to him, or at all honestly. I feel foolish.
prob is
5/8=1/10+5/14m
Thanks smart people for helping a rusty mom.
Click to expand...
Presumably you are looking for the least common multiple of 8, 10, and 14, which will be the least common denominator of 5/8, 1/10, and 5/14. I'm guessing that the equation is [MATH]\frac{5}{8} = \frac{1}{10} + \frac{5}{14}m[/MATH], rather than [MATH]\frac{5}{8} = \frac{1}{10} + \frac{5}{14m}[/MATH], but this LCD will help either way.

There are many ways to do this, so it would be very helpful if you could give us any information on what he has learned (for example, show us his attempt, or an example he was given). It happens that I wrote a blog post about this recently, collecting a number of answers to similar questions that illustrate different ways to do it.

The most basic way, starting with the definition of LCD, is just to list multiples of each number, and look for a number that shows up in all the lists. (When the LCD is very large, this is a very inefficient way to do it, but it is important to understand the goal before learning other methods.)

Here are the beginnings of three lists of multiples:

8, 16, 24, 32, 40, ...​
10, 20, 30, 40, ...​
14, 28, 42, 56, ...​

We've found a common multiple of 8 and 10 already; our LCD will be a multiple of that, so we could continue by just listing multiples of 40 and looking for one that's also a multiple of 14. Or we could just continue the lists we've already started.

Now, if your son has learned a more sophisticated method, it will be best to move on to that; but this way will work if necessary.
 
Rustymamma said:
Hello
struggling helping my son with math. Problem is to clear fractions using lcd and use distributive property. Easy enough, but I can’t seem to find the lcd for 8,10&14 in a manner which I can explain and make simple to him, or at all honestly. I feel foolish.
prob is
5/8=1/10+5/14m
Thanks smart people for helping a rusty mom.
Click to expand...

you can teach him how to find the LCM in easy ways. But first he needs to know about
  • Factors
  • Prime Factors
  • Multiples
Factor is, If a number is divisible by another number without a remainder that the second number is a factor of the first number.

Prime Factor is, Numbers with exactly two distinct factors are called Prime Numbers. In other words,A number only divisible by 1 and the same number itself is the prime number.

Multiple is, A number that obtained by multiplying the given whole number by any whole number is a Multiple.

Find the factors,
There are few methods to find the factors,
example:
factors of 36
36 = 1 x 36
36 = 2 x 18
36 = 3 x 12
36 = 4 x 9
36 = 6 x 6

So the
Factors of 36 are,
1 , 2 , 3 , 4 , 6 , 9 , 12 , 18 and 36

There are few methods to find LCM. It is lot to explain. I have written an article about this in here with examples. Hope that will help you. It also explains how to get the HCF.

Here is a one method to find LCM,

LCM of 3, 4, 6

Multiples of 3 : 3, 6, 9, 12, 18, 21, 24, 27, 30, 33, 36, 39, …
Multiples of 4 : 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, …
Multiples of 6 : 6, 12, 18, 24, 30, 36, 42, 48, 54, …

Now you can see 12, 24 and 36 are some common multiples between 3, 4 and 6.
We want the least one. So the LCM is 12.
 
Last edited:
Thank you all very much for your time. I can’t share what he did on his own because it is illegible due to the hot tears and angry erasing that took place. I was able to introduce prime factors to help him solve LCM. Again thank you for the taking the time to explain it so well. It was very helpful and I suspect that prime factors were a principal recently introduced at school as he had a spark of recollection when seeing them. Stay smart
 
Factor: \(\displaystyle 8=2^3,~10=2\cdot 5~\&~14=2\cdot 7\).
List prime factors; \(\displaystyle 2,~5,~7\).
Take the greatest power of each: \(\displaystyle 2^3\cdot5\cdot 6=280\).
The is the least common multiple or \(\displaystyle LCD\).
 
pka said:
Factor: \(\displaystyle 8=2^3,~10=2\cdot 5~\&~14=2\cdot 7\).
List prime factors; \(\displaystyle 2,~5,~7\).
Take the greatest power of each: \(\displaystyle 2^3\cdot5\cdot {\color{red}7}=280\).
The is the least common multiple or \(\displaystyle LCD\).
Click to expand...
Corrected above; you meant 7, typed 6.
 
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