what is the least common denominator of 1/2, 2/7x, and 5/x?
14x
Oh, finding the least common denominator is like finding a needle in a haystack. So, let's play a little game called "Denominator Hide and Seek." Ready?
The denominator 1/2 is pretty shy, so it hides in the bushes. Oh look, here it is!
The denominator 2/7x is a bit mischievous, so it hides in a tree. Hmm, I think I see it waving at us!
Lastly, the denominator 5/x is a quick little fella, so it runs into a cave. Oh, it's sneaky, but I caught a glimpse of it!
Now, let's bring them all together. We need to find a common hiding spot for all these denominators. And, ta-da! The least common denominator is 2 * 7x * x = 14x².
Who knew finding least common denominators could be such an adventurous game?
To find the least common denominator (LCD) of fractions, you will need to find the least common multiple (LCM) of the denominators.
For the given fractions: 1/2, 2/7x, and 5/x, the denominators are 2, 7x, and x, respectively.
To find the LCM, you can follow these steps:
Step 1: Factorize each denominator into prime factors.
2 = 2^1
7x = 7 * x^1
x = x^1
Step 2: Determine the highest power of each factor, as it appears in any of the denominators.
The highest power of 2 is 2^1.
The highest power of 7 is 7^1.
The highest power of x is x^1.
Step 3: Multiply the highest powers of the factors.
2^1 * 7^1 * x^1 = 14x
Therefore, the least common denominator (LCD) of 1/2, 2/7x, and 5/x is 14x.
To find the least common denominator (LCD) of fractions, you need to find the smallest common multiple of their denominators.
Let's find the denominators of the given fractions:
1/2 has a denominator of 2.
2/7x can be rewritten as 2/(7x), which has a denominator of 7x.
5/x has a denominator of x.
Next, let's find the smallest common multiple of these denominators, which will be their LCD.
To find the LCD, list the multiples of each denominator:
Multiples of 2 are: 2, 4, 6, 8, 10, 12, ...
Multiples of 7x are: 7x, 14x, 21x, 28x, ...
Multiples of x are: x, 2x, 3x, 4x, ...
From the lists above, you can see that the smallest common multiple of 2, 7x, and x is 14x.
Therefore, the least common denominator (LCD) of the fractions 1/2, 2/7x, and 5/x is 14x.