Total ring of fractions
Okay kiddo, imagine you have a bunch of fractions like 1/2, 3/4, and 5/6. Now, what if you want to do math with these fractions, like adding or multiplying them together? Well, sometimes it can be tricky because they all have different denominators (the bottom number in the fraction).
That's where the total ring of fractions comes in! It's like a special club for all the fractions where they can hang out together and do math easily. To join the club, we need to make all the denominators the same. We do this by finding what's called the least common multiple (LCM) of all the denominators.
Once we have the LCM, we can create new fractions with this LCM as the denominator. For example, if the fractions were 1/2, 3/4, and 5/6, the LCM would be 12. So we can create three new fractions with 12 as the denominator: 6/12, 9/12, and 10/12.
Now that all the fractions have the same denominator, we can add or multiply them like normal! And that's the magic of the total ring of fractions - it lets us do math with fractions easily by making all the denominators the same.
That's where the total ring of fractions comes in! It's like a special club for all the fractions where they can hang out together and do math easily. To join the club, we need to make all the denominators the same. We do this by finding what's called the least common multiple (LCM) of all the denominators.
Once we have the LCM, we can create new fractions with this LCM as the denominator. For example, if the fractions were 1/2, 3/4, and 5/6, the LCM would be 12. So we can create three new fractions with 12 as the denominator: 6/12, 9/12, and 10/12.
Now that all the fractions have the same denominator, we can add or multiply them like normal! And that's the magic of the total ring of fractions - it lets us do math with fractions easily by making all the denominators the same.