Adding and subtracting fractions with unlike denominators word problems
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Silvia is growing tomato plants and studying their heights. Here is her data. So the beefsteak tomato type had a height of 3 and 1/4 feet, Roma 2 and 7/8 feet, cherry 3 and 1/2 feet. And they ask us, what is the difference between the heights of the beefsteak, so that's that one right over there, and the Roma tomato plants? So they want us to find the distance between these two heights. So this cherry tomato height was really unnecessary for the sake of this problem. So we want to find the difference in these two heights. So we want to subtract the smaller of these from the larger of these. So we're really trying to evaluate what 3 and 1/4 minus 2 and 7/8 is. Now, the first thing that I like to do is convert both of these into mixed numbers. Sorry, they're already mixed numbers-- to convert both of these into improper fractions. So 3 and 1/4 is the same thing as 3 plus 1/4, which is the same thing as 12/4 plus 1/4. That's the same thing as 3 and 1/4. And from that, we're going to subtract 2 and 7/8. 2 and 7/8 is the same thing as 2 plus 7/8. 2 is the same thing as 16/8 plus 7/8. So this is essentially what we are trying to figure out. Now, what is 12/4 plus 1/4? It's 13/4, 13 over 4. And then, what's 16/8 plus 7/8? Well, that's 23/8. So this is going to be minus 23 over eight. Now, we're subtracting one fraction from another. But we have different denominators. So we can't make sense of this until we have the same denominator. And so what is the least common multiple of these two denominators, of both 4 and 8? What is the smallest number that is divisible by both 4 and 8? Well, 8 is divisible by 8. And 8 is also divisible by 4. So if we can rewrite 13/4 as having 8 as a denominator, then we are all set. So let's try to do that. So we're going to write both of these with 8 as the denominator. This one already has it. So 13/4, I'm going to have it with 8 as the denominator. So to get from 4 to 8, we have to multiply the denominator by 2. So in order to not change the value of the fraction, we have to multiply the numerator by that exact same value. We've got to multiply it by 2. So this becomes 26/8. And from 26/8, we're going to subtract 23/8. And so this is going to be over 8-- 26 minus 23, which is equal to, and we deserve our drum roll now, is 3. So it's 3/8. So the difference between the heights of the beefsteak and Roma tomato plants-- 3/8. And everything we've been doing insofar has been in feet, so 3/8 of a foot.