How To Add Mixed Fractions With Like Denominators

silvia is growing tomato plantsand studying their heights. here is her data. so the beefsteak tomato typehad a height of 3 and 1/4 feet, roma 2 and 7/8 feet,cherry 3 and 1/2 feet. and they ask us, whatis the difference

How To Add Mixed Fractions With Like Denominators, between the heightsof the beefsteak, so that's that oneright over there, and the roma tomato plants? so they want us to find thedistance between these two

heights. so this cherry tomato heightwas really unnecessary for the sake of this problem. so we want to find thedifference in these two so we want to subtractthe smaller of these from the larger of these. so we're really trying toevaluate what 3 and 1/4 minus 2 and 7/8 is. now, the first thing that i liketo do is convert both of these

into mixed numbers. sorry, they're alreadymixed numbers-- to convert both of theseinto improper fractions. so 3 and 1/4 isthe same thing as 3 plus 1/4, which is the samething as 12/4 plus 1/4. that's the samething as 3 and 1/4. and from that, we're goingto subtract 2 and 7/8. 2 and 7/8 is the samething as 2 plus 7/8. 2 is the same thingas 16/8 plus 7/8.

so this is essentially whatwe 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 beminus 23 over eight. now, we're subtractingone fraction from another. but we have differentdenominators. so we can't makesense of this until we

have the same denominator. and so what is the leastcommon multiple of these two denominators, of both 4 and 8? what is the smallest number thatis 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 ashaving 8 as a denominator, then we are all set. so let's try to do that.

so we're going to writeboth of these with 8 as the denominator. this one already has it. so 13/4, i'm going to haveit with 8 as the denominator. so to get from 4 to 8, we haveto multiply the denominator by 2. so in order to not changethe value of the fraction, we have to multiplythe numerator by that exact same value.

we've got to multiply it by 2. so this becomes 26/8. and from 26/8, we'regoing to subtract 23/8. and so this is going to beover 8-- 26 minus 23, which is equal to, and we deserveour drum roll now, is 3. so it's 3/8. so the difference betweenthe heights of the beefsteak and roma tomato plants-- 3/8. and everything we'vebeen doing insofar

has been in feet,so 3/8 of a foot.