Topic B: Foundations
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Subtracting mixed numbers with like denominators
Let's figure out what 11 and 12/16 minus 5 and 8/16 is. And then we might have to simplify it down to lowest terms. So the way I like to do these is to kind of separate out the whole number part of the mixed numbers from the fractional part. So I can rewrite this number right over here as 11 plus 12/16. And from that, I am going to subtract-- and I'll put parentheses here because I'm going to break this part open. I'm going to subtract 5 plus 8/16. 5 and 8/16-- same thing as 5 plus 8/16. But I have to remember, I'm subtracting it. I'm subtracting this whole thing. So I could rewrite it as-- I'll rewrite this part-- 11 plus 12/16. And I'm subtracting 5 plus 8/16. So I can distribute the negative sign. So it's going to be minus 5, negative 1 times 5. And then negative 1 times positive 8/16. So it's going to be minus 8/16. And then I like to do the whole number parts separately and then the fractional parts separately. So let's do the whole number parts. We have 11 minus 5. I'll write it here, 11 minus 5. We'll do that part. That's the whole number part. And then we have plus 12/16. Let me do this in pink maybe, plus 12/16, minus 8/16. And 11 minus 5 is 6. And I have 6 plus. And then our denominators are the same here, so we're going to get something over 16. And 12 minus 8 is 4. So this is the same thing as 6 plus 4 over 16, which is the same thing as-- writing it as a mixed number-- 6 and 4/16. And this is the right quantity, but we can simplify it. 4/16 can be simplified. Both the numerator and the denominator are divisible by 4. They both have the factor 4. So let's divide both the numerator and denominator by 4. Divided by 4. Divided by 4. Since we're dividing by the same thing, we're not changing its quantity. And so this is equal to-- we still have the whole number part, 6, but the fraction part is now 1, 1/4. So we get 6 and 1/4.