Video: Operations on Mixed Numbers in Two-Step Word Problems

Amelia is entering a baking contest. She wants to make a total of 6 pies so that she can choose the best one as her entry. If the recipe for one pie calls for 2 1/4 cups of flour, and she has 14 cups in total, how many cups of flour will she have left?

03:15

Video Transcript

Amelia is entering a baking contest. She wants to make a total of six pies so that she can choose the best one as her entry. If the recipe for one pie calls for two and a quarter cups of flour, and she has 14 cups in total, how many cups of flour will she have left?

So if we take a look at this problem, we can see that there is a proportional relationship between the number of pies and the cups of flour needed. So if Amelia needs two and quarter cups of flour for one pie, then what calculation will we need to carry out to find out how to solve this problem? Well, what we want to do first of all is find out how many cups of flour are required for six pies. So we’re gonna do six multiplied by two and a quarter. What we’re gonna look at is take a look at a couple of ways we can carry out this calculation.

So first of all, in the calculation on the left-hand side, what we’re going to do is convert two and a quarter into a top-heavy or improper fraction. So when we do that, we’re gonna get six multiplied by nine over four or nine-quarters. And we got that because there are eight-quarters in two whole ones. And then we’ve got one other quarter. So, that’s nine-quarters or nine over four. Also, we can think about it in the way that was shown in pink. And that is we multiply our integer value by the denominator, so here two multiplied by four. Then we add on what the numerator was, which in this case was one. And then we put it over the original denominator. Okay, so we’ve got six multiplied by nine over four.

So what we can do first of all is cross cancel. So we can divide six and our four, because that’s on the denominator, by two. And when we do that, we get three and two. So we’ve got three multiplied by nine over two, which is gonna give us 27 over two. And that’s because what we do is we multiply the three by the nine because we can think of three as three over one. So if we multiply fractions, we multiply the numerators then multiply the denominators. So we’d have three multiplied by nine, as we said, which gives us our 27, and then one multiplied by two, which gives us two.

So we’ve got 27 over two, which is an improper fraction. So, what are we gonna do now to turn us back into a mixed number? Well, two goes into 27 13 times with one left over. So we’re gonna get 13 and a half. Okay, great. So let’s have a quick look at the other method.

Well, the other method is to split it into parts. So first of all, we have six multiplied by two, and then we add six multiplied by a quarter. Well, six multiplied by two is 12. And then if we cross cancel, we’ll get three multiplied by a half. And that’s because both six and four would divide by two. So we’ve got three multiplied by a half, which is three over two or three-halves, which we can also write as one and a half. So now, we’ve got 12 plus one and a half, which is 13 and a half, like we got in the first method.

Okay, great. But have we solved the problem? Well, no, because what we want to know is, in total, how many cups of flour will be left over? Well, if we’ve got 14 cups of flour in total, then what we need to do is take 13 and a half away from 14, which is equal to a half. So therefore, Amelia will have half a cup of flour left over.

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