Video: Solving Word Problems by Adding Two Mixed Numbers

If a man bought 1 kg of apples for 8 1/4 pounds and 1 kg of oranges for 4 1/2 pounds, how much did he pay in total?

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Video Transcript

If a man bought one kilogram of apples for eight and a quarter pounds and one kilogram of oranges for four and a half pounds, how much did he pay in total?

Here we’ve got two amounts of money that we’re given. And we’re given them as mixed numbers. Our first mixed number is eight and a quarter. A man buys one kilogram of apples for eight and a quarter pounds. And our second mixed number is four and a half. The same man buys one kilogram of oranges for four and a half pounds. And we’re asked to calculate how much the man paid in total.

So, to find the answer, we need to add our two mixed numbers together, eight and a quarter plus four and a half. Now we know a mixed number is a whole number and a fraction. So, the way we could find the answer is to add both whole numbers together, then both fractions together, and then find the overall total.

First of all, let’s partition both mixed numbers into the whole number and fraction parts. Eight and a quarter is eight and the fraction part is one-quarter. The whole number part of four and a half is four and the fraction on the end is one-half.

Let’s begin by adding the whole number parts together. Eight plus four equals 12. The total of the whole number parts of our mixed numbers is 12. Now let’s add the two fraction parts together. What’s one-quarter plus one-half? We might know what the answer to this is just by visualizing the fractions and thinking about what they look like. But let’s do this the way that we would normally add two fractions together.

Usually, we’d say to ourselves that the two denominators are different, so we can’t add them together at the moment. Instead, we need to convert one of the fractions so that they both have the same denominator. We can convert the second fraction, one-half, into quarters. To turn halves into quarters, we multiply the denominator by two. And to keep the value of the fraction the same, we also need to double the numerator, the top number. One times two is two. And so, we know one-half is the same as two-quarters.

Let’s change our calculation. So, now it reads one-quarter plus two-quarters. How many quarters do we have if we add one-quarter and two-quarters together? We have three-quarters. Because our answer is going to be a mixed number, we can see what it is already. But let’s write out the final addition just to be sure. 12 plus three-quarters equals 12 and three-quarters.

How did we arrive at this answer? First, we looked at both mixed numbers that we needed to add together. And we partitioned them into their whole number parts and their fraction parts. To find the total, we added the whole number parts, which gave us an answer of 12. And then, we added the fraction parts. Because both fractions have different denominators, we converted one of them so they both showed quarters.

By adding the two fraction parts together, we got an answer of three-quarters. And then, finally, we added 12 and three-quarters together to give us our answer. And so, if a man buys one kilogram of apples for eight and a quarter pounds and a kilogram of oranges for four and a half pounds, he will pay twelve and three-quarter pounds in total.

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