Multiplying decimals two-step word problems | Grade 5 (TX TEKS) | Khan Academy

We're told that Marta babysits to earn extra money. She has saved $48.25. On Saturday, she works for eight hours and earns $13.50 an hour. How much money does Marta have all together?

Pause this video and see if you can work through that.

All right, so let's just write out what's going on. She already has $48.25, so we'll just assume everything is in dollars here; I don't have to keep writing the dollar sign. Then she makes some more money on Saturday. She works for eight hours and earns $13.50 an hour. So just on Saturday, how much is she going to earn? She's going to earn 8 times $13.50.

So, she starts with $48.25 and then on Saturday, she earns this much right over here. Now, order of operations would tell us to do the multiplication first, but just to make that very clear, I'm going to put parentheses here. This is what she started with and then she makes this much on Saturday.

So, let's figure out what this is. The first step is to calculate what 8 * 13.50 is. I’ll do that right over here: $13.50 times 8. The way I'm going to think about it is let's just ignore the decimal for a second. Let's just pretend like it's $13.50 * 8. There are many ways to think about where to put the decimal. Actually, let me do that over here: 13.50 * 8.

So, 8 * 0 is 0, 8 * 5 is 40, regroup the four. 3 * 8 is 24 plus 4 is 28, and then I'm writing a little bit messy here, so this was a zero and then that was a four. 3 * 8 is 24 plus 4 is 28; regroup that two. 1 * 8 is 8 plus 2 is 10. We get 108.

So, the digits for this are also going to be similar. We're going to have 10.80 here. But the question is, where is the decimal sign? There are several ways you could reason through this. You could say, "Well, let's see, 13 * 8 is 80 plus 24. It's going to be about 104," so this should be a little bit more than 104.

Another way you could think about it is to go from $13.50 to $1,350; you would have to multiply by 100. You'd have to move this decimal twice to the right. Therefore, this answer is going to be 100 times bigger than this one.

You could also divide by 100, and really what you're doing there, some of you might have already learned, when you're multiplying decimals, you can count how many digits are to the right of the decimal among both numbers. There are only two up here, one and two. So, when you take the product, you're going to have one or two numbers to the right of the decimal as well.

Either way, Marta now has $18.

Let's do another example. We are told that Maddie ran around a 0.85 km track five times. Aaron ran 2.75 kilometers. How much farther did Maddie run than Aaron?

Again, pause the video and try to work through this.

All right, so first let's think about how far Maddie ran. The track is 0.85 km and they ran around that five times. So, we will calculate this: Maddie ran. If we want to know how much more Maddie ran than Aaron, then we would subtract from that how much Aaron ran. So, we have 0.85 * 5.

Now, order of operations would tell us to do the multiplication first, but just to make doubly sure, we can put some parentheses around there. So let's first figure out what 0.85 * 5 is.

I'm going to do the same thing; I’m first just going to think about what 85 * 5 is:
5 * 5 is 25,
8 * 5 is 40 plus 2 is 42.

So this is going to have the same digits here: 4.25. Where do you think I'm going to put the decimal? Well, once again, we could say, "All right, this is not quite one but it's close to one," so if you multiply that times five, it should be a little bit less than five. So if I put the decimal right over here, that is a little bit less than five; this is looking pretty good.

Another way to think about it is, I have two digits to the right of the decimal in total. Another way you could think about it is to go from 8500 to 85; you need to multiply by 100 because you need to move the decimal over two spaces to the right. Therefore, this answer right over here is going to be 100 times larger than what we need over here.

So then you divide by 100; you move the decimal back two spaces to the left to get to 4.25. But Maddie ran 4.25 kilometers more than Aaron.