Multiplying decimals two-step word problems
The narrator says 'Marta now has $108', but $108 is only her Saturday pay. With her $48.25 savings she has $156.25. A note and the questions correct this.
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The video sets up two-step word problems that combine multiplying decimals with adding or subtracting: Marta's savings plus her Saturday babysitting pay, and how much farther Maddie ran than Aaron. It multiplies as if there were no decimals, then places the decimal point by estimating or counting decimal places. Careful: the narrator stops after the multiplication step in both problems, so you must finish the second step yourself.
You'll be able to
- write an expression like 48.25 + (8 x 13.50) for a two-step word problem.
- multiply a decimal by a whole number and place the decimal point correctly.
- finish a two-step problem by adding or subtracting after multiplying.
Key words
- order of operations
- The rule that you multiply before you add or subtract unless parentheses say otherwise.
- parentheses
- Brackets ( ) that show which part of an expression to work out first.
- estimate
- A rough answer using easier numbers, used to check where the decimal point goes.
Transcript
- [Instructor] We're told that Marta babysits to earn extra money. She has saved $48.25. On Saturday, she works for eight hours and earned $13.50 an hour. How much money does Marta have altogether? Pause this video and see if you can work through that. All right, so let's just write out what's going on.
So 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. And then she makes some more money. On Saturday, she works for eight hours and earned 13.50 an hour. So just on Saturday, how much is she going to earn?
She's going to earn eight 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. So first step, what is eight times 13.50? So I'll do that right over here, 13.50 times 8. And the way I'm going to think about it is let's just ignore the decimal for second.
Let's just pretend like it's 1,350 times 8. And then there's many ways to think about where to put the decimal. Actually, let me do that over here. 1,350 times 8. So 8 times 0 is 0. 8 times 5 is 40. Regroup the 4. 3 times 8 is 24, plus 4, is 28. And then, actually, I'm writing a little bit messy here.
So this was a 0 and then that was a 4. 3 times 8 is 24, plus 4 is 28. Regroup that two. 1 times 8 is 8, plus 2 is 10. We get 10,800. So the digits for this are also going to be similar. We're going to have 10,800 here. But the question is, where is the decimal sign?
There's several ways you could reason through this. You could say, "Well, let's see, 13 times 8 is 80 plus 24. It's going to be about 104. So this should be a little bit more than 104." So that might be a good reason to put the decimal right over here. 108 gets us there.
Another way you could think about it is to go from 13.50. 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. And so this answer's gonna be 100 times bigger than this one. So 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 amongst both numbers. There's only two up here, one, two. And so when you take the product, you're going to have one, two numbers to the right of the decimal as well.
Either way, Marta now has $108. Let's do another example. We are told Maddie ran around a 0.85 kilometer track five times. Aaron ran 2.75 kilometers. How much farther did Maddie run than Aaron? Again, pause the video. Try to work through this. All right, so first, let's think about how far Maddie ran.
The track is 0.85, 85 kilometers, and they ran, or she ran around that five times. And so we will, this is what Maddie ran. Maddie. And if we wanna know how much more Maddie ran than Aaron, well, then we would subtract from that how much Aaron ran. So minus 2.75.
So this right over here is what Aaron ran. 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 times 5 is. So 0.85 times 5. And I'm gonna do the same thing.
I'm first just gonna think about what 85 times 5 is. 5 times 5 is 25, 8 times 5 is 40, plus 2 is 42. So this is going to have the same digits here, four, two, five. Where do you think I'm gonna 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 5, it should be a little bit less than 5." So if I put the decimal right over here, that is a little bit less than 5. This is looking pretty good. Another way to think about it is I have two digits to the right of the decimal in total.
Two digits to the right of the decimal in total. Another way you could think about it is to go from 85/100 to 85, you need to multiply by 100. You essentially need to move the decimal over two spaces to the right. And so this answer right over here is gonna 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.
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