Amy has a master's degree in secondary education and has taught math at a public charter high school.
In this lesson, we will talk about multiplication; multiplication with numbers that end in zeroes. Multiplication is repeated addition. It is telling you that you have several groups of a certain number to add together. So, 4 * 3 (four times three) means that you have three groups of 4 that you need to add together: 4 + 4 + 4.
So what happens if we add zeroes behind our numbers? Like, what if we multiply 40 * 30 together? You can see that this means we have thirty groups of 40. This is quite a bit to add together manually. So what can you do? You can follow this little trick for multiplying with numbers that end with zeroes.
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Multiplying by Zeroes
The trick involves counting the zeroes. So, to multiply 40 * 30, you would multiply the 4 * 3 and then count the zeroes. Your answer is what you get from multiplying the non-zero numbers and then writing the number of zeroes you have counted.
So, for the problem 40 * 30, your non-zero numbers are 4 and 3. You have two zeroes, one from the 40 and one from the 30. Then your answer comes from multiplying 4 *3 and adding the number of zeroes behind it. So, 4 * 3 is equal to 12, so 40 * 30 is equal to 12 with two zeroes after it: 1,200.
This trick will serve you well when you are taking math tests and you want an easy and quick way to answer these problems. Let's take a look at a couple more example problems.
Multiply 100 * 20.
In this problem, we see that our non-zero numbers are 1 and 2. How many zeroes do we have? We have three: two from the 100 and one from the 20. So, your answer is 1 * 2 = 2 with three zeroes behind it: 2,000.
In A Word Problem
Now, what if we had a word problem?
Sarah is starting a pay-it-forward campaign where she sends a nice message to 30 of her friends asking all of them to send it to 10 more people. How many people will her 30 friends reach?
This is a word problem, so we need to figure out what two numbers we are multiplying together. This problem tells us that 30 of Sarah's friends are sending Sarah's message to 10 more people each. So that means we need to multiply the 30 and the 10: 30 * 10. We are multiplying with numbers that end with zeroes. Our non-zero numbers are 1 and 3. We have two zeroes, one from the 30 and one from the 10. Our answer is 1 * 3 = 3 with two zeroes behind it: 300. And we are done!
Let's review what we've learned.
Multiplication is repeated addition. To multiply two numbers that end with zeroes, we multiply the non-zero digits and count the number of zeroes we have. Our answer is what we get from multiplying the non-zero numbers followed by the number of zeroes we have counted.
Students should be able to meet these objectives by completing this lesson:
- Describe multiplication
- Explain the trick for multiplying numbers ending in zeroes and give examples
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How to Multiply Numbers Ending in Zeroes
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