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Table of Contents
Multiplying multi-digit numbers can become a daunting and tedious process, but shortcuts and techniques help make the process bearable and simpler.
See the fact file below for more information on the multiplying multi-digit numbers or alternatively, you can download our 28-page Numbers And Operations In Base Ten: Multi-Digit Multiplication CCSS 5.NBT.5 worksheet pack to utilise within the classroom or home environment.
Key Facts & Information
LEARNING OBJECTIVE:
- At the end of the lesson, students will be able to multiply multi-digit whole numbers using standard algorithms and other techniques. Students will also be able to estimate the product of multi-digit numbers by rounding off the factors.
A NOTE FOR THE TEACHER
- When multiplying multi-digit numbers, take note of the following:
- It usually helps to write the whole numbers in expanded form
- Always double check your solutions when doing long multiplication
- When multiplying numbers with multiple zeros, there are helpful shortcuts and techniques that make the process easier
THEORY:
- Multiplying multi-digit numbers can become a daunting and tedious process, but shortcuts and techniques help make the process bearable and simpler. Before we get into some of these techniques, letβs look at how the process of long multiplication works. Take, for example, 24 x 12.
- On the left, we can see how we broke down each factor into its expanded form based on the place values of each factor. For each box in yellow, we multiplied the intersection of numbers. After doing so, we added all numbers in the boxes in yellow to get the final product of 24 and 12, which is 288.
- On the right, we have an example of how long multiplication works. We first multiplied the ones place in 12 to 24 to get 48. Next, we multiplied the tens place in 12 to 24 to get 240. Take note of the extra zero since we are multiplying in the tens place!
- This process, however, is still a bit tedious, and not everyone has the luxury of time to set up the table. If we only need a rough estimate of the product, we can hasten the process by rounding off the factors to the nearest tens or hundreds. Take, for example, 295 x 22. We can round off 295 to the nearest hundreds and 24 to the nearest tens to get 300 x 20. These numbers are much easier to multiply with each other, and the resulting product after long multiplication will be 6000. We can verify that this is a rough estimate since 295 x 22 is actually equal to 6490, which isnβt too far off from 6000.
- For 300 x 20, we can make the process simpler by using another technique. This technique involves simply multiplying the non-zero digits (i.e. 3 and 2), and simply adding the number of zeros to the final product. In this case, there are 3 zeros, so after multiplying 3 and 2 to get 6, we can add the 3 zeros to the right of six to get 6000.
- Why is this technique possible?
- Well, if we look at one of the expanded forms of 300 x 20, we get (3 x 100) x (2 x 10). We can remove the parentheses since the expression only involves multiplication. After doing so, we can rearrange the numbers by pairing up different digits: 3 x 2 x 100 x 10 Simplifying this, we get 6 x 1000, which is simply adding 3 zeros to the right of 6. From doing so, we can verify that the technique holds true since the result is still 6000.
Numbers And Operations In Base Ten: Multi-Digit Multiplication CCSS 5.NBT.5 Worksheets
This is a fantastic bundle that includes everything you need to know about Numbers And Operations In Base Ten: Multi-Digit Multiplication across 28 in-depth pages. These are ready-to-use worksheets that align with the Common Core CCSS code 5.NBT.5 for Numbers And Operations In Base Ten: Multi-Digit Multiplication.
Table of contents
- A lesson plan
- Warm up activity
- Math theory explained
- Assisted learning activities
- Independent learning activities
- Extension activities and games
- Answer keys
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Use With Any Curriculum
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