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Published byRodney Frankum Modified over 4 years ago

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Partial Products Multiplication How to multiply multi- digit numbers

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What is a partial product? / Partial means part of and when we use this method, we are breaking the numbers or factors into smaller parts--I am calling them chunks because you are familiar with that term from reading! But we are working with a smaller part first before we put the factors all together to find the product. Can you see the word part in partial?

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What do I do first? / When multiplying with multi-digits, the first thing we want to do is use expanded notation to break down the numbers or factors into smaller chunks. This helps us do one piece at a time. / For example, let’s break down the top number in this number sentence: / 543 can be expanded to 500 + 40 + 3 / x 3 / When multiplying with multi-digits, the first thing we want to do is use expanded notation to break down the numbers or factors into smaller chunks. This helps us do one piece at a time. / For example, let’s break down the top number in this number sentence: / 543 can be expanded to 500 + 40 + 3 / x 3

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Step 2 / You will want to set up the problem vertically and make sure to include the bottom number with each chunk of the expanded number. / For example, 543 x 3 should look like this: / 500+ 40+ 3 / X 3 x3 x 3 / You will want to set up the problem vertically and make sure to include the bottom number with each chunk of the expanded number. / For example, 543 x 3 should look like this: / 500+ 40+ 3 / X 3 x3 x 3

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Step 3 / Do the work of multiplying each chunk. You can work from the left to the right or the right to the left. / 500+ 40 + 3 X 3 x3 x3 1500 120 9 / Do the work of multiplying each chunk. You can work from the left to the right or the right to the left. / 500+ 40 + 3 X 3 x3 x3 1500 120 9

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Step 4 / Now you will add all the chunks or partial products together. Make sure you are aligning the numbers with the correct place value spacing: / 1500 / 120 / + 9 1629 / Now you will add all the chunks or partial products together. Make sure you are aligning the numbers with the correct place value spacing: / 1500 / 120 / + 9 1629

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Step 5 / Check your work! / 1. Did you add all the parts? Did you add them all correctly? / 2. Are your place values aligned correctly? / These two points are very important and usually where any mistakes are made. / Check your work! / 1. Did you add all the parts? Did you add them all correctly? / 2. Are your place values aligned correctly? / These two points are very important and usually where any mistakes are made.

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Step 6 / Did you know you can ALSO check your work by using the traditional method of multiplying? / ‘543 / X 3 / 1629 / Did you know you can ALSO check your work by using the traditional method of multiplying? / ‘543 / X 3 / 1629

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Let’s try this again / Remember, we want to use expanded notation first. / 658 will look like this 600 + 50 + 8 / x5 / Now we want to set up the problem like this: / 600 + 50 + 8 / X 5 x5 x5 Now do the multiplying! / 3000 + 250 + 40 = 3290 / Remember, we want to use expanded notation first. / 658 will look like this 600 + 50 + 8 / x5 / Now we want to set up the problem like this: / 600 + 50 + 8 / X 5 x5 x5 Now do the multiplying! / 3000 + 250 + 40 = 3290

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How did you do? / Are you ready to try it on your own? / Of course, you can work with a table buddy if you’d prefer… / Are you ready to try it on your own? / Of course, you can work with a table buddy if you’d prefer…

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