Featured titleMath

Partial products - multiplying in parts

Math

Partial products means we multiply numbers part-by-part. For example, 5 x 36 is done as 5 x 30 and 5 x 6, and those two parts are added. You can quite easily do these in your head when one number has two digits and the other has one. This concept is very important, as it is the basis for the regular multi-digit multiplication algorithm studied in 4th grade. I also teach it in my book Math Mammoth Multiplication 2 at - available both as an inexpensive download ($5.10) and as a printed copy.

Year

2022

Duration

34m

IMDb

0

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Comments

10 Comments

user9383419145485Oct 22, 2025

We can think of 8 x 7 (for example) as 5 groups of 7 plus 2 groups of 7. In other words, we break down the product 8 x 7 into parts, into "partial products". This is easily illustrated with an array. Using partial products, or multiplying by parts, allows us to do multiplications such as 15 x 7 using mental math. It goes like this: 15 x 7 is 10 x 7 plus 5 x 7, which equals 70 + 35 = 105. There are other ways, too! Math Mammoth Grade 3 curriculum Multiplying with the Area Model (online activity)

Chelsie MOct 22, 2025

We can think of 8 x 7 (for example) as 5 groups of 7 plus 2 groups of 7. In other words, we break down the product 8 x 7 into parts, into "partial products". This is easily illustrated with an array. Using partial products, or multiplying by parts, allows us to do multiplications such as 15 x 7 using mental math. It goes like this: 15 x 7 is 10 x 7 plus 5 x 7, which equals 70 + 35 = 105. There are other ways, too! Math Mammoth Grade 3 curriculum Multiplying with the Area Model (online activity)

Kamene GoroOct 22, 2025

We can also divide in parts (not only multiply). Simply think of the quotient as consisting of a sum or difference, and divide each part separately. For example, 824 / 4 can be done as (800/4) + (24/4), and that can easily be done in your head. The reason we can do so boils down to the distributive property, and the fact that each division can be written as a multiplication. This lesson is part of the Math Mammoth Grade 6 curriculum. Find out more: See more 6th grade math videos:

SkalesOct 22, 2025

We can also divide in parts (not only multiply). Simply think of the quotient as consisting of a sum or difference, and divide each part separately. For example, 824 / 4 can be done as (800/4) + (24/4), and that can easily be done in your head. The reason we can do so boils down to the distributive property, and the fact that each division can be written as a multiplication. This lesson is part of the Math Mammoth Grade 6 curriculum. Find out more: See more 6th grade math videos:

merryrianaOct 22, 2025

I show how to solve a 2-digit by 2-digit multiplication problem with the partial products algorithm. You can see the same multiplication illustrated with an area model here: This lesson is part of the Math Mammoth Grade 6 curriculum. Learn more: See more 6th grade math videos:

user4121114070630Oct 22, 2025

I show how to solve a 2-digit by 2-digit multiplication problem with the partial products algorithm. You can see the same multiplication illustrated with an area model here: This lesson is part of the Math Mammoth Grade 6 curriculum. Learn more: See more 6th grade math videos:

Mauriiciia LepfoundzOct 22, 2025

The partial products algorithm allows anyone (even students who are "bad" at math) to learn how to multiply 2- and 3-digit numbers! It is also easy to see why it works. You don't have to be a math whiz! Partial products means that we multiply in part-by-part. For example, 7 x 534 is done as 7 x 500, 7 x 30, and 7 x 4, and lastly those parts are added. This topic is also explained (along with practice problems) in my book Math Mammoth Multiplication 2 at - available both as an inexpensive download ($5.10) and as a printed copy.

الفنان نور الزينOct 22, 2025

The partial products algorithm allows anyone (even students who are "bad" at math) to learn how to multiply 2- and 3-digit numbers! It is also easy to see why it works. You don't have to be a math whiz! Partial products means that we multiply in part-by-part. For example, 7 x 534 is done as 7 x 500, 7 x 30, and 7 x 4, and lastly those parts are added. This topic is also explained (along with practice problems) in my book Math Mammoth Multiplication 2 at - available both as an inexpensive download ($5.10) and as a printed copy.

SocialIntrovert3020Oct 22, 2025

The area of a two-part rectangle gives us a simple visual model to illustrate partial products (the distributive property), here called "multiplying in parts". This video belongs to a lesson from the Math Mammoth Grade 6 curriculum. See more math videos for 6th grade:

MoyuOct 22, 2025

The area of a two-part rectangle gives us a simple visual model to illustrate partial products (the distributive property), here called "multiplying in parts". This video belongs to a lesson from the Math Mammoth Grade 6 curriculum. See more math videos for 6th grade: