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The Relation between Multiplication and Division

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Multiplication and division are closely related, given that division is the inverse operation of multiplication. When we divide, we look to separate into equal groups, while multiplication involves joining equal groups.

In today’s post, we’re going to learn to use multiplication as a strategy to solve division problems, which will be really useful for daily life!

We’ll start with a basic multiplication. If we have 4 x 5 = 20, its inverse relations (in the form of a division) will be the following:

20 ÷ 5 = 4

20 ÷ 4 = 5

In the same way, if we take the division 30 ÷ 3 = 10, its inverse relations (in the form of a multiplication) will be the following:

3 x 10 = 30

10 x 3 = 30

In both examples, we can see that we use the same three numbers. This is because when we multiply two numbers (which we call factors), we get a result that we call a product. If we divide this product by one of the factors, we get the other factor as a result.

Example of division solved through multiplication


Here we have:

  • A total number of objects: 28 slices in total
  • A number of sets: 7 people
  • Representation: 42 ÷ 7 = ___

To calculate the exact number of portions that will be given to each person, we have to look for a number that when multiplied by 7 gives us 28. What will it be?

7    x    1    =    7                                  7    x    6    =    42
7    x    2    =    14                                7    x    7    =    49
7    x    3    =    21                                7    x    8    =    56
7    x    4    =    28                                7    x    9    =    63
7    x    5    =    35                                7    x    10  =    70

Great! 4 is the number that gives us 28 when we multiply it by 7. Since the multiplication is the inverse operation to division, 28 divided by 7 equals 4.

Therefore the answer to our exercise is:


Remember that if you want to improve your multiplication and division, the best thing to do is review the times tables and practice with our exercises. Either way, review our post on divisions and practice with our division exercises.

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