Multiplication and Division

Remainders

In the previous pages, we divided numbers equally. For instance, at the beginning of the lesson, we divided 10 tickets equally between 5 people. Each person received 2 tickets. What happens when a number can't be equally divided?

For example, consider the situation below.

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  Let's say we have 10 tickets...

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  Let's say we have 10 tickets... that we are dividing between 3 friends.

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  We'll try solving the problem 10 / 3.

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  Let's see how many tickets we can give to each of our friends...

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  Let's see how many tickets we can give to each of our friends...

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  Let's see how many tickets we can give to each of our friends... One...

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  Let's see how many tickets we can give to each of our friends... One...

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  Let's see how many tickets we can give to each of our friends... One...

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  Let's see how many tickets we can give to each of our friends... One... Two...

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  Let's see how many tickets we can give to each of our friends... One... Two...

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  Let's see how many tickets we can give to each of our friends... One... Two...

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  Let's see how many tickets we can give to each of our friends... One... Two... Three.

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  What happens now? We have 3 friends and only 1 ticket is left.

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  That means 1 is the remainder, or the amount left over.

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  We're ready to write our quotient.

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  Each friend has three tickets, so we'll write 3.

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  Then, we'll write our remainder. That's 1. See how we wrote it next to the lowercase letter r?

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  So, 10 / 3 = 3 r1. We can read this quotient as three remainder one. 10 tickets divided by 3 friends means each friend gets 3 tickets with 1 ticket left over. 

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You can see from the slideshow that the remainder (1) is smaller than the number we divided by (3). That will always be the case when the problem has a remainder. For example, look at each of these problems below:

21 / 5 = 4 r1

The remainder of 1 is smaller than 5.

76 / 6 = 12 r4

The remainder of 4 is smaller than 6.

If the remainder is larger, that means the amount left over is too large. You'll need to try dividing again. For example, if you have 4 friends and 7 tickets left over, you know that each friend can get at least one more ticket.