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# Remainders - A Little Left Over

We teased the exciting world of remainders in the last section. Let's get down to business. When you divide one number by another, sometimes they division is nice and even. Four (4) divided by two (2) gives you the answer of two (2). But what happens if you divide five (5) by two (2)? Two goes into five two times, but then there is this one (1) left over. That amount is called the remainder. You will get remainders when you are dividing whole numbers and you are not using decimal values.

Examples:
5 ÷ 2 = 2 with remainder 1
7 ÷ 2 = 3 with remainder 1
5 ÷ 3 = 1 with remainder 2

If you write out the values in a longer format, you will begin to see how remainders work. When you divide five (5) by two (2) you get two sets of two and then an extra one (1).

Example:
5 ÷ 2 = 2 with remainder 1
5 = 2 + 2 + 1 (that 1 will be your remainder)

# Less Than Ten

In the last page we did some division with numbers less than ten. We skipped a few values because they had remainders. Let's fill in some of the blanks now.

3 ÷ 2 = 1 with remainder 1 (2 + 1)
5 ÷ 2 = 2 with remainder 1 (2 + 2 + 1)
7 ÷ 2 = 3 with remainder 1 (2 + 2 + 2 + 1)
9 ÷ 2 = 4 with remainder 1 (2 + 2 + 2 + 2 + 1)

4 ÷ 3 = 1 with remainder 1 (3 + 1)
5 ÷ 3 = 1 with remainder 2 (3 + 2)
7 ÷ 3 = 2 with remainder 1 (3 + 3 + 1)
8 ÷ 3 = 2 with remainder 2 (3 + 3 + 2)

5 ÷ 4 = 1 with remainder 1 (4 + 1)
6 ÷ 4 = 1 with remainder 2 (4 + 2)
7 ÷ 4 = 1 with remainder 3 (4 + 3)
9 ÷ 4 = 2 with remainder 1 (4 + 4 +1)

6 ÷ 4 = 1 with remainder 1 (5 + 1)
7 ÷ 4 = 1 with remainder 2 (5 + 2)
8 ÷ 4 = 1 with remainder 3 (5 + 3)
9 ÷ 4 = 1 with remainder 4 (5 + 4)

Do you see any patterns? Remainders can never be larger than the number you are dividing by. Even if you are dividing any number by fifty-one (51) you can't have a remainder greater than or equal to fifty-one. It's doesn't matter what number you use.

# Beyond Remainders

We mentioned decimals. For basic math, you will have remainders. As you move forward in math and division, you will learn that remainders are only a good starting point. You will eventually learn how to make decimals. Decimals are number values that are smaller than one. You might notice we skipped division of the number two (2) divided by three (3). We will get to values that are less than one in fractions, decimals, and ratios.

## RELATED ACTIVITIES

 One-Digit Division Quiz(With Remainders) - Play Activity One and Two-Digit Division Quiz (No Remainders) - Play Activity

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