Division is splitting a total number of items into equal groups. A division sentence tells us how many equal groups we make and how many items are in each group.
Think of division as sharing fairly. If you have 12 cookies and 4 friends, you give each friend 3 cookies. That’s 12 ÷ 4 = 3.
When you divide any number by 1, you are splitting it into just one group. The quotient is always the original number.
Dividing by 1 is like asking, "If I keep all the items together in one group, how many are in that group?" The answer is always the number you started with.
When you divide 1 by any number (except 0), you are trying to split one item into equal groups. Since one whole item cannot be split into multiple whole pieces, the quotient is less than 1. In third grade, we focus on the fact that 1 divided by 1 equals 1.
For now, remember this rule: Any number divided by itself equals 1, so 1 ÷ 1 = 1.
When 0 is divided by any number, it means you start with nothing and try to split it into groups. If you have zero items to share, each group gets zero items.
Zero divided by any number (except 0) is always 0. You cannot share what you do not have.
Division by zero is undefined. It does not make sense to ask how many groups of zero you can make from a number, or to try to split items into zero groups.
You can divide 0 by a number (0 ÷ 5 = 0), but you can never divide by 0 (5 ÷ 0 is not allowed). If you see division by zero, it is an error.
A complete division sentence has three parts: the dividend, the divisor, and the quotient. Always check that your number sentence makes a true fact.
When writing or solving division sentences, ask yourself: Does this make sense with what I know about sharing items? This will help you spot errors, especially with 0 and 1.