Third Grade Math: Finding the Quotient

How to Divide Numbers

What Is a Quotient?

In a division problem, the quotient is the number you get when you divide one number into another. For example, 6 ÷ 2 = 3. In this problem, three is the quotient. If the answer ends up having a remainder, the whole number is the quotient. For example, if an answer is 7.5, seven is the quotient and .5 is the remainder.

Dividing Single-Digit Numbers

You can learn tricks to make dividing much easier. One way to approach single-digit division problems is to draw the problem as a picture. Let's say the problem is 8 ÷ 2. You can draw eight little stars and then make a circle around each group of two stars. The total number of groups is the quotient (in this case, the answer is four). This strategy works because anytime you divide, you are making groups of equal parts.

Dividing by Multiplying

If you already know your times tables, you can use them to solve division problems. All you have to do is reverse the problem. For example, you can solve 10 ÷ 2 by asking, 'What number times two equals ten?'

Then you can use trial and error. Does four times two make ten? No, it makes eight. So you need to try a bigger number. How about five? Five times two equals ten! So 10 ÷ 2 = 5.

You can always try this trick with division problems, and once you master division, you can reverse the trick to solve harder multiplication problems. Here are some practice problems. The first one is done for you:

1. 10 ÷ 2

Solve by multiplying two with different numbers. The answer is five.

2. 8 ÷ 4

3. 5 ÷ 2

4. 3 ÷ 1

5. 6 ÷ 3

Answers

1. 10 ÷ 2 = 5
2. 8 ÷ 4 = 2
3. 5 ÷ 2 = 2.5
4. 3 ÷ 1 = 3
5. 6 ÷ 3 = 2

Unique Division Problems

Any number divided by zero equals zero. This is because you are dividing the dividend into zero groups. For instance, 6 ÷ 0 = 0 because you are creating zero groups out of six (the dividend).

Alternatively, when you divide any number by one, you get that number. Seven divided into groups of one makes seven groups (7 ÷ 1 = 7).

Examples: 5 ÷ 0 = 0, 7 ÷ 0= 0, 12 ÷ 0 = 0; 5 ÷ 1 = 5, 7 ÷ 1 = 7, 12 ÷ 1 = 12