How Do You Solve Division in 3rd Grade

Students solidify their knowledge of multiplication and division facts in 3rd grade. It's important to memorize all of the multiplication and division tables, but it's also necessary to understand how these number operations relate to one another.

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Solving Division Problems in 3rd Grade

Division problems have three parts: a dividend, a divisor and a quotient. The dividend is the number that's going to be divided up. For instance, if you have a group of 20 students, and you're going to divide them into groups, 20 would be the dividend.

The divisor is the next number in a division problem. It tells you the number of units that are in each group that you're dividing the larger number into. If we divided the big group of 20 students into smaller groups of four students each, the divisor would be four.

The quotient is usually the answer to the division problem. It tells you how many groups you can make from the dividend that are the size of the divisor. If we divided the 20 students into groups with four students each, we could make five groups of students, so five is the quotient (20 ÷ 4 = 5). In other words, 20 students divided into groups of four gives you five groups.

You can practice division with small objects, like pennies or pieces of candy. Start with a total number of objects for your dividend, like 12. Then, pick a divisor, like four. Divide the total number of objects into groups of four. The number of groups you have, in this case three, is the quotient (12 ÷ 4 = 3).

Dividing as Reverse Multiplication

Another way to think about division is that it's the opposite, or inverse, of multiplication. Take another look at the examples given earlier. We said that 20 ÷ 4 = 5, and 12 ÷ 4 = 3. In each of these problems, the quotient multiplied by the divisor equals the dividend: 5 x 4 = 20 and 3 x 4 = 12.

You can see this visually, using objects. You already divided 20 students into groups of four to get five groups. Now, you have five groups of four students each (5 x 4), which gives you 20 students. You can also divide your 12 objects into groups of four to get three groups. Now, you have three groups of four objects (3 x 4), which is equal to 12 objects.

So now, when you're solving division problems, you can use your knowledge of multiplication facts. For the problem 30 ÷ 5 = ?, you can ask yourself, 'What number multiplied by five equals 30?' The answer is six (6 x 5 = 30), so 30 ÷ 5 = 6.

Division Practice Problems

1. What is the quotient of 15 ÷ 3?

What number multiplied by three equals 15? We know that 5 x 3 = 15, so the quotient is five.

2. Find the quotient of 18 ÷ 6.

The quotient is the number that we can multiply by six to get 18. Since 6 x 3 = 18, three is the quotient.

3. Find the missing number: 25 ÷ 5 = ?

To find the missing number, which is the quotient, we need to figure out what number times five equals 25. Since 5 x 5 = 25, the missing number, or quotient, is five.

Finding the Dividend or Divisor

Once you've mastered basic division problems like the ones above, you're ready to solve 'unknown number' equations. These are division problems that give you either the divisor or the dividend and the quotient. Your job is to find the missing number.

A sample problem is, 'Eight divided by what number equals two?' It's written like this: 8 ÷ ? = 2. If you have your division tables memorized, you'll know right away that 8 ÷ 4 = 2. If you don't, you can also solve the problem by asking yourself, 'Two times what number equals eight?' You know that 2 x 4 = 8, so four is the divisor in this problem.

Sometimes the dividend is missing in the problem. For example, your teacher might ask, 'What number divided by seven equals two?' It would be written like this: ? ÷ 7 = 2. If you already know that 14 ÷ 7 = 2, then you can solve this problem quickly. If you can't remember, though, you can also ask yourself, 'Two times seven equals what number?' Since 2 x 7 = 14, the missing dividend for this problem is 14.

Unknown Number Practice Problems

For these practice problems, the question is written in words. Write it as a numerical equation, and then solve it.

1. What number divided by six equals six?

First, write the equation out as ? ÷ 6 = 6. Since 6 x 6 = 36, the unknown dividend is 36.

2. The number 27 divided by what number equals nine?

This problem can be written as an equation, like this: 27 ÷ ? = 9. Since 9 x 3 = 27, the missing divisor is three.

3. What number divided by four equals four?

Write out the equation like this: ? ÷ 4 = 4. Then, multiply four by four to get 16 (4 x 4 = 16). The missing dividend is 16.
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