Long Division Math Practice Problems

What Is the Partial Quotients Method of Solving Long Division Problems?

The Partial Quotients Method is associated with the Everyday Mathematics curriculum, and it's likely different from how you learned to do long division as a child. This method uses a number of steps to reach the quotient, or answer, of a division problem. Each step results in a partial answer, and these partial answers are added together to find the quotient.

Consider the problem 500/7. The first step of the Partial Quotients Method is to multiply 7 by a number that results in a product smaller than 500. Unlike other trial-and-error methods used for long division, you don't have to get as close to 500 as possible.

Let's multiply 7 x 50, which equals 50. Then, subtract 350 from 500 to get an answer of 150. Write 50 on the right side of the division problem. You'll use it later.

Now you're working with 150. Choose another number to multiply by 7. Let's try 20: 7 x 20 = 140. Next, subtract 150 - 140 = 10. Write 20 underneath the 50.

Since 7 only goes into 10 one time, write a 1 underneath the 20. Multiply 7 by 1, and subtract it from 10 for a remainder of 3. Add the numbers on the right side of your division problem (50 + 20 + 1) for a final answer of 71 with a remainder of 3.

Long Division Practice Problems

1. 54 ÷ 6

If your child struggles with multiplication facts, he or she may have a hard time with long division. Before embarking on long division, you might want to review the basic multiplication facts with your son or daughter. The answer to this problem is 9.

2. 952 ÷ 2

The quotient is 476. Both this problem and the previous one don't have remainders, meaning they factor evenly. If you want to challenge your child, you can provide problems with numbers that aren't evenly divided.

3. 796 ÷ 20

Because 20 x 39 = 780, there is a remainder of 16. In later grades, students will learn to rewrite remainders as decimals, but if your child is just beginning to learn long division, he or she will simply write the answer like this: 39 R16.

4. The recipe for an apple pie requires 20 apples. If a baker has 421 apples, how many pies can he make?

To solve, your child should divide the number of apples by the number needed to bake a pie (421 ÷ 20). The answer is 21 R1, which means the baker can make 21 pies, and he'll have one apple left over.