**Introduction**

In this lesson, you will learn to use the division algorithm with larger numbers.

Previously, you learned how to do long division when dividing by a one-digit number or divisor. You use the same division steps when the number being divided by (the divisor) has multiple digits.

This video illustrates the lesson material below. Watching the video is optional.

**Practicing Long Division with Two Digits**

This example demonstrates how to use the division algorithm with bigger numbers. Use the steps for division:

- Put the number being divided (the dividend) under the box and the other number (the divisor) to the left of the box.
- Starting on the left, determine how many times the divisor can go into the first digit of the dividend.
- Write that number above the digit and subtract the product of that number and the divisor from the dividend.
- Repeat steps 2 and 3, moving to the right.

**Example 1**

\(5986\div82\)

Begin by drawing the division symbol. Put 5986 underneath it, and 82 to the left of the symbol:

\begin {align*}

\require{enclose}82\enclose{longdiv}{5986}

\end {align*}

Starting on the left, look at the first value in the dividend, or the number being divided. In this case, 5. How many times can 82 go into 5? The answer is zero. Because it is zero, move to the next number. How many times does 82 go into 59. Again, the answer is zero. Move another digit to the right. How many times does 82 go into 598?

With problems like these, it is not always easy to know the answer. You may need to guess or estimate. Start with 7. \(82\times7=574\). 574 is close to 598 while still being less than 598. The 7 will go above the 8 because it is the last digit we have used so far.

Subtract, \(598-574=24\). Carry down the number in the next column to the right, which is 6. Now you are working with 246.

Figure 1

How many times does 82 go into 246?

To help you guess, you can choose to think of this problem in terms of the multiplication facts you know. If we only consider the tens column of the divisor for a minute, in this case 8, and the first two digits of the dividend, we might recognize that 8 goes into 24. \(8\times3=24\).

Start with 3. \(82\times3=246\). The 3 will go above the 6 because it is the last digit we have used so far. Subtract 246.

Figure 2

Since the answer is 0, that means there are no leftover or remaining parts. The correct answer is 73.

Remember: It’s okay to guess and have to erase as you work through this process. With more practice, you’ll become better at it, and it will go faster. It will also be easier and faster if you have your multiplication facts memorized, so keep working on those!

**Things to Remember**

- Make sure to bring down the numbers for remaining place values while completing the division equation.
- Memorizing the multiplication facts will make division easier.
- Division can involve a lot of trial and error. It's okay if it takes a few tries to figure out which number is part of the correct answer.

### Practice Problems

Evaluate the following expressions:- \(152 \div 8 = ?\) (Solution
- \(1620 \div 20 = ?\) (Solution
- \(2349 \div 87 = ?\) (Video Solution
- \(3003 \div 39 = ?\) (Solution
- \(14363 \div 53 = ?\) (Video Solution
- \(45696 \div 64 = ?\) (Solution

**Need More Help?**

- Study other Math Lessons in the Resource Center.
- Visit the Online Tutoring Resources in the Resource Center.
- Contact your Instructor.
- If you still need help, Schedule a Tutor.