Lesson Plan - Get It!
The new book you bought has 345 pages. If you read 15 pages per day, how many days will it take you to finish the book? What operation can be used to solve this problem?
Long division involves dividing, multiplying, and subtracting.
Breaking the problems into smaller steps will help you solve the problems. The image below shows a division bar with important terms relating to division:
- dividend the number that is being divided into equal parts
- divisor the number that the dividend is divided by
- quotient the answer or result of the division problem
- remainder the amount that is left over after dividing
Watch Math Antics - Long Division with 2-Digit Divisors, a video that will walk you through the steps of solving a long division problem with a 2-digit divisor. As you watch the video (it will stop at 9:35), focus on finding the answers to the following questions:
- How does using a multiplication table help you with division?
- What happens when the divisor is bigger than the first digit in the dividend?
Discuss the questions with a parent or teacher after you watch:
When dividing a two- or three-digit number by a two-digit number, the same steps are followed until there are no more numbers remaining in the dividend and you have a solution. Some problems will have an amount left over after dividing the numbers in the dividend, and that is the remainder. Not all problems will have a remainder.
If you can remember these four words, "Daddy," "Mother," "Sister," "Brother," you can remember the steps for long division.
Bring down (Brother)
Let's look at how to set up and solve the problem from the beginning of the lesson:
The new book you bought has 345 pages. If you read 15 pages a day, how many days will it take you to finish the book? What operation can be used to solve this problem?
Since you have a total, 345, and you are dividing it into equal groups, 15 pages per day, the division problem is 345 ÷ 15.
Step 1 Rewrite the problem.
- The dividend is 345, since that is the total number of pages being divided. This number is written inside the division bar.
- The divisor is 15, since that is the number of equal groups, or pages, being divided into 345. This number is written outside the division bar.
Step 2 Begin dividing by finding how many equal groups of the divisor, 15, you can divide into 345. 15 cannot divide into 3 because 15 is greater than 3. A helpful hint to keep in mind is if the divisor has 2 digits, look at the first 2 digits of the dividend when you start dividing. Since 15 cannot divide into 3, a zero can be placed in the quotient above the 3.
- How many 15s can be divided into 34?
- Use the Multiplication Table (Math Tools) to find how many 15s gets close to 34, but not over 34.
- 15 x 2 = 30 and 15 x 3 = 45, so 15 divides into 34 two times. The first part of our quotient is 2 and it is written above the 4 in 34.
Step 3 Multiply the digit of the quotient, which is 2, by the divisor, which is 15. Write the answer below the dividend and subtract. Then, bring down the next digit in your dividend.
This is a good spot to stop and check your work so far. All of the steps of long division have been done: divide, multiply, subtract, bring down. After you subtract, compare that number, the difference, to the divisor.
- The difference should be equal to or less than the divisor. If it is, you can continue dividing and repeat the steps again. Repeat the steps again until all of the digits in the dividend have been brought down.
- If the difference is greater than the divisor, check your subtraction work again. If you subtracted correctly, try a larger number in the quotient and subtract again.
Step 4 After you subtracted and brought down the next digit in the dividend, your new dividend is 45. Divide 45 by 15, which is 3. The 3 is written in the quotient. Multiply 3 x 15, which is 45. Subtract 45 and get a result of zero. The problem is finished and there is no remainder.
Discuss with a parent or teacher:
- Is it possible to have a three-digit quotient when you divide a three-digit dividend by a two-digit divisor? Explain your thoughts.
- How do you know when you are finished dividing?
In the Got It? section, you will practice dividing numbers with a two-digit divisor with interactive practice.