Lesson 3: Division Review


Activity 1: Rules of Divisibility

Materials: Interactive Notebook
You know that multiplication can be described as "repeated addition" because it can be thought of as a shortcut for adding a number to itself a bunch of times. For example, 4 times 7 is the same as 4 added 7 times: 4 × 7 = 4 + 4 + 4 + 4 + 4 + 4 + 4 = 28.

In the same way, division can be thought of as "repeated subtraction." Let's say you want to evenly divide 18 pieces of candy into groups of three. How many groups of 3 would you get? The problem is written as 18 divided by 3, and one way you could find the answer is to start counting out groups of 3 candies until there is no more candy.
Because there are six groups of three in eighteen, 18 ÷ 3 = 6.
This is a perfectly reasonable and effective way to do division, but it does have one drawback: it takes a long time. This would be especially true for a more complex problem such as 741 ÷ 3. But fear not! The algorithm for division can be used to accurately and quickly find the quotient for longer problems.

Before reviewing how to solve division problems, it's helpful to know some facts about divisibility. What does it mean for a number to be divisible by another number? If one number is divisible by another, it means that the quotient has no remainder. For example, 10 is divisible by 5 (10 ÷ 5 = 2), but is not divisible by 3 (10 ÷ 3 = 3 R 1). So how do you know if a number is divisible without actually dividing? You learn the rules of divisibility.

Complete the "Rules of Divisibility" page to learn more about these helpful rules. Then, store this page in your Interactive Notebook for future reference.
Student Activity Page
Your child will some rules of divisibility to help him quickly identify if a number is evenly divisible by a factor.
  • The numbers that are divisible by 2 are 658, 330, 902, and 1,096.
  • The numbers that are divisible by 3 are 603, 321, and 450.
  • The numbers that are divisible by 4 are 448, 316, 740, and 3,912.
  • The numbers that are divisible by 5 are 180, 365, 230, and 8,995.
  • The numbers that are divisible by 6 are 306, 234, and 5,214.
  • The numbers that are divisible by 9 are 702, 117, and 2,466.
  • The numbers that are divisible by 10 are 560, 900, and 710.
  • The numbers that are divisible by 12 are 612, 444, 324, and 9,180.

Activity 2: Long Division

The rules of divisibility will prove useful to you as you practice the algorithm for long division. You've learned this algorithm before, so let's review the steps using the following website.
Web Link
Long division can seem long, but you might notice that it's really a set of steps that is repeated until the final answer is found. Let's see how this works with a word problem.
In a division problem, the dividend is the number amount that is being divided. In this case, the number of dinosaurs (162) is the dividend. The divisor is the number doing the dividing. It can represent either the number of groups or the number of items to be put into groups. In this problem, Jeromy is placing dinosaurs on three shelves, so the divisor (3) represents the number of groups, meaning the three shelves. You can use the divisibility rules to find that 162 is divisible by 3, so there will not be a remainder in this problem.
The division algorithm allowed you to figure out that Jeromy can place 54 plastic dinosaurs on each of his three shelves.

Let's try another one.
In this problem, 630 buttons will be divided, so 630 is the dividend. The divisor is 45, and it represents the number of items (buttons) in each group. The problem asks you to find the number of groups needed. You can see that this divisor has two digits. No matter how many digits are in the divisor, you follow the same algorithm steps.
Wendy needs 14 storage cups to hold all her buttons. As you can see, long division helps you find how many items go into a set number of groups or how many groups of items you have in all.

Now use the standard algorithm to practice solving division problems on the "Long Division" activity sheets.
Student Activity Page
Student Activity Page
Your child will review and practice the standard algorithm for long division with both one and two digit divisors. In the examples and practice problems given, you or your child may notice that none of them involve remainders. While dealing with remainders in long division is an important skill, the primary focus of this activity is ensuring that the student can fluently use the steps in long division. How to understand and solve problems involving remainders will be taught later in this lesson.

If your child needs more review of the steps in long division, have him watch the video at the following web link.
Web Link

Answer Key:

  1. 828 ÷ 6 = 138
  2. 9,608 ÷ 8 = 1,201
  3. 5,453 ÷ 7 = 779
  4. A cash prize of $7,638 is to be divided equally among three winners. How much will each winner receive? ($2,546) $7,638 ÷ 3 = $2,546
  5. 8,505 ÷ 21 = 405
  6. 6,664 ÷ 56 = 119
  7. 6,468 ÷ 44 = 147
  8. A batch of 3,750 bumper stickers must be packed into shipping boxes with 25 bumper stickers in each box. How many shipping boxes will be needed to pack all the bumper stickers? (150 boxes)
    3,750 ÷ 25 = 150