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Course: Arithmetic (all content) > Unit 3

Lesson 9: Division intro
Math
Arithmetic (all content)
Multiplication and division
Division intro
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Intro to division

Google Classroom
Use arrays and word problems to visualize division.

What is division?

Division lets us separate a number of objects into equal-size groups.
The symbol for division is ÷ .
To divide, we need to know the total number of objects. We also need to know either the number of groups or the number of objects in each group.

Equal groups

Let's look at an example:
The Big Pink Bubble Gum Company is holding a bubble blowing contest. They have 18 gumballs to share equally between 3 people.
A division problem always starts with the total number of objects.
The total number of gumballs is 18.
The gumballs will be divided equally between 3 people. So the number of equal groups is 3.
In this problem, we are dividing 18 gumballs into 3 groups. We can show this with the expression 18 ÷ 3.
Let's try another one:
The Big Pink Bubble Gum Company decides to use 16 gumballs in the competition.
They will have 4 people blowing bubbles.
Problem 1A
There are a total of
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
gumballs that will be divided evenly into
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
groups.

Problem 1B
Which expression can we use to show 16 gumballs divided into 4 equal-size groups?
Choose 1 answer:

Using arrays

We can use arrays to show division.
An array is an arrangement of objects in equal-size rows.
18 gumballs shared equally between 3 people can be shown with this array:
The 18 gumballs have been divided equally between 3 rows.
This array shows the expression 18÷3.
When we divide 18 gumballs into 3 groups, how many gumballs are in each group?
We can find the answer to the division problem by counting the number of dots in each row.
18÷3=6

Practice problem 2

Problem 2A
This array shows a total of
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
dots divided equally into
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
rows.

Problem 2B
Which expression can be used to represent the array?
Choose 1 answer:

Problem 2C
There are
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
dots in each row.

Problem 2D
28÷7=
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

Practice problem 3

This array has 35 dots divided into 5 equal rows.
Problem 3
35÷5=
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

Equal shares

This type of problem is similar to the ones we just solved. However, in this case, we know the number of objects in each group instead of the number of equal groups.
Let's look at an example:
Peng's Pony Rides has 20 ponies. The ponies take kids on rides all day. At the end of the day, the ponies rest in their stables. Each stable holds 4 ponies.
We have a total of 20 ponies.
We also know the number of equal shares in each group. Each stable holds 4 ponies.
We can use division to figure out how many stables Peng needs for all his ponies.
Problem 4
Which number should our division problem start with?
Choose 1 answer:

The expression for 20 ponies divided into equal groups of 4 is 20 ÷ 4.

Let's try another problem

Peng's Pony Rides has a total of 20 ponies. They built bigger stables. Each stable now holds 10 ponies.
Problem 5A
There are a total of
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
ponies. The ponies will be divided into equal-size groups with
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
ponies in each group.

Problem 5B
Which expression can we use to show a total of the 20 ponies divided into groups with 10 ponies in each group?
Choose 1 answer:

Problem 5C
Which image could we use to show 20 ponies divided equally into groups with 10 ponies in each group?
Choose 1 answer:

Problem 5D
20÷10=
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

Connecting division and multiplication

The array shows a total of 30 dots. The dots have been divided into 6 equal rows with 5 dots in each row.
The equation 30 ÷ 6=5 represents the array.
We could also say the array is made up of 6 rows of dots with 5 dots in each row.
The equation 6 × 5 = 30 also represents the array.
In both equations, 30 is the total number of dots, 6 is the number of equal-size groups, and 5 is the number of dots in each group.

Let's try another one.

Problem 6
Which equations represent the following array?
Choose all answers that apply:

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