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.
Let's look at an example:
The Big Pink Bubble Gum Company is holding a bubble blowing contest. They have
gumballs to share equally between people.
A division problem always starts with the total number of objects.
The total number of gumballs is
The gumballs will be divided equally between
people. So the number of equal groups is .
In this problem, we are dividing
gumballs into groups. We can show this with the expression
Let's try another one:
The Big Pink Bubble Gum Company decides to use
gumballs in the competition.
They will have
people blowing bubbles.
There are a total of
gumballs that will be divided evenly into
Which expression can we use to show
gumballs divided into equal-size groups?
We can use arrays to show division.
An array is an arrangement of objects in equal-size rows.
gumballs have been divided equally between rows.
This array shows the expression
When we divide
gumballs into 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.
Practice problem 2
This array shows a total of
dots divided equally into
Which expression can be used to represent the array?
dots in each row.
Practice problem 3
This array has
dots divided into equal rows.
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
ponies. The ponies take kids on rides all day. At the end of the day, the ponies rest in their stables. Each stable holds ponies.
We have a total of
We also know the number of equal shares in each group. Each stable holds
We can use division to figure out how many stables Peng needs for all his ponies.
Which number should our division problem start with?
The expression for
ponies divided into equal groups of is
Let's try another problem
Peng's Pony Rides has a total of
ponies. They built bigger stables. Each stable now holds ponies.
There are a total of
ponies. The ponies will be divided into equal-size groups with
ponies in each group.
Which expression can we use to show a total of the
ponies divided into groups with ponies in each group?
Which image could we use to show
ponies divided equally into groups with ponies in each group?
Connecting division and multiplication
The array shows a total of
dots. The dots have been divided into equal rows with dots in each row.
represents the array.
We could also say the array is made up of
rows of dots with dots in each row.
= also represents the array.
In both equations,
is the total number of dots, is the number of equal-size groups, and is the number of dots in each group.
Let's try another one.
Which equations represent the following array?
Want to join the conversation?
- Why is the division sign like this ÷ or this /?(22 votes)
- The division symbol is a just a empty "fraction" with "numerator" and "denominator" represented as a simple dot.
20 divided by 10
20 => numerator (the "top" of the fraction.)
10 => denominator (the "bottom" of the fraction.)
Some people uses a slash symbol which means the same thing.
Just for your curiosity:
The "divide sign" is called Obelus. It was used as a division symbol by a Swiss mathematician Johann Heinrich Rahn on his algebra book entitled Teutsche Algebra in 1659.(5 votes)
- What is 27 divide into 2?(10 votes)
- Why dose these problem are up and down and all at a time?(7 votes)
- These numbers go "up and down" or increase and decrease all the time because we are trying to "simplify". Division by itself divides big numbers into small parts. So, a big number (or any number) divided by (any other number) will give us a smaller amount.(4 votes)
- Is Division the opposite of Multiplication?(7 votes)
- Is 98,765,432/2= 49382716. Or did I do the math wrong?(7 votes)
- yes your answer is correct. given I don't know what math you did you may have just coincidentally found the answer but you probably got it right(7 votes)
- So what if I ran into a question like 7,000 divided by 4? What would I do to figure it out?(7 votes)
- Isn’t ‘/‘ technically also a symbol of division? In the first paragraph it doesn’t mention it, but I thought they both worked.(6 votes)
- Yes, both work the same. Your teacher might try to trick you by using different signs(1 vote)
- Is there going to be long division?(5 votes)
- what is 100 +50000000000000000000000000+2222222+6666+8(3 votes)