Division is splitting a number into equal groups.
Properties are like rules that can help you solve division problems.
Let's learn three properties of division.
Dividing a number by 1 equals the number itself.
Take a look:
14 ÷ 1 = 14
672 ÷ 1 = 672
78,271 ÷ 1 = 78,271
Imagine dividing a number into just 1 group.
What you get is that same group.
There are two rules under this property:
1️⃣ Dividing a number by 0 is not possible.
81 ÷ 0 cannot be solved. It doesn't mean anything.
2️⃣ Dividing 0 by a number always equals zero.
0 ÷ 72 = 0
0 ÷ 281 = 0
Imagine trying to divide "nothing" into even parts.
What you get is still "nothing".
Any number divided by itself equals 1.
This property is similar to the Identity Property of multiplication.
Look at these examples:
14 ÷ 14 = 1
473 ÷ 473 = 1
82,491 ÷ 82,491 = 1
No matter how big the number is, the quotient is still 1.
That's what happens when you divide a number by itself.
The order of numbers is always important in division.
Swapping the dividend and divisor changes the answer.
56 ÷ 8 is not the same as 8 ÷ 56.
If you have multiple division operations in an equation, changing the order of which numbers you divide first will change the answer.
Let's try to understand this with an example:
(100 ÷ 10) ÷ 5 ≠ 100 ÷ (10 ÷ 5)
Tip: ≠ means not equal to.
First, let's see what the left side equals, and then compare it to the right side.
(100 ÷ 10) ÷ 5 = ?
Parenthesis ( ) tell you which operation to do first.
What's 100 divided by 10?
(100 ÷ 10) ÷ 5 =
10 ÷ 5 =
2
Awesome! We figured out that the left side equals 2.
Now let's see if we get the same answer by changing the order of our division operations.
100 ÷ (10 ÷ 5) =
100 ÷ 2 =
50
We got two different answers. 🙈
2 ≠ 50
This shows us that the associative property does NOT work for division.
Distributing numbers does not work for division.
For example:
45 ÷ (3 + 6) = ?
Let's solve this equation correctly first:
45 ÷ (3 + 6) =
45 ÷ 9 = 5
The answer we got is 5. ✅
Now, what value do we get if we try to distribute the division?
(45 ÷ 3) + (45 ÷ 6) =
15 + (45 ÷ 6) =
15 + 7 remainder 3
The answer we got is different from our previous answer.
So we see that division is not distributive. 👏
Great job learning about the properties of division.
Now, let's practice.