How many 3's are in 24?
Remember that in multiplication, 3 x 8 = 24, so there are eight 3's in 24.
We write division as follows:
In this example, 24 ÷ 3 = 8, 24 is the dividend, 3 is the divisor and 8 is the quotient.
In multiplication, 8 x 3 = 24, where 8 and 3 are factors and 24 is the product.
Division can also be thought of as repeated subtraction. If we want to find how many 4's are in 20, then subtract 4 repeatedly and count how many times it was subtracted.
20 - 4 = 16
16 - 4 = 12
12 - 4 = 8
8 - 4 = 4
4 - 4 = 0
We subtracted 5 times.
So, there are five 4's in 20. We write 20 ÷ 4 = 5.
Properties of Division
Is division commutative, such that 20 ÷ 4 = 4 ÷ 20?
Is it associative, such that (250 ÷ 10) ÷ 5 = 250 ÷ (10 ÷ 5)?
Test it yourself.
Any number a divided by 0 is unidentified or $\frac{a}{0}= $ a ÷ 0 is unidentified.
Now what if we want to find how many 6's are in 3167? There is a remainder 5?
This will be illustrated using the long division.
Step 1: We use 31 since it’s greater than 6, instead of
using 3 only. How many 6’s are in 31?
Step 2: Using 16 instead of using 1, how many 6’s are in 16?
Step 3: How many 6’s in 47?
To shorten this process, we exclude all the 0’s and bringing down one digit at a time.
Check by multiplying the quotient
by the divisor: 527 x 6 = 3162. Since there is a remainder, then add this, 3162
+ 5 = 3167 and we got the dividend back which is 3167.
There are times when the remainder is 0, for
example below
The quotient and the divisor are
factors in finding the dividend such that 45 x 5 = 225.
