As we try to define it we'll use this sample equation:
X ÷ Y = Z r
These are the component parts of a division problem:
X is the dividend - the amount being divided up
Y is the divisor - the unit doing the dividing
Z is the quotient - the result of having done this division
r is the remainder if the problem does not come out evenly
Y and Z are factors of X if the division problem comes out evenly (without a remainder)
X is evenly divisible if the division problem comes out without a remainder
Here are some sample problems, before we go on with more definitions:
9 ÷ 3 = 3 or nine divided by three equals three; three and three are factors of nine
10 ÷ 3 = 3 r1 or ten divided by three equals three with a remainder of one
10 ÷ 2 = 5 or ten divided by two equals five; two and five are factors of ten
We can call division repeated subtraction, so Z is the number of times can I remove Y from X before I get to zero.
- 10 - 2 = 8
- 8 - 2 = 6
- 6 - 2 = 4
- 4 - 2 = 2
- 2 - 2 = 0 ZERO
We can say division is determining how many times one quantity goes into another number, so Z is the number of times that we can put Y into X before X is "full".
- 0 + 2 = 2
- 2 + 2 = 4
- 4 + 2 = 6
- 6 + 2 = 8
- 8 + 2 = 10 FULL
We can call division sharing where Z is the number of people who can share X evenly. Each share contains Y pieces.
In this case 5 people can share 10 evenly if each share is 2 pieces.
Here's a division problem that might amuse you - artwork was adapted from the Arif & Ali blog.
There are lots of other ways to describe division, but this is enough for now.