Division is the opposite of multiplication. In multiplication, we start at zero and jump to the right a given number of times to the answer. In division we start on a number and jump to the left to zero counting the number of jumps. In division, the number of jumps to zero is the answer.
We start at 6 and start jumping by 2's to the left towards zero. We count each jump.
0-----1-----2-----3-----4-----5-----6
It took three jumps to get to zero, so 6÷2=3.
The numbers involved in division are called the dividend (the number we start with), the divisor (the number we subtract by or the size of the jumps we make) and the answer is called the qoutient. Let's divide 6 by 2. The equation is written 6÷2. 6 is the dividend and 2 is the divisor.
You can learn the result of division for some common small numbers by using the multiplication table in reverse. Find the dividend in the middle of the chart with the proper divisor on the left, then follow the column to the top to find the quotient.
What happens if the jumps don't exactly land on zero. The left over is called the remainder. Let's try 9÷2 and see what happens.
0-----1-----2-----3-----4-----5-----6-----7-----8-----9
We made 4 jumps to the left and landed on one. That means 9÷2 is 4 with a remainder of 1. What we are actually saying is that 4×2+1=9. (Remember from our order of operations that multiplication is carried out before addition.) This illustrates the division algorithm. Any whole number is the product of a whole number and a quotient plus a remainder.
To divide larger numbers, we need another method of deconstructing numbers. And for that method we need to extend our alphabet to include a new type of number. We need the operation of subtraction and we need the concept of negative numbers to do subtraction. We will introduce negative numbers in the next blog and use the operation of subtraction to extend division to large numbers.
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