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Division
Division is the action of splitting something into (smaller) parts. For instance, a cake is usually divided into slices: all the slices put together make up the cake again.
The same reasoning holds with numbers: 12 divided by 4 is 3, because if we split a 12 inches long stick into 4 equal pieces, each piece will be 3 inches long.
We could split the same 12-inch stick in different ways:
- in 6 pieces, in which case each piece would be 2 inches long;
- in 12 pieces, in which case each piece would be 1 inch long;
- in 5 pieces, in which case each piece would be 2.4 inches long.
Division is often written with ÷ or /, as in: 12 ÷ 4 = 3. The / symbol is usually preferred on computers, because their keyboards rarely have a ÷ key.
Division is the inverse of multiplication:
- 12 ÷ 4 = 3
- 3 × 4 = 12
- 3 × 4 ÷ 4 = 3, which shows that applying to the number 3 a multiplication by 4, then a division by 4, gives the original number 3.
A special case with division is that we can't divide by zero. To see why, let us imagine that we can and see how that would be impossible:
- Imagine that the result of 12 divided by zero is some number that we call N: 12 ÷ 0 = N.
- Since division is the inverse of multiplication, it must be true that N × 0 = 12.
- However, multiplication by 0 always gives 0 as a result: if we take zero pieces of cake, then we still have no cake.
- Therefore, there is no number that could replace N above and make that multiplication true.
- Since our reasoning was logical, and our conclusion is impossible, we now know that our starting point (the fact that we can divide by zero) was false.
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