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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:

1. Imagine that the result of 12 divided by zero is some number that we call N: 12 ÷ 0 = N.
2. Since division is the inverse of multiplication, it must be true that N × 0 = 12.
3. However, multiplication by 0 always gives 0 as a result: if we take zero pieces of cake, then we still have no cake.
4. Therefore, there is no number that could replace N above and make that multiplication true.
5. 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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