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Division can be thought of as the opposite of multiplication:

0 ÷ 3 is the same as saying "what number when multiplied by 3 results in 0"; answer: 0.

3 ÷ 0 is the same as saying "what number when multiplied by 0 results in 3"; no number when multiplied by 0 results in 3 (as 0 times anything is 0), thus it can't be done.

Alternatively, division tells you how many times you need to, or can, subtract the divisor from the dividend to get to zero.

If you start with a dividend of zero and a non-zero divisor, you don't need to, nor can you, subtract the divisor to get to zero.

If you start with a non-zero dividend, and a zero divisor, no matter how many times you subtract the divisor you will never get to zero - the dividend stays the same.

With a zero dividend and a zero divisor, you have reached zero when you start, BUT you can subtract the divisor and the dividend will then become (stay) zero; thus zero divided by zero is any number you want - in calculus there are rules which specify the value to use in different circumstances.

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Q: Why can you divide 0 by 3 but not 3 by 0?
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Related questions

What is 3 divided by 0 equal to?

Undefined: You cannot divide by zero


Why you can divide 0 by 3 but not 3 by 0?

3*0 = 0 Dividing both sides by 3 gives 0 = 0/3 and therefore 0/3 is defined and is equal to 0. However, there is no number, k, such that k*0 = 3 and so division by 0 is not defined. If there were such a number k, then you could divide both sides by k to give 0 = 3/k. But there is no such k.


What is 3 divided by 0 as a percentage?

Undefined: You cannot divide by zero


What remainders can you get when you divide by 3?

2, 1 or 0.


What is 0 over 1 divide by 3?

Anything with a zero in the numerator will be equal to 0. If your problem is 0/1/3, then it's 0.


Why can divide 0 by 3 but not 3 by 0?

The operation, division, is not symmetric. There is a number, x, such that x*3 = 0. In fact x is also 0. But there is no number, y, such that y*0 = 3.


Can 0 be divided by 3?

Undefined: You cannot divide by zero


What is the answer to x plus 5 divide by 3 equals to 0?

x = -5/3


What is 8 divide 8-1 plus 3-1 plus 0 equals?

8/8 - 1 + 3 - 1 + 0 = 1-1+3-1+0 = 0 + 3 - 1 + 0 = 3 - 1 = 2


Is 3 divided by 0 is an integer?

Undefined: You cannot divide by zero


How can you divide 180 and 3?

To divide 180 by 3: ask your self what is 18 divided by 3 (how many groups of 3 in 18) . The answer is 6 ( 6x3 = 18). So 6 is the first number in your answer. now ask yourself what is 0 divided by . The answer is 0. So 0 is the second number in your answer. 180 divided by 3 = 60


What is the problem if 0 divide by 0 include as a fraction?

Undefined: You cannot divide by zero