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Why can you divide 0 by 3 but not 3 by 0?
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.
When do you use a placeholder zero in the quotient?
When you're quotient is in the hundredths place or more or when you're dividend or divisor has a placeholder zero as well.
What happens to the quotient when the dividend and divisor are mutiplied by the same number?
As long as the number is not zero, the quotient remains unchanged. If the multiplier is zero then the quotient is undefined.
How many times 19 can go into 17?
The answer is 0 times with a remainder of 17. When dividing 17 by 19, the divisor is larger than the dividend, so the division cannot be completed evenly. The quotient would be 0, and the remainder would be the original dividend, which is 17 in this case.
What is the difference between a divisor and dividend?
Divisor: the number by which a dividend is divided Dividend: a number to be divided
