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### Grade 6 - Mathematics1.30 Division by Zero

 1. Division by zero is not defined. Consider 8/0 = ? Is it possible to assign any whole number to this quotient? Suppose 8/0 = a, where 'a' is a whole number. Since division is the inverse operation of multiplication, we will have 0 x a = 8. Since 'a' is a whole number and we know that the product of a whole number and zero is always zero. Hence, 0 x a cannot be 8. Thus there is no whole number which when multiplied by zero will ever give us a non-zero whole number. Therefore 8/0 cannot be equal to any whole number. Consider the case, 0/0. Suppose, 0/0 = a. Then we get 0 x a = 0. But whatever the whole number "a" may be, 0 x a is always zero. For example, 6 x 0 = 0, 8 x 0 = 0, 25 x 0 = 0, ............... Hence the supposed "a" can assume any whole number. In other words, 0/0 can represent any whole number. It cannot be any one number. It has innumerable answers. 2. When zero is divided by any non-zero whole number, the quotient is always zero. Consider 0/7. Suppose 0/7 = a Then, 7 x a = 0. Since the product of two whole numbers is zero, at least one of them has to be zero. But 7 is not equal to zero; which means a = 0. Therefore 0/7 = 0. Directions: Choose the correct answer. Also write at least 10 examples of your own.
 Q 1: 0/761Not definedZero Q 2: 86/0ZeroNot defined Q 3: 0/86Not definedZero Q 4: 0/6ZeroNot defined Q 5: 27/0Not definedZero Q 6: 761/0ZeroNot defined Q 7: 6/0Not definedZero Q 8: 0/27Not definedZero Question 9: This question is available to subscribers only! Question 10: This question is available to subscribers only!

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