## Friday, July 23, 2010

### A Thinking Question....

When 1 is divided by 1, the answer as we know the answer will be 1. Similarly when 2 is divided by 2, 3 is divided by 3 and 4 is divided by 4, we know that the answer will still be equal to 1.
However, is it true that when x is divided by x, the answer will always be 1? If not, when is x  divided by x not equal to 1?

1. When x is = 0

2. There is a exception to this assumption because the algebraic expression 'x' is an unknown value. As it is an unknown value, 0 is also a possible value represented by 'x'. As 0 divided by 0 is infinity, the assumption of x/x =1 cannot be applied.

3. This statement is true with the exception of x=0

4. With the exception that x =0, x will not always be 1. Being said that 0 cannot be divided by itself as it will give us infinity, the statement given above cannot be approved.

5. It is not true that when x is divided by x, the answer will always be 1. x is undefined, and so can be any number. This range of numbers include 0, and so when 0 is divided by 0, the answer is infinity. Thus, when x is divided by x, the answer need not always be 1.

6. If the number X is a value such as 0, the answer would be zero or infinity. Even so, it is almost impossible for X to be zero. So you can say that X divided by X is not always 1.

7. x=unknown
x can be any number
x can also be 0
0/0=Infinity
Infinity is not equal to 1

8. when x is 0, the expression becomes a ∞ value

9. when x = to any positive number like 1 or two, or a negative number , x ÷ x = 1 but if x is equivalent to 0, 0÷0=0 as any number divided by 0 = 0

10. x/x is not always equals 1. It only applies when x≥1 or when x≤-1. It does not apply when x=0 as 0/0=∞

11. When x=0, the answer will be infinity ∞.

12. When X=0, then 0/0 is infinite.

13. When x=0. Since whatever divided by 0=∞, x ≠ 0

14. If the value of X is 0, the value of the answer will not be 1 as 0÷0=∞ and infinity is not equals to 1

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16. x can be any number on its own or part of the whole equation as long as the resulting divisor or denominator(for fractions) is not equal to 0. This is because of the rule of not dividing by 0 to produce the result of ∞. And ∞ ≠ 1. This already makes the original equation wrong and therefore the resulting divisor or denominator cannot be 0.(If the rule is not given in maths test, then all the answers would be ∞!) Some may question why x could have been another number in an equation. For this, if x = 3, compare (x*3) divided by (x*3) with (x*0) divided by (x*0).

17. x/x does not equal to one when x is 0. If x is 0, x/x would be 0/0. 0/0 will give infinity, which is obviously not one.