Math

1/why can 0 be divided by any number , but any number cann't be divided by 0?

2/ Mr. Cruz is planning to give each of his students 2 pencils for their math test . Pencils come in packs of 8 . If he has 32 students ,can he open enough packs to give all his students pencils but have none left over ?
32 divide 8=4
Help me..

1. The principal property of 0 is that for any real a, a*0 = 0

Now, suppose that we want to divide by 0. That means that if
a/0 = b, then
a = b*0

But b*0 is 0 for any b. That is, there is no real value of b for which b*0 is a nonzero number a.

Think of the quotient when the divisor shrinks:

1/.1 = 10
1/.01 = 100
1/.0000001 = 10,000,000
as the divisor gets smaller, the quotient gets larger. Finally, when the divisor is zero, the quotient is larger than any possible value. That is why it is undefined.

As for the pencils, he want 2 per student. That means he needs 64 pencils.
Since 8 divides 64, he can get exactly 64/8 = 8 packs of pencils and use them all up.

posted by Steve

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