Answer:
The closure property of the integers means that if we have a and b, integers then:
a + b = c will also be an integer.
(i will also use the fact that if a and b are integers, then a*b is also an integer)
Now suppose that we have two rational numbers.
a/b and c/d.
where a, b, c and d are integers. (b and d are different than zero)
the sum of those two numbers can be written as:
Now, a*d, b*c and b*d are integers (because integers are closed under multiplication)
and because a*d and b*c are integers, then:
a*d + b*c is also an integer.
Then:
(a*d + b*c)/(b*d)
is the quotient between two integers, which is a rational number.
Then we can conclude that the rational numbers are closed under the addition operation.
-8
How I got it:
-8 + 8 = 0
Hope this helps! Happy thanksgiving, here's a turkey!
Step-by-step explanation:
yes, if your teacher meant to include the default factors of every positive integer number : 1 and the number itself.
these are the 2 positive integer factors.
if a positive number can only be divided without remainder by 1 or by itself (with result 1), then it is per definition a prime number.
if the number can be divided without remainder by another number, then we are not dealing with a prime number.
but if your teacher did not have these default factors in mind, then no :
example : 15
15 has only 2 factors : 3 and 5.
both are positive integer numbers.
and yet 15 is not a prime number.
but back to my first point, 15 also has formally the factors 1 and 15. so, if we count them too, then we have suddenly 4 factors. and the original statement fits again.
