Question

•The product of two rational numbers with different signs is always ....
•The product of a rational numbers with its reciprocal is always .......
•The numbers of integers between two consecutive integers is .........
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Answer 1

multiplying two rationals is thesame as multiplying two such fractions, which will result in another fraction of this same form since integers are closed under multiplication. Thus, multiplying two rational numbers produces another rational number.

The product of rational number with its reciprocal is always equal to 1

An integer with a units digit of 5 occurs once every 10consecutive integers. There are 300 integers between 200 and 500, so there must be 30 values with a units digit of 5.

Answer 2

1. It is always negative.

Let the first number be positive. Then, the second number is negative (according to condition).

a * (-b) = -ab, where a > 0, b > 0. (the numbers under consideration are a and -b)

Now, the otherwise:

(-a) * b = -ab, where a > 0, b > 0. (the numbers under consideration are -a and b)

2. 1 (one).

Let the number be x. Then its reciprocal is $\frac{1}{x}$

Now, $x * \frac{1}{x} = 1$

A number divided by itself gives one as the quotient, and no remainder (this is fundamental-ish).

3. 0 (zero).

Let z be an integer. The integer next to it shall be z + 1, and none else.

These are also consecutive. Apparently, there is no integer between them.