Question

The fractions 3/a and 7/b are equivalent to decimals that terminate. Which best describes the product of a and b ?

a) It is a prime number.

b) It cannot be an odd number.

c) It is of the form 21k, where k could be multiples of 2 or 5.

d) It is of the form 21k, where k could be multiples of 7 or 9.

Answer 1

Answer:

A it can be prime number

because prime number can be integers

Answer 2

Given:

The fractions 3/a and 7/b are equivalent to decimals that terminate.

To find:

The correct option.

Solution:

To answer this question, first of all, we should know that a fraction is said to give a terminating decimal number only when its denominator contains the multiples of 2 or 5.

So,

as given, the fractions 3/a and 7/b are equivalent to decimals that terminate

So, this means,

a and b are multiples of 2 or 5.

So,

the product of a and b is also multiples of 2 or 5.

The product of a and b can be written in the form of 21k where k can be multiples of 2 or 5 as it will always give multiples of 2 or 5.

The product of a and b cannot be a prime number. Also, the product of a and b can be either odd (when k = 5 or multiples of 5) or even (when k = 2 or multiples of 2).

The product of a and b could not be multiples of 7 or 9, as it will make the decimal non terminating.

Hence, the correct option is c) It is of the form 21k, where k could be multiples of 2 or 5.