Question

Determine which of the numbers in the set below are rational.

Group of answer choices:
A) {4/7}
B) { -16, 35 }
C) { -16, 35, 4/7, 5.75, -9.5 }
D) { 5.75, -9.5 }
E) None are rational

Answer 1

Sets A, B, C, and D all contain rational numbers, as they can be expressed as fractions with integers in the numerator and non-zero integers in the denominator. Therefore, none of the options contain exclusively irrational numbers.

Step-by-step explanation:

To determine which of the numbers in the various sets are rational, we first need to recall the definition of rational numbers. A rational number is any number that can be expressed as the quotient (or fraction) of two integers, where the denominator is not zero. Now, let's consider each set:

• Set A {4/7} is a single fraction with both numerator and denominator as integers, and the denominator is not zero, so 4/7 is a rational number.
• Set B { -16, 35 } includes two integers. All integers are rational numbers because they can be expressed as the fraction of the integer itself over 1 (for example, -16 can be written as -16/1).
• Set C { -16, 35, 4/7, 5.75, -9.5 } combines integers, a fraction, and two decimals that can be converted to fractions (5.75 = 23/4 and -9.5 = -19/2). All these numbers are rational.
• Set D { 5.75, -9.5 }, as previously mentioned, both numbers can be written as fractions, so both are rational numbers.

Option E, 'None are rational', is incorrect because rational numbers are present in all the other options.