Question

Which of the following rational numbers are in lowest terms (i.e. have no common factors)?• 30/12• 221/1105•4011/93• 19/190 •I and II are in lowest terms.•I and IV are in lowest terms.•Only III is in lowest terms. •II, III, and IV are in lowest terms.•None of the numbers are in lowest terms.

Answer 1

Given the rational numbers:

`\begin{gathered} (30)/(12) \\ \\ (221)/(1105) \\ \\ (401)/(93) \\ \\ (19)/(190) \end{gathered}`

Let's determine the rational numbers that are in lowest terms.

If a rational number is in lowest terms, it means the numerator and denominator have no common factor.

Let's start from the first number:

• (a). 30/12

30 and 12 have common factors: 2, 3, and 6

Therefore, it is NOT in its lowest term.

• (b). 221/1105

221 and 1105 have common factors of 13, 17, and 221

Therefore, it is NOT in its lowest term.

• (c). 4011/93

4011 and 93 have a common factor of 3

Therefore, the rational number is NOT in its lowest term.

• (d). 19/190

19 and 190 have a common factor of 19.

Since they have a common factor, the rational number is NOT in its lowest term.

Therefore, none of the numbers are in lowest terms.

• ANSWER:

None of the numbers are in lowest terms.​