Which inequality is true?

Question

A number line going from negative 3 to positive 3 in increments of 1.
StartFraction 5 Over 6 EndFraction less-than negative one-third
2 and one-third greater-than 2 and one-sixth
2 less-than negative 2 and one-half
1 and one-fourth greater-than 1 and one-third

Answer 1

To determine which inequality is true, let's evaluate each one:

1. \(\frac{5}{6} < -\frac{1}{3}\):

   • The value of \(\frac{5}{6}\) is approximately \(0.833\).
   • The value of \(-\frac{1}{3}\) is approximately \(-0.333\).
   • Since \(0.833\) is greater than \(-0.333\), this inequality is false.

2. \(2 \frac{1}{3} > 2 \frac{1}{6}\):

   • Convert to improper fractions: \(2 \frac{1}{3} = \frac{7}{3}\) and \(2 \frac{1}{6} = \frac{13}{6}\).
   • Compare \(\frac{7}{3} = \frac{14}{6}\) (after multiplying by 2).
   • Since \(\frac{14}{6} > \frac{13}{6}\), this inequality is true.

3. \(2 < -2 \frac{1}{2}\):

   • The value of \(2\) is \(2\) and the value of \(-2 \frac{1}{2}\) is approximately \(-2.5\).
   • Since \(2\) is greater than \(-2.5\), this inequality is false.

4. \(1 \frac{1}{4} > 1 \frac{1}{3}\):

   • Convert to improper fractions: \(1 \frac{1}{4} = \frac{5}{4}\) and \(1 \frac{1}{3} = \frac{4}{3}\).
   • Since \(\frac{5}{4} = 1.25\) and \(\frac{4}{3} \approx 1.3333\), it can be noted that \(1.25 < 1.3333\), so this inequality is false.

Summarizing the results:

• The only true inequality is \(2 \frac{1}{3} > 2 \frac{1}{6}\).