Questions: Marcus is 5 7/24 feet tall. Ben is 5 5/16 feet tall. Which of the two boys is taller? Justify your answer.

Solution Steps

To determine which of the two boys is taller, we need to compare their heights. Since their heights are given as mixed numbers, we should first convert these mixed numbers to improper fractions. Then, we can find a common denominator to compare the fractions directly.

Marcus's height is given as \(5 \frac{7}{24}\) feet. To convert this to an improper fraction: \[ 5 \frac{7}{24} = \frac{5 \times 24 + 7}{24} = \frac{120 + 7}{24} = \frac{127}{24} \]

Ben's height is given as \(5 \frac{5}{16}\) feet. To convert this to an improper fraction: \[ 5 \frac{5}{16} = \frac{5 \times 16 + 5}{16} = \frac{80 + 5}{16} = \frac{85}{16} \]

To compare \(\frac{127}{24}\) and \(\frac{85}{16}\), we need a common denominator. The least common multiple (LCM) of 24 and 16 is 48.

Convert \(\frac{127}{24}\) to a fraction with a denominator of 48: \[ \frac{127}{24} = \frac{127 \times 2}{24 \times 2} = \frac{254}{48} \]

Convert \(\frac{85}{16}\) to a fraction with a denominator of 48: \[ \frac{85}{16} = \frac{85 \times 3}{16 \times 3} = \frac{255}{48} \]

Now, compare \(\frac{254}{48}\) and \(\frac{255}{48}\): \[ \frac{254}{48} < \frac{255}{48} \]

Thus, \(\frac{127}{24} < \frac{85}{16}\).

Final Answer