Marcus is 5 7/24 feet tall. ben is 5 5/16 feet tall. which boy is taller? explain

To determine which boy is taller, we need to compare Marcus' height of \(5 \frac{7}{24}\) feet and Ben's height of \(5 \frac{5}{16}\) feet.

### Step 1: Convert both heights to improper fractions.

- Marcus' height: 
  \[
  5 \frac{7}{24} = \frac{5 \times 24 + 7}{24} = \frac{120 + 7}{24} = \frac{127}{24} \, \text{feet}
  \]

- Ben's height: 
  \[
  5 \frac{5}{16} = \frac{5 \times 16 + 5}{16} = \frac{80 + 5}{16} = \frac{85}{16} \, \text{feet}
  \]

### Step 2: Find a common denominator to compare these fractions.

The least common denominator (LCD) between 24 and 16 is 48. Now, convert both fractions:

- Marcus' height:
  \[
  \frac{127}{24} = \frac{127 \times 2}{24 \times 2} = \frac{254}{48}
  \]

- Ben's height:
  \[
  \frac{85}{16} = \frac{85 \times 3}{16 \times 3} = \frac{255}{48}
  \]

### Step 3: Compare the heights.

Now that both fractions have the same denominator, we can compare the numerators:
- Marcus: \(\frac{254}{48}\)
- Ben: \(\frac{255}{48}\)

Since \(255 > 254\), **Ben is taller** than Marcus.

### Conclusion:
Ben, who is \(5 \frac{5}{16}\) feet tall, is taller than Marcus, who is \(5 \frac{7}{24}\) feet tall, by \(\frac{1}{48}\) feet.

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Do you want more details or have any questions?

Here are some related questions to explore:

1. How would you convert a mixed number into a decimal and compare their heights that way?
2. Can you express their height difference in inches?
3. What is the difference between Marcus and Ben's heights in centimeters?
4. How would the calculation change if their heights were measured in inches?
5. Can you explain how to find the least common denominator?

**Tip**: When comparing fractions, it's often useful to convert them to a common denominator or decimal for easier comparison.

Marcus is 5 7/24 feet tall. Ben is 5 5/16 feet tall. Which boy is taller? Explain.

Determine which boy is taller by comparing the fractional heights of Marcus (5 7/24 feet) and Ben (5 5/16 feet). This detailed step-by-step solution covers concepts like converting mixed numbers to improper fractions, finding the least common denominator, and comparing fractions. Suitable for students in Grades 6-8.

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