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Which number is greater than [tex]$69 \frac{1}{6}$[/tex]?

A. [tex]$69 \frac{5}{7}$[/tex]
B. [tex]$\frac{682}{10}$[/tex]
C. [tex]$68 \frac{7}{10}$[/tex]
D. [tex]$68 \frac{1}{4}$[/tex]

Answer :

To determine which number is greater than [tex]\(69 \frac{1}{6}\)[/tex], we need to compare each of the given numbers with [tex]\(69 \frac{1}{6}\)[/tex]. Here’s how we can do the comparison:

1. Convert the mixed number [tex]\(69 \frac{1}{6}\)[/tex] to a decimal:
- [tex]\(69 \frac{1}{6} = 69 + \frac{1}{6} = 69 + 0.1667 \approx 69.1667\)[/tex]

2. Next, we convert each of the other numbers to a decimal:

- [tex]\(69 \frac{5}{7} = 69 + \frac{5}{7} = 69 + 0.7143 \approx 69.7143\)[/tex]
- [tex]\(\frac{682}{10} = 68.2\)[/tex]
- [tex]\(68 \frac{7}{10} = 68 + \frac{7}{10} = 68 + 0.7 = 68.7\)[/tex]
- [tex]\(68 \frac{1}{4} = 68 + \frac{1}{4} = 68 + 0.25 = 68.25\)[/tex]

3. Now, we compare each of these numbers to [tex]\(69.1667\)[/tex]:
- [tex]\(69.7143 > 69.1667\)[/tex]
- [tex]\(68.2 < 69.1667\)[/tex]
- [tex]\(68.7 < 69.1667\)[/tex]
- [tex]\(68.25 < 69.1667\)[/tex]

From these comparisons, we see that the only number greater than [tex]\(69 \frac{1}{6}\)[/tex] is [tex]\(69 \frac{5}{7}\)[/tex].

Therefore, [tex]\(69 \frac{5}{7}\)[/tex] is the number greater than [tex]\(69 \frac{1}{6}\)[/tex].

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