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Which numbers are greater than [tex]118 \frac{2}{13}[/tex]?

A. [tex]118 \frac{8}{14}[/tex]
B. [tex]117 \frac{2}{7}[/tex]
C. [tex]\frac{1,660}{14}[/tex]
D. [tex]119 \frac{2}{8}[/tex]

Answer :

Sure! Let's go through each number step-by-step to determine which ones are greater than [tex]\( 118 \frac{2}{13} \)[/tex].

### 1. Convert [tex]\( 118 \frac{2}{13} \)[/tex] to a decimal:
First, convert the fraction [tex]\(\frac{2}{13}\)[/tex] to a decimal:
[tex]\[ \frac{2}{13} \approx 0.1538 \][/tex]

Now, add this to the whole number part:
[tex]\[ 118 + 0.1538 = 118.1538 \][/tex]

So, [tex]\( 118 \frac{2}{13} \approx 118.1538 \)[/tex]

### 2. Evaluate each given number as a decimal:
#### a. [tex]\( 118 \frac{8}{14} \)[/tex]
Convert [tex]\(\frac{8}{14}\)[/tex] to a decimal:
[tex]\[ \frac{8}{14} = \frac{4}{7} \approx 0.5714 \][/tex]

Now, add this to the whole number part:
[tex]\[ 118 + 0.5714 = 118.5714 \][/tex]

#### b. [tex]\( 117 \frac{2}{7} \)[/tex]
Convert [tex]\(\frac{2}{7}\)[/tex] to a decimal:
[tex]\[ \frac{2}{7} \approx 0.2857 \][/tex]

Now, add this to the whole number part:
[tex]\[ 117 + 0.2857 = 117.2857 \][/tex]

#### c. [tex]\(\frac{1660}{14}\)[/tex]
Divide the numerator by the denominator:
[tex]\[ \frac{1660}{14} \approx 118.5714 \][/tex]

#### d. [tex]\( 119 \frac{2}{8} \)[/tex]
Convert [tex]\(\frac{2}{8}\)[/tex] to a decimal:
[tex]\[ \frac{2}{8} = 0.25 \][/tex]

Now, add this to the whole number part:
[tex]\[ 119 + 0.25 = 119.25 \][/tex]

### 3. Compare each decimal with [tex]\( 118.1538 \)[/tex]:
- [tex]\(118.5714 > 118.1538\)[/tex]
- [tex]\(117.2857 < 118.1538\)[/tex]
- [tex]\(118.5714 > 118.1538\)[/tex]
- [tex]\(119.25 > 118.1538\)[/tex]

### 4. Identify the numbers greater than [tex]\( 118 \frac{2}{13} \)[/tex]:
The numbers greater than [tex]\( 118 \frac{2}{13} \)[/tex] are:
- [tex]\( 118 \frac{8}{14} \)[/tex]
- [tex]\( \frac{1,660}{14} \)[/tex]
- [tex]\( 119 \frac{2}{8} \)[/tex]

So the numbers greater than [tex]\( 118 \frac{2}{13} \)[/tex] are:
[tex]\[ 118 \frac{8}{14}, \frac{1,660}{14}, \text{and } 119 \frac{2}{8} \][/tex]

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