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Which of the following is a true statement?

A. [tex]$\frac{5}{6} \ \textgreater \ \frac{10}{12}$[/tex]

B. [tex]$\frac{8}{16} = \frac{1}{4}$[/tex]

C. [tex]$\frac{3}{4} \ \textless \ \frac{4}{6}$[/tex]

D. [tex]$\frac{11}{15} \ \textless \ \frac{4}{5}$[/tex]

Sagot :

To determine which of the given statements is true, we'll analyze each one step by step.

### Statement 1: [tex]\(\frac{5}{6} > \frac{10}{12}\)[/tex]

First, let's simplify [tex]\(\frac{10}{12}\)[/tex]:

[tex]\[ \frac{10}{12} = \frac{10 \div 2}{12 \div 2} = \frac{5}{6} \][/tex]

Now we compare [tex]\(\frac{5}{6}\)[/tex] with [tex]\(\frac{5}{6}\)[/tex]:

[tex]\[ \frac{5}{6} = \frac{5}{6} \][/tex]

Hence,

[tex]\[ \frac{5}{6} > \frac{10}{12} \quad \text{is false} \][/tex]

### Statement 2: [tex]\(\frac{8}{16} = \frac{1}{4}\)[/tex]

Next, let's simplify [tex]\(\frac{8}{16}\)[/tex]:

[tex]\[ \frac{8}{16} = \frac{8 \div 8}{16 \div 8} = \frac{1}{2} \quad \text{(not } \frac{1}{4}\text{)} \][/tex]

Therefore,

[tex]\[ \frac{8}{16} = \frac{1}{4} \quad \text{is false} \][/tex]

### Statement 3: [tex]\(\frac{3}{4} < \frac{4}{6}\)[/tex]

Next, let's simplify [tex]\(\frac{4}{6}\)[/tex]:

[tex]\[ \frac{4}{6} = \frac{4 \div 2}{6 \div 2} = \frac{2}{3} \][/tex]

Now we compare [tex]\(\frac{3}{4}\)[/tex] with [tex]\(\frac{2}{3}\)[/tex]:

First, convert them to common denominators or decimals:

[tex]\[ \frac{3}{4} = 0.75 \quad \text{and} \quad \frac{2}{3} \approx 0.6667 \][/tex]

Since [tex]\(0.75\)[/tex] is greater than [tex]\(0.6667\)[/tex],

[tex]\[ \frac{3}{4} < \frac{4}{6} \quad \text{is false} \][/tex]

### Statement 4: [tex]\(\frac{11}{15} < \frac{4}{5}\)[/tex]

Let's express [tex]\(\frac{4}{5}\)[/tex] and [tex]\(\frac{11}{15}\)[/tex] with a common denominator, [tex]\(15\)[/tex]:

[tex]\[ \frac{4}{5} = \frac{4 \times 3}{5 \times 3} = \frac{12}{15} \][/tex]

Now we compare [tex]\(\frac{11}{15}\)[/tex] with [tex]\(\frac{12}{15}\)[/tex]:

[tex]\[ \frac{11}{15} < \frac{12}{15} \][/tex]

This is true.

### Conclusion

Out of all the provided comparisons, the true statement is:

[tex]\[ \frac{11}{15} < \frac{4}{5} \][/tex]
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