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Which of the following is a true statement?

A. [tex]\frac{6}{16} \ \textgreater \ \frac{5}{10}[/tex]

B. [tex]\frac{3}{5} \ \textless \ \frac{6}{16}[/tex]

C. [tex]\frac{4}{8} \ \textless \ \frac{6}{16}[/tex]

D. [tex]\frac{6}{16} \ \textgreater \ \frac{8}{24}[/tex]


Sagot :

To determine which of the given statements is true, we need to compare the fractions accurately. Here are the detailed steps for each comparison:

1. Compare [tex]\(\frac{6}{16}\)[/tex] and [tex]\(\frac{5}{10}\)[/tex]:

Simplify each fraction:
[tex]\[ \frac{6}{16} = \frac{3}{8} \][/tex]
[tex]\[ \frac{5}{10} = \frac{1}{2} \][/tex]

Compare:
[tex]\[ \frac{3}{8} < \frac{1}{2} \][/tex]

Therefore, [tex]\(\frac{6}{16} < \frac{5}{10}\)[/tex] is true, so [tex]\(\frac{6}{16} > \(\frac{5}{10}\)[/tex] is false.

2. Compare [tex]\(\frac{3}{5}\)[/tex] and [tex]\(\frac{6}{16}\)[/tex]:

Simplify [tex]\(\frac{6}{16}\)[/tex]:
[tex]\[ \frac{6}{16} = \frac{3}{8} \][/tex]

Compare:
[tex]\[ \frac{3}{5} > \frac{3}{8} \][/tex]

Therefore, [tex]\(\(\frac{3}{5} < \frac{6}{16}\)[/tex] is false.

3. Compare [tex]\(\frac{4}{8}\)[/tex] and [tex]\(\frac{6}{16}\)[/tex]:

Simplify both fractions:
[tex]\[ \frac{4}{8} = \frac{1}{2} \][/tex]
[tex]\[ \frac{6}{16} = \frac{3}{8} \][/tex]

Compare:
[tex]\[ \frac{1}{2} > \frac{3}{8} \][/tex]

Therefore, [tex]\(\(\frac{4}{8} < \frac{6}{16}\)[/tex] is false.

4. Compare [tex]\(\frac{6}{16}\)[/tex] and [tex]\(\frac{8}{24}\)[/tex]:

Simplify both fractions:
[tex]\[ \frac{6}{16} = \frac{3}{8} \][/tex]
[tex]\[ \frac{8}{24} = \frac{1}{3} \][/tex]

Compare:
[tex]\[ \frac{3}{8} > \frac{1}{3} \][/tex]

Therefore, [tex]\(\(\frac{6}{16} > \frac{8}{24}\)[/tex] is true.

So, the true statement is:
[tex]\[ \(\frac{6}{16} > \frac{8}{24}\) \][/tex]

The correct answer is the fourth statement, which means the true statement is:
[tex]\(\frac{6}{16} > \frac{8}{24}\)[/tex].