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First, rewrite [tex]\frac{5}{6}[/tex] and [tex]\frac{13}{15}[/tex] so that they have a common denominator. Then, use [tex]\ \textless \ , =, [/tex] or [tex]\ \textgreater \ [/tex] to order [tex]\frac{5}{6}[/tex] and [tex]\frac{13}{15}[/tex].

[tex]\frac{5}{6} = \frac{\square}{\square} \quad ; \quad \frac{13}{15} = \frac{\square}{\square}[/tex]

Choose the correct symbol:

[tex]\square \ \textless \ [/tex]
[tex]\square \ \textgreater \ [/tex]
[tex]\square =[/tex]

Complete the statement:

[tex]\frac{5}{6} \square \frac{13}{15}[/tex]

Answer :

Let's find a common denominator for the fractions [tex]\(\frac{5}{6}\)[/tex] and [tex]\(\frac{13}{15}\)[/tex] and compare them.

### Step 1: Find the Least Common Denominator (LCD)

To combine or compare fractions, they need to have the same denominator. The least common denominator is the least common multiple (LCM) of the denominators.

- The denominators are 6 and 15.
- List the multiples:
- Multiples of 6: 6, 12, 18, 24, 30, 36, ...
- Multiples of 15: 15, 30, 45, ...

The smallest common multiple of both is 30. So, the least common denominator is 30.

### Step 2: Rewriting Fractions with the Common Denominator

Now, convert each fraction to have the denominator of 30:

1. Convert [tex]\(\frac{5}{6}\)[/tex] to a fraction with a denominator of 30:
- [tex]\(\frac{5}{6} = \frac{5 \times 5}{6 \times 5} = \frac{25}{30}\)[/tex]

2. Convert [tex]\(\frac{13}{15}\)[/tex] to a fraction with a denominator of 30:
- [tex]\(\frac{13}{15} = \frac{13 \times 2}{15 \times 2} = \frac{26}{30}\)[/tex]

### Step 3: Compare the Fractions

Now compare [tex]\(\frac{25}{30}\)[/tex] and [tex]\(\frac{26}{30}\)[/tex].

- [tex]\(\frac{25}{30} < \frac{26}{30}\)[/tex]

### Conclusion

The original comparison is:
[tex]\[
\frac{5}{6} < \frac{13}{15}
\][/tex]

Thus, we have:
[tex]\[
\frac{5}{6} = \frac{25}{30} \quad ; \quad \frac{13}{15} = \frac{26}{30}
\][/tex]
[tex]\[
25 < 26
\][/tex]
[tex]\[
\frac{5}{6} < \frac{13}{15}
\][/tex]

This step-by-step solution confirms that [tex]\(\frac{5}{6}\)[/tex] is less than [tex]\(\frac{13}{15}\)[/tex].

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