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Check for understanding:

Using the symbols "<" or ">", compare: [tex]\frac{5}{6}[/tex] and [tex]\frac{24}{30}[/tex]. Show how you determined your answer.

Answer :

To compare the two fractions [tex]\(\frac{5}{6}\)[/tex] and [tex]\(\frac{24}{30}\)[/tex] using the symbols < or >, we can follow these steps:

1. Simplify the Fractions (if needed):
- The fraction [tex]\(\frac{24}{30}\)[/tex] can be simplified by finding the greatest common divisor (GCD) of 24 and 30, which is 6.
- Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{24 \div 6}{30 \div 6} = \frac{4}{5}
\][/tex]
- So, [tex]\(\frac{24}{30}\)[/tex] simplifies to [tex]\(\frac{4}{5}\)[/tex].

2. Convert to Decimals:
- Convert both fractions to decimals to easily compare them:
- [tex]\(\frac{5}{6}\)[/tex] as a decimal is approximately 0.8333.
- [tex]\(\frac{4}{5}\)[/tex] as a decimal is exactly 0.8.

3. Compare the Decimal Values:
- Compare the decimal values:
- 0.8333 (which represents [tex]\(\frac{5}{6}\)[/tex]) and
- 0.8 (which represents [tex]\(\frac{4}{5}\)[/tex]).

4. Determine Comparison:
- Since 0.8333 is greater than 0.8, we conclude that [tex]\(\frac{5}{6} > \frac{24}{30}\)[/tex].

Therefore, [tex]\(\frac{5}{6}\)[/tex] is greater than [tex]\(\frac{24}{30}\)[/tex].

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