Answer :
To compare the fractions [tex]\( \frac{5}{6} \)[/tex] and [tex]\( \frac{24}{30} \)[/tex] using the [tex]\(\frac{5}{6} - \frac{24}{30}\)[/tex]:
1. Simplify the Second Fraction:
First, simplify the fraction [tex]\(\frac{24}{30}\)[/tex].
[tex]\[
\frac{24}{30} = \frac{24 \div 6}{30 \div 6} = \frac{4}{5}
\][/tex]
2. Find a Common Denominator:
To subtract fractions, they must have the same denominator. The denominators for [tex]\(\frac{5}{6}\)[/tex] and [tex]\(\frac{4}{5}\)[/tex] are 6 and 5. The common denominator is the least common multiple (LCM) of 6 and 5, which is 30.
3. Convert the Fractions:
Convert each fraction to have the common denominator of 30.
[tex]\[
\frac{5}{6} = \frac{5 \times 5}{6 \times 5} = \frac{25}{30}
\][/tex]
[tex]\[
\frac{4}{5} = \frac{4 \times 6}{5 \times 6} = \frac{24}{30}
\][/tex]
4. Subtract the Fractions:
Now subtract the second fraction from the first.
[tex]\[
\frac{25}{30} - \frac{24}{30} = \frac{25 - 24}{30} = \frac{1}{30}
\][/tex]
5. Interpret the Result:
The result is [tex]\(\frac{1}{30}\)[/tex], which is a positive number. This means that [tex]\(\frac{5}{6}\)[/tex] is greater than [tex]\(\frac{4}{5}\)[/tex].
Therefore, using the symbols [tex]\(<\)[/tex] or [tex]\(>\)[/tex], we get:
[tex]\[
\frac{5}{6} > \frac{24}{30}
\][/tex]
1. Simplify the Second Fraction:
First, simplify the fraction [tex]\(\frac{24}{30}\)[/tex].
[tex]\[
\frac{24}{30} = \frac{24 \div 6}{30 \div 6} = \frac{4}{5}
\][/tex]
2. Find a Common Denominator:
To subtract fractions, they must have the same denominator. The denominators for [tex]\(\frac{5}{6}\)[/tex] and [tex]\(\frac{4}{5}\)[/tex] are 6 and 5. The common denominator is the least common multiple (LCM) of 6 and 5, which is 30.
3. Convert the Fractions:
Convert each fraction to have the common denominator of 30.
[tex]\[
\frac{5}{6} = \frac{5 \times 5}{6 \times 5} = \frac{25}{30}
\][/tex]
[tex]\[
\frac{4}{5} = \frac{4 \times 6}{5 \times 6} = \frac{24}{30}
\][/tex]
4. Subtract the Fractions:
Now subtract the second fraction from the first.
[tex]\[
\frac{25}{30} - \frac{24}{30} = \frac{25 - 24}{30} = \frac{1}{30}
\][/tex]
5. Interpret the Result:
The result is [tex]\(\frac{1}{30}\)[/tex], which is a positive number. This means that [tex]\(\frac{5}{6}\)[/tex] is greater than [tex]\(\frac{4}{5}\)[/tex].
Therefore, using the symbols [tex]\(<\)[/tex] or [tex]\(>\)[/tex], we get:
[tex]\[
\frac{5}{6} > \frac{24}{30}
\][/tex]
