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Answer :
To compare the fractions [tex]\(\frac{6}{8}\)[/tex] and [tex]\(\frac{4}{5}\)[/tex], we'll find a common denominator and then compare the numerators.
1. Identify the least common denominator (LCD):
The denominators we have are 8 and 5. The least common multiple of 8 and 5 is 40. So, the common denominator is 40.
2. Convert [tex]\(\frac{6}{8}\)[/tex] to an equivalent fraction with a denominator of 40:
- To find the new numerator, we need to determine what we multiply 8 by to get 40. Since [tex]\(8 \times 5 = 40\)[/tex], we multiply the numerator by the same factor:
- [tex]\(6 \times 5 = 30\)[/tex]
- So, [tex]\(\frac{6}{8} = \frac{30}{40}\)[/tex].
3. Convert [tex]\(\frac{4}{5}\)[/tex] to an equivalent fraction with a denominator of 40:
- To find the new numerator, determine what we multiply 5 by to get 40. Since [tex]\(5 \times 8 = 40\)[/tex], we multiply the numerator by the same factor:
- [tex]\(4 \times 8 = 32\)[/tex]
- So, [tex]\(\frac{4}{5} = \frac{32}{40}\)[/tex].
4. Compare the numerators:
- Now that both fractions have the same denominator, compare the numerators: 30 and 32.
- Since 30 is less than 32, it follows that [tex]\(\frac{30}{40} < \frac{32}{40}\)[/tex].
Therefore, [tex]\(\frac{6}{8} < \frac{4}{5}\)[/tex].
1. Identify the least common denominator (LCD):
The denominators we have are 8 and 5. The least common multiple of 8 and 5 is 40. So, the common denominator is 40.
2. Convert [tex]\(\frac{6}{8}\)[/tex] to an equivalent fraction with a denominator of 40:
- To find the new numerator, we need to determine what we multiply 8 by to get 40. Since [tex]\(8 \times 5 = 40\)[/tex], we multiply the numerator by the same factor:
- [tex]\(6 \times 5 = 30\)[/tex]
- So, [tex]\(\frac{6}{8} = \frac{30}{40}\)[/tex].
3. Convert [tex]\(\frac{4}{5}\)[/tex] to an equivalent fraction with a denominator of 40:
- To find the new numerator, determine what we multiply 5 by to get 40. Since [tex]\(5 \times 8 = 40\)[/tex], we multiply the numerator by the same factor:
- [tex]\(4 \times 8 = 32\)[/tex]
- So, [tex]\(\frac{4}{5} = \frac{32}{40}\)[/tex].
4. Compare the numerators:
- Now that both fractions have the same denominator, compare the numerators: 30 and 32.
- Since 30 is less than 32, it follows that [tex]\(\frac{30}{40} < \frac{32}{40}\)[/tex].
Therefore, [tex]\(\frac{6}{8} < \frac{4}{5}\)[/tex].
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