To compare the fractions [tex]\(\frac{3}{4}\)[/tex] and [tex]\(\frac{7}{6}\)[/tex] using benchmarks, follow these steps:
1. Understand the Fractions:
- First, identify the fractions: [tex]\(\frac{3}{4}\)[/tex] and [tex]\(\frac{7}{6}\)[/tex].
2. Convert Fractions to Decimals:
- Convert each fraction to its decimal form to make comparison easier.
- For [tex]\(\frac{3}{4}\)[/tex]:
[tex]\[
\frac{3}{4} = 0.75
\][/tex]
- For [tex]\(\frac{7}{6}\)[/tex]:
[tex]\[
\frac{7}{6} = 1.1666666666666667 \text{ (approximately 1.167)}
\][/tex]
3. Compare Decimal Values using Benchmarks:
- Use the converted decimal values [tex]\(0.75\)[/tex] and [tex]\(1.167\)[/tex] as benchmarks for comparison.
4. Draw Conclusion:
- Compare [tex]\(0.75\)[/tex] and [tex]\(1.167\)[/tex]:
[tex]\[
0.75 < 1.167
\][/tex]
- Therefore, the fraction [tex]\(\frac{3}{4}\)[/tex] is less than [tex]\(\frac{7}{6}\)[/tex].
Hence, the final comparison result is:
[tex]\[
\frac{3}{4} \text{ is less than } \frac{7}{6}
\][/tex]
