To compare the fractions [tex]\(\frac{7}{10}\)[/tex] and [tex]\(\frac{9}{8}\)[/tex] using a benchmark, follow these step-by-step instructions:
1. Convert Fractions to Decimals:
- For [tex]\(\frac{7}{10}\)[/tex]:
[tex]\[
\frac{7}{10} = 0.7
\][/tex]
- For [tex]\(\frac{9}{8}\)[/tex]:
[tex]\[
\frac{9}{8} = 1.125
\][/tex]
2. Compare the Decimals:
- We have the decimals [tex]\(0.7\)[/tex] and [tex]\(1.125\)[/tex].
3. Determine Which Decimal is Greater:
- In comparing [tex]\(0.7\)[/tex] and [tex]\(1.125\)[/tex]:
[tex]\[
0.7 < 1.125
\][/tex]
4. Conclusion:
- Since [tex]\(0.7 < 1.125\)[/tex], [tex]\(\frac{7}{10} < \frac{9}{8}\)[/tex].
Thus, [tex]\(\frac{7}{10}\)[/tex] is less than [tex]\(\frac{9}{8}\)[/tex].
