Question

complete the sentence describing the comparison. \\(\frac{4}{10}\\) is less than \\(\frac{8}{100}\\). next, complete the equation. \\(\frac{4 \times 10}{10 \times 10} = \frac{40}{100}\\) now, complete the sentence describing the comparison. \\(\frac{40}{100}\\) is greater than \\(\frac{8}{100}\\). \\(\frac{4}{10}\\) is greater than \\(\frac{8}{100}\\).

Explanation:

Step1: Compare \(\frac{4}{10}\) and \(\frac{8}{100}\)

Convert \(\frac{4}{10}\) to hundredths: \(\frac{4\times10}{10\times10}=\frac{40}{100}\). Now compare \(\frac{40}{100}\) and \(\frac{8}{100}\). Since \(40 > 8\), \(\frac{40}{100}>\frac{8}{100}\), so \(\frac{4}{10}\) (which is \(\frac{40}{100}\)) is greater than \(\frac{8}{100}\). The initial thought that \(\frac{4}{10}<\frac{8}{100}\) was wrong; correcting it, \(\frac{4}{10}\) (or \(\frac{40}{100}\)) is greater than \(\frac{8}{100}\).

Step2: Verify the fraction conversion

\(\frac{4\times10}{10\times10}=\frac{40}{100}\) is correct as multiplying numerator and denominator by 10 converts tenths to hundredths.

Step3: Final comparison

\(\frac{40}{100}\) (same as \(\frac{4}{10}\)) has numerator 40, \(\frac{8}{100}\) has numerator 8. \(40 > 8\), so both \(\frac{40}{100}\) and \(\frac{4}{10}\) are greater than \(\frac{8}{100}\).

Answer:

• The correct comparison for \(\frac{4}{10}\) and \(\frac{8}{100}\) is "greater than".
• The equation \(\frac{4\times10}{10\times10}=\frac{40}{100}\) is correct.
• Both \(\frac{40}{100}\) and \(\frac{4}{10}\) are greater than \(\frac{8}{100}\).