Fractions, Decimals, and Percents - Quantitative Reasoning

1. What is the rule to convert a percent $p\%$ to a fraction in simplest form?

   Write $\frac{p}{100}$ and reduce. Expressing the percentage as a fraction over 100 and simplifying gives the reduced form.

2. What is the decimal form of $\frac{3}{4}$?

   $0.75$. Dividing 3 by 4 yields this terminating decimal.

3. What is the percent form of $\frac{7}{8}$?

   $87.5\%$. Multiplying $\frac{7}{8}$ by 100 gives this percentage equivalent.

4. What is the decimal form of $37.5\%$?

   $0.375$. Dividing 37.5 by 100 converts the percentage to this decimal.

5. What is $25\%$ of $60$?

   $15$. Multiplying 60 by 0.25 determines 25% of the amount.

6. What is the decimal form of $\frac{2}{5}$?

   $0.4$. Dividing 2 by 5 produces this terminating decimal.

7. What is the rule to convert a percent $p\%$ to a decimal?

   Compute $\frac{p}{100}$. Dividing the percentage value by 100 expresses it as a decimal equivalent.

8. What is the fraction in simplest form for the decimal $0.125$?

   $\frac{1}{8}$. Writing 0.125 as $\frac{125}{1000}$ and reducing yields this simplest fraction.

9. What is the fraction in simplest form for the repeating decimal $0.\overline{3}$?

   $\frac{1}{3}$. The repeating decimal 0.333... equals $\frac{1}{3}$ as its fractional equivalent.

10. What is the decimal form of $\frac{1}{4}$?

    $0.25$. Dividing 1 by 4 produces this terminating decimal.

11. What is the percent increase from $50$ to $60$?

    $20\%$. The formula for percent increase is $\frac{60-50}{50} \times 100$, yielding this result.

12. What is $15\%$ of $80$?

    $12$. Multiplying 80 by 0.15 calculates 15% of the value.

13. What is the fraction in simplest form for $12.5\%$?

    $\frac{1}{8}$. Dividing 12.5 by 100 and reducing gives this simplest fraction.

14. What is the fraction in simplest form for $20\%$?

    $\frac{1}{5}$. Dividing 20 by 100 and simplifying yields this reduced fraction.

15. What is the percent form of $\frac{1}{2}$?

    $50\%$. Multiplying $\frac{1}{2}$ by 100 converts it to this percentage.

16. What is the percent form of $\frac{1}{4}$?

    $25\%$. Multiplying $\frac{1}{4}$ by 100 gives this percentage equivalent.

17. What is the rule to convert a fraction $\frac{a}{b}$ to a decimal?

    Compute $a \div b$. Dividing the numerator by the denominator directly yields the decimal representation of the fraction.

18. What is the decimal form of $\frac{7}{8}$?

    $0.875$. Dividing 7 by 8 results in this terminating decimal.

19. What is the fraction in simplest form for the decimal $0.2$?

    $\frac{1}{5}$. Expressing 0.2 as $\frac{2}{10}$ and simplifying results in this fraction.

20. What is the rule to convert a decimal $d$ to a percent?

    Compute $100d\%$. Multiplying the decimal by 100 converts it to an equivalent percentage value.

21. What is the percent form of $\frac{2}{5}$?

    $40\%$. Multiplying $\frac{2}{5}$ by 100 converts it to this percentage.

22. What is the percent form of the decimal $0.08$?

    $8\%$. Multiplying 0.08 by 100 expresses the decimal as this percentage.

23. What is the percent form of $\frac{3}{4}$?

    $75\%$. Multiplying $\frac{3}{4}$ by 100 results in this percentage.

24. What is the percent decrease from $80$ to $68$?

    $15\%$. The percent decrease formula is $\frac{80-68}{80} \times 100$, resulting in this value.

25. What is the decimal form of $\frac{1}{2}$?

    $0.5$. Dividing 1 by 2 results in this terminating decimal.

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