Ratios & Proportions - SAT Math

1. Express the ratio of 15 minutes to 1 hour as a fraction.

   $\frac{1}{4}$. Convert 1 hour to 60 minutes, then simplify $\frac{15}{60}$.

2. Solve the proportion: $\frac{3}{4} = \frac{x}{8}$.

   $x = 6$. Cross-multiply: $3 \times 8 = 4 \times x$, so $24 = 4x$.

3. Solve for $x$: $\frac{x}{12} = \frac{3}{4}$.

   $x = 9$. Cross multiply: $4x = 36$, so $x = 9$.

4. Convert the fraction $\frac{3}{4}$ to a ratio.

   $3:4$. A fraction $\frac{a}{b}$ is equivalent to the ratio $a:b$.

5. What is the definition of a proportion?

   A proportion is an equation stating two ratios are equal. Two ratios set equal to each other form an equation.

6. If $x : y = 5 : 2$, what is $\frac{y}{x}$?

   $\frac{2}{5}$. For $x:y = 5:2$, we have $\frac{y}{x} = \frac{2}{5}$.

7. Express 25% as a ratio.

   $1:4$. 25% means 25 out of 100, which simplifies to $1:4$.

8. Identify the extremes in the proportion $\frac{a}{b} = \frac{c}{d}$.

   Extremes are $a$ and $d$. The outer terms in a proportion are the extremes.

9. Simplify the ratio 50:100.

   $1:2$. Divide both terms by their GCD of 50.

10. Express 3 out of 8 as a ratio.

    $3:8$. Direct conversion from part-to-whole relationship.

11. What is the ratio of 5 to 20 in simplest form?

    $1:4$. Divide both terms by their GCD of 5.

12. What is the formula for converting a ratio to a percentage?

    Multiply the ratio by 100. Convert the ratio to decimal form, then multiply by 100.

13. Express the proportion $\frac{1}{2} = \frac{n}{6}$ in words.

    1 is to 2 as $n$ is to 6. Standard verbal form of expressing proportional relationships.

14. What is the value of $x$ if $2:3 = 4:x$?

    $x = 6$. Cross-multiply: $2x = 12$, so $x = 6$.

15. Solve for $x$: $\frac{4}{x} = \frac{8}{16}$.

    $x = 8$. Cross multiply: $4 \times 16 = 8x$, so $x = 8$.

16. What is the definition of a ratio?

    A comparison of two quantities by division. Shows how many times one quantity contains another.

17. What is the simplest form of the ratio 18:24?

    $3:4$. Divide both terms by their GCD of 6.

18. Find the missing value in the proportion $\frac{9}{x} = \frac{3}{5}$.

    $x = 15$. Cross multiply: $9 \times 5 = 3 \times x$, so $45 = 3x$.

19. If $x : y = 3 : 4$, what is $\frac{x}{y}$?

    $\frac{3}{4}$. Ratio notation directly converts to fraction form.

20. What is $x$ if $\frac{2}{x} = \frac{5}{10}$?

    $x = 4$. Cross multiply: $2 \times 10 = 5x$, so $x = 4$.

21. State the formula for a proportion involving $a$, $b$, $c$, and $d$.

    $\frac{a}{b} = \frac{c}{d}$. Two ratios set equal, forming an equation.

22. What is the reciprocal of a ratio $\frac{a}{b}$?

    Reciprocal is $\frac{b}{a}$. Flip the numerator and denominator to find the reciprocal.

23. State the Cross-Multiplication Rule for proportions.

    $a \times d = b \times c$ for $\frac{a}{b} = \frac{c}{d}$. Product of extremes equals product of means.

24. Identify the missing term: $\frac{3}{4} = \frac{x}{8}$.

    $x = 6$. Cross multiply: $3 \times 8 = 4 \times x$, so $24 = 4x$.

25. Find the value of $x$ if $\frac{x}{6} = \frac{3}{2}$.

    $x = 9$. Cross multiply: $2x = 18$, so $x = 9$.

26. Find the value of $x$ if $\frac{5}{x} = \frac{10}{15}$.

    $x = 7.5$. Cross multiply: $5 \times 15 = 10x$, so $x = 7.5$.

27. Convert the ratio $5:10$ to its simplest form.

    $1:2$. Divide both terms by their GCD of 5.

28. Express the ratio $\frac{2}{5}$ as a percentage.

    40%. Convert to decimal: $0.4 = 40\%$.

29. Determine if $\frac{8}{12}$ and $\frac{2}{3}$ are equivalent.

    Yes, they are equivalent. Both ratios simplify to $\frac{2}{3}$ when reduced.

30. Which ratio is equivalent to $\frac{2}{3}$? $\frac{4}{6}$ or $\frac{3}{5}$?

    $\frac{4}{6}$. Multiply numerator and denominator of $\frac{2}{3}$ by 2.

31. If $x$ is to $y$ as $3$ is to $4$, express this as a proportion.

    $\frac{x}{y} = \frac{3}{4}$. Direct translation of the verbal proportion statement.

32. Find the missing term: $7:x = 14:28$.

    $x = 14$. Cross-multiply: $7 \times 28 = 14x$, so $196 = 14x$.

33. Convert the ratio 7:28 to its simplest form.

    $1:4$. Divide both terms by their GCD of 7.

34. What is the value of $x$ if $5:x = 2:3$?

    $x = 7.5$. Cross multiply: $5 \times 3 = x \times 2$, so $15 = 2x$.

35. State the formula for a proportion.

    $\frac{a}{b} = \frac{c}{d}$, where $a, b, c, d$ are quantities. States that two ratios are equal to each other.

36. Identify the means in the proportion $\frac{a}{b} = \frac{c}{d}$.

    Means are $b$ and $c$. The middle terms in a proportion are the means.

37. What is the simplest form of the ratio 10:25?

    $2:5$. Divide both terms by their GCD of 5.

38. Simplify the ratio 16:64.

    $1:4$. Divide both terms by their GCD of 16.

39. Find the missing value: $\frac{7}{x} = \frac{14}{28}$.

    $x = 14$. Cross multiply: $7 \times 28 = 14x$, so $x = 14$.

40. What is the simplest form of the ratio 12:48?

    $1:4$. Divide both terms by their GCD of 12.

41. If $a : b = 7 : 3$, what is $\frac{b}{a}$?

    $\frac{3}{7}$. For $a:b = 7:3$, we have $\frac{b}{a} = \frac{3}{7}$.

42. What is the cross-multiplication step in $\frac{a}{b} = \frac{c}{d}$?

    $ad = bc$. Multiply the outer terms and inner terms.

43. Find the missing term: $\frac{6}{9} = \frac{x}{3}$.

    $x = 2$. Cross multiply: $6 \times 3 = 9x$, so $x = 2$.

44. Determine if $\frac{15}{25}$ and $\frac{3}{5}$ are equivalent.

    Yes, they are equivalent. Both ratios reduce to $\frac{3}{5}$ in simplest form.

45. Convert the ratio 9:36 to simplest form.

    $1:4$. Divide both terms by their GCD of 9.

46. What is the formula for finding the ratio of $a$ to $b$?

    Ratio = $\frac{a}{b}$. Expresses the relationship between two quantities.

47. What is the ratio of 8 to 12 in simplest form?

    $\frac{2}{3}$. Divide both numbers by their GCD of 4.

48. Identify the ratio form for $a:b = c:d$.

    $\frac{a}{b} = \frac{c}{d}$. Colon notation converts to fraction form.

49. Express the ratio 20:5 in simplest form.

    $4:1$. Divide both terms by their GCD of 5.

50. Solve for $x$: $\frac{3}{x} = \frac{5}{15}$.

    $x = 9$. Cross multiply: $3 \times 15 = 5x$, so $x = 9$.

51. If $\frac{a}{b} = \frac{3}{5}$, what is $\frac{b}{a}$?

    $\frac{5}{3}$. Reciprocal of $\frac{3}{5}$ is $\frac{5}{3}$.

52. If $a : b = 4 : 5$, what is the value of $\frac{a}{b}$?

    $\frac{4}{5}$. Ratio notation $a:b$ equals the fraction $\frac{a}{b}$.

53. Express the ratio 14:42 in simplest form.

    $1:3$. Divide both terms by their GCD of 14.

54. Convert the ratio 21:49 to simplest form.

    $3:7$. Divide both terms by their GCD of 7.

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