Create and Use Equivalent Ratio Tables - 6th Grade Math

1. Find the next row in an equivalent ratio table if one row is $(4,10)$ and you double both terms.

   $(8,20)$. Multiply both values by 2 to maintain the ratio.

2. What is the missing value in the equivalent ratio table: $5:9 = ?:27$

   $15$. Since $27 = 9 \times 3$, multiply $5$ by $3$ to get $15$.

3. Find the missing value: if $4:7$ is equivalent to $x:21$, what is $x$?

   $x=12$. Cross multiply: $4 \times 21 = 7 \times x$, so $84 = 7x$.

4. Use tables to compare: which is larger, $\frac{2}{9}$ or $\frac{1}{4}$?

   $\frac{1}{4}$ is larger. Compare: $\frac{1}{4} = 0.25 > \frac{2}{9} \approx 0.222$.

5. What is $x$ if the table shows a constant ratio $\frac{y}{x}=5$ and $y=35$?

   $x=7$. Divide: $x = 35 \div 5 = 7$.

6. What is the missing value in this equivalent ratio table: $6:9=\square:27$?

   $18$. Since $27÷9=3$, multiply $6×3=18$ to get the equivalent ratio.

7. Which point matches the equivalent ratio to $2:3$ when multiplied by $4$?

   $(8,12)$. Multiply both terms of $2:3$ by $4$ to get $8:12$.

8. Use tables to compare: which is larger, $\frac{3}{4}$ or $\frac{5}{7}$?

   $\frac{3}{4}$ is larger. Compare: $\frac{3}{4} = 0.75 > \frac{5}{7} \approx 0.714$.

9. What is the missing value in the equivalent ratio table: $4:11 = 12:?$

   $33$. Since $12 = 4 \times 3$, multiply $11$ by $3$ to get $33$.

10. What does it mean for two ratios to be equivalent?

    They compare quantities with the same multiplicative relationship. Same ratio means same multiplication factor between corresponding terms.

11. Which ratio is larger: $3:8$ or $2:5$? (Compare using unit rates $\frac{y}{x}$.)

    $2:5$. $\frac{2}{5} = 0.4 > \frac{3}{8} = 0.375$, so $2:5$ is larger.

12. What is the missing value in the equivalent ratio table: $9:5 = 45:?$

    $25$. Since $45 = 9 \times 5$, multiply $5$ by $5$ to get $25$.

13. Find the missing $x$ in the table with constant ratio $\frac{y}{x}=\frac{3}{4}$ when $y=21$.

    $x=28$. Solve: $21 = x \times \frac{3}{4}$, so $x = 21 \times \frac{4}{3} = 28$.

14. Identify whether the table is proportional: $(2,6)$, $(3,9)$, $(5,15)$.

    Yes; $\frac{y}{x}=3$ for all rows. Each y-value equals 3 times its x-value.

15. What is the constant of proportionality $k$ if a table follows $y=kx$ and includes $(4,14)$?

    $k=\frac{14}{4}=\frac{7}{2}$. Divide $y$ by $x$ to find the constant ratio.

16. What does it mean for two ratios $a:b$ and $c:d$ to be equivalent?

    $\frac{a}{b}=\frac{c}{d}$ (same multiplicative relationship). Cross products are equal when ratios are equivalent.

17. What is the missing value $x$ if the ratio is $4:7$ and $y=21$ corresponds to $7$?

    $x=12$. Since $21÷7=3$, multiply $4×3=12$ to maintain the ratio.

18. What is the unit rate (per $1$) for the ratio $12$ miles in $3$ hours?

    $4$ miles per $1$ hour. Divide $12$ miles by $3$ hours to find miles per hour.

19. What is the missing value in this equivalent ratio table: $5:8=20:\square$?

    $32$. Since $20÷5=4$, multiply $8×4=32$ to get the equivalent ratio.

20. What point should you plot for the ratio $3:7$ if $x$ is first and $y$ is second?

    $(3,7)$. Plot the first term as x-coordinate and second as y-coordinate.

21. Identify the ordered pair you plot for a ratio table with columns $x$ and $y$.

    Plot each row as the ordered pair $(x,y)$. First column gives x-coordinate, second gives y-coordinate.

22. Identify the ordered pair that is NOT equivalent to the ratio $4:6$ (choices: $(2,3)$, $(8,12)$, $(6,10)$).

    $(6,10)$. $4:6$ simplifies to $2:3$, but $6:10$ simplifies to $3:5$.

23. What is the missing value in the equivalent ratio table: $3:4 = ?:12$

    $9$. Since $12 = 4 \times 3$, multiply $3$ by $3$ to get $9$.

24. Which ordered pair matches the ratio $5:2$ when the first term is $15$?

    $(15,6)$. Scale by 3: $5 \times 3 = 15$ and $2 \times 3 = 6$.

25. What is the missing value in the equivalent ratio table: $8:3 = ?:15$

    $40$. Since $15 = 3 \times 5$, multiply $8$ by $5$ to get $40$.

26. Which point fits the ratio $2:5$: $(4,10)$ or $(4,12)$?

    $(4,10)$. Check if $\frac{4}{10}=\frac{2}{5}$; yes, so $(4,10)$ fits.

27. Complete the equivalent ratio table for $6:1$: when the second term is $4$, what is the first?

    $24$. Scale factor is $4 \div 1 = 4$, so $6 \times 4 = 24$.

28. What operation creates an equivalent ratio from $a:b$ using a whole number $k$?

    Multiply both terms by $k$: $a\cdot k:b\cdot k$. Multiplying both parts by the same number preserves the ratio.

29. What is the missing value in the equivalent ratio table: $2:5 = 6:?$

    $15$. Since $6 = 2 \times 3$, multiply $5$ by $3$ to get $15$.

30. Which point lies on the same proportional relationship as $(6,9)$: $(4,6)$ or $(4,8)$?

    $(4,6)$. Both simplify to ratio $2:3$ (check: $\frac{6}{9}=\frac{4}{6}=\frac{2}{3}$).

31. Find the missing value in the table if $(x,y)$ follow $2:7$ and $x=10$.

    $y=35$. Since $10÷2=5$, multiply $7×5=35$ to maintain the ratio.

32. What is the missing ordered pair in an equivalent ratio table if $(3,9)$ and $(6,18)$ are included and $x=9$?

    $(9,27)$. The ratio is $1:3$, so when $x=9$, $y=9 \times 3 = 27$.

33. Which ratio is larger: $3:4$ or $5:8$? (Compare using $\frac{a}{b}$.)

    $3:4$. Compare $\frac{3}{4}=0.75$ and $\frac{5}{8}=0.625$; $0.75>0.625$.

34. Identify the point to plot for the ratio row $x=12$ and $y=18$.

    $(12,18)$. The x-value comes first, y-value second in the ordered pair.

35. Which table shows equivalent ratios to $3:5$: A) $(3,5),(6,10)$ or B) $(3,5),(6,11)$?

    A) $(3,5)$ and $(6,10)$. Table A maintains $\frac{3}{5}$ ratio; B changes it to $\frac{6}{11}$.

36. What is $y$ if the table shows a constant ratio $\frac{y}{x}=3$ and $x=8$?

    $y=24$. Multiply: $y = 3 \times 8 = 24$.

37. What operation makes an equivalent ratio from $a:b$ when both terms share a factor $k$?

    Divide both terms by $k$: $\frac{a}{k}:\frac{b}{k}$. Dividing both parts by the same number preserves the ratio.

38. Find the missing $y$ in the table with constant ratio $\frac{y}{x}=\frac{2}{5}$ when $x=15$.

    $y=6$. Calculate: $y = 15 \times \frac{2}{5} = 6$.

39. Identify the point to plot when the ratio table row is $x=6$ and $y=9$.

    $(6,9)$. Plot the $x$-coordinate first, then the $y$-coordinate.

40. Identify whether the table is proportional: $(2,6)$, $(3,10)$, $(4,12)$.

    No; $\frac{y}{x}$ is not constant. Ratios vary: $\frac{6}{2}=3$, $\frac{10}{3}\approx 3.33$, $\frac{12}{4}=3$.

41. Complete the equivalent ratio table for $2:3$: when the first term is $10$, what is the second?

    $15$. Scale factor is $10 \div 2 = 5$, so $3 \times 5 = 15$.

42. What is the missing value in the equivalent ratio table: $6:7 = ?:35$

    $30$. Since $35 = 7 \times 5$, multiply $6$ by $5$ to get $30$.

43. What is the missing value in the equivalent ratio table: $7:2 = 28:?$

    $8$. Since $28 = 7 \times 4$, multiply $2$ by $4$ to get $8$.

44. What is the constant of proportionality $k$ for the ratio table where $y$ depends on $x$?

    $k=\frac{y}{x}$ (constant for all pairs). The ratio of $y$ to $x$ stays constant in proportional relationships.

45. What is the missing value in this equivalent ratio table: $2:3=\square:12$?

    $8$. Since $12÷3=4$, multiply $2×4=8$ to get the equivalent ratio.

46. What is the constant of proportionality $k$ if a ratio table follows $y=kx$?

    $k=\frac{y}{x}$ for any row with $x\neq 0$. The constant ratio between y and x values.

47. What operation makes an equivalent ratio from $a:b$ using a whole number $k$?

    Multiply both terms by $k$: $a \cdot k:b \cdot k$. Multiplying both parts by the same number preserves the ratio.

48. Identify the ordered pair you plot from a ratio table with columns $x$ and $y$.

    Plot each row as $(x,y)$. Each ratio table row represents a coordinate point.

49. What operation can simplify a ratio $a:b$ when both terms share a factor $k$?

    Divide both terms by $k$: $\frac{a}{k} : \frac{b}{k}$. Dividing both parts by their common factor simplifies the ratio.

50. Find the missing value: if $3:5$ is equivalent to $9:x$, what is $x$?

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

51. What is the missing value $y$ if the ratio is $3:5$ and $x=12$ corresponds to $3$?

    $y=20$. Since $12÷3=4$, multiply $5×4=20$ to maintain the ratio.

52. What is the unit rate (per $1$) for the ratio $15$ dollars for $5$ notebooks?

    $3$ dollars per $1$ notebook. Divide $15$ dollars by $5$ notebooks to find cost per notebook.

53. What is $y$ if $y=\frac{3}{2}x$ and $x=10$ in a ratio table?

    $y=15$. Substitute $x=10$ into $y=\frac{3}{2}×10=15$.

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