6th Grade Math Flashcards: Create And Use Equivalent Ratio Tables

What this deck covers

This deck focuses on Create And Use Equivalent Ratio Tables, giving you a quick way to review the definitions, rules, and examples that matter most for 6th Grade Math.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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