Create and Use Equivalent Ratio Tables - 6th Grade Math
Card 1 of 25
What is the missing ordered pair in an equivalent ratio table if $(3,9)$ and $(6,18)$ are included and $x=9$?
What is the missing ordered pair in an equivalent ratio table if $(3,9)$ and $(6,18)$ are included and $x=9$?
Tap to reveal answer
$(9,27)$. The ratio is $1:3$, so when $x=9$, $y=9 \times 3 = 27$.
$(9,27)$. The ratio is $1:3$, so when $x=9$, $y=9 \times 3 = 27$.
← Didn't Know|Knew It →
Identify the ordered pair that is NOT equivalent to the ratio $4:6$ (choices: $(2,3)$, $(8,12)$, $(6,10)$).
Identify the ordered pair that is NOT equivalent to the ratio $4:6$ (choices: $(2,3)$, $(8,12)$, $(6,10)$).
Tap to reveal answer
$(6,10)$. $4:6$ simplifies to $2:3$, but $6:10$ simplifies to $3:5$.
$(6,10)$. $4:6$ simplifies to $2:3$, but $6:10$ simplifies to $3:5$.
← Didn't Know|Knew It →
What does it mean for two ratios to be equivalent?
What does it mean for two ratios to be equivalent?
Tap to reveal answer
They compare quantities with the same multiplicative relationship. Same ratio means same multiplication factor between corresponding terms.
They compare quantities with the same multiplicative relationship. Same ratio means same multiplication factor between corresponding terms.
← Didn't Know|Knew It →
What operation makes an equivalent ratio from $a:b$ when both terms share a factor $k$?
What operation makes an equivalent ratio from $a:b$ when both terms share a factor $k$?
Tap to reveal answer
Divide both terms by $k$: $\frac{a}{k}:\frac{b}{k}$. Dividing both parts by the same number preserves the ratio.
Divide both terms by $k$: $\frac{a}{k}:\frac{b}{k}$. Dividing both parts by the same number preserves the ratio.
← Didn't Know|Knew It →
What is the missing value in the equivalent ratio table: $2:5 = 6:?$
What is the missing value in the equivalent ratio table: $2:5 = 6:?$
Tap to reveal answer
$15$. Since $6 = 2 \times 3$, multiply $5$ by $3$ to get $15$.
$15$. Since $6 = 2 \times 3$, multiply $5$ by $3$ to get $15$.
← Didn't Know|Knew It →
What is the missing value in the equivalent ratio table: $3:4 = ?:12$
What is the missing value in the equivalent ratio table: $3:4 = ?:12$
Tap to reveal answer
$9$. Since $12 = 4 \times 3$, multiply $3$ by $3$ to get $9$.
$9$. Since $12 = 4 \times 3$, multiply $3$ by $3$ to get $9$.
← Didn't Know|Knew It →
What is the missing value in the equivalent ratio table: $7:2 = 28:?$
What is the missing value in the equivalent ratio table: $7:2 = 28:?$
Tap to reveal answer
$8$. Since $28 = 7 \times 4$, multiply $2$ by $4$ to get $8$.
$8$. Since $28 = 7 \times 4$, multiply $2$ by $4$ to get $8$.
← Didn't Know|Knew It →
What is the missing value in the equivalent ratio table: $5:9 = ?:27$
What is the missing value in the equivalent ratio table: $5:9 = ?:27$
Tap to reveal answer
$15$. Since $27 = 9 \times 3$, multiply $5$ by $3$ to get $15$.
$15$. Since $27 = 9 \times 3$, multiply $5$ by $3$ to get $15$.
← Didn't Know|Knew It →
What is the missing value in the equivalent ratio table: $4:11 = 12:?$
What is the missing value in the equivalent ratio table: $4:11 = 12:?$
Tap to reveal answer
$33$. Since $12 = 4 \times 3$, multiply $11$ by $3$ to get $33$.
$33$. Since $12 = 4 \times 3$, multiply $11$ by $3$ to get $33$.
← Didn't Know|Knew It →
What operation makes an equivalent ratio from $a:b$ using a whole number $k$?
What operation makes an equivalent ratio from $a:b$ using a whole number $k$?
Tap to reveal answer
Multiply both terms by $k$: $a \cdot k:b \cdot k$. Multiplying both parts by the same number preserves the ratio.
Multiply both terms by $k$: $a \cdot k:b \cdot k$. Multiplying both parts by the same number preserves the ratio.
← Didn't Know|Knew It →
What is the missing value in the equivalent ratio table: $6:7 = ?:35$
What is the missing value in the equivalent ratio table: $6:7 = ?:35$
Tap to reveal answer
$30$. Since $35 = 7 \times 5$, multiply $6$ by $5$ to get $30$.
$30$. Since $35 = 7 \times 5$, multiply $6$ by $5$ to get $30$.
← Didn't Know|Knew It →
What operation can simplify a ratio $a:b$ when both terms share a factor $k$?
What operation can simplify a ratio $a:b$ when both terms share a factor $k$?
Tap to reveal answer
Divide both terms by $k$: $ \frac{a}{k} : \frac{b}{k} $. Dividing both parts by their common factor simplifies the ratio.
Divide both terms by $k$: $ \frac{a}{k} : \frac{b}{k} $. Dividing both parts by their common factor simplifies the ratio.
← Didn't Know|Knew It →
What is the missing value $y$ if the ratio is $3:5$ and $x=12$ corresponds to $3$?
What is the missing value $y$ if the ratio is $3:5$ and $x=12$ corresponds to $3$?
Tap to reveal answer
$y=20$. Since $12÷3=4$, multiply $5×4=20$ to maintain the ratio.
$y=20$. Since $12÷3=4$, multiply $5×4=20$ to maintain the ratio.
← Didn't Know|Knew It →
What is the constant of proportionality $k$ for the ratio table where $y$ depends on $x$?
What is the constant of proportionality $k$ for the ratio table where $y$ depends on $x$?
Tap to reveal answer
$k=\frac{y}{x}$ (constant for all pairs). The ratio of $y$ to $x$ stays constant in proportional relationships.
$k=\frac{y}{x}$ (constant for all pairs). The ratio of $y$ to $x$ stays constant in proportional relationships.
← Didn't Know|Knew It →
What operation creates an equivalent ratio from $a:b$ using a whole number $k$?
What operation creates an equivalent ratio from $a:b$ using a whole number $k$?
Tap to reveal answer
Multiply both terms by $k$: $a\cdot k:b\cdot k$. Multiplying both parts by the same number preserves the ratio.
Multiply both terms by $k$: $a\cdot k:b\cdot k$. Multiplying both parts by the same number preserves the ratio.
← Didn't Know|Knew It →
What does it mean for two ratios $a:b$ and $c:d$ to be equivalent?
What does it mean for two ratios $a:b$ and $c:d$ to be equivalent?
Tap to reveal answer
$\frac{a}{b}=\frac{c}{d}$ (same multiplicative relationship). Cross products are equal when ratios are equivalent.
$\frac{a}{b}=\frac{c}{d}$ (same multiplicative relationship). Cross products are equal when ratios are equivalent.
← Didn't Know|Knew It →
Which table shows equivalent ratios to $3:5$: A) $(3,5),(6,10)$ or B) $(3,5),(6,11)$?
Which table shows equivalent ratios to $3:5$: A) $(3,5),(6,10)$ or B) $(3,5),(6,11)$?
Tap to reveal answer
A) $(3,5)$ and $(6,10)$. Table A maintains $\frac{3}{5}$ ratio; B changes it to $\frac{6}{11}$.
A) $(3,5)$ and $(6,10)$. Table A maintains $\frac{3}{5}$ ratio; B changes it to $\frac{6}{11}$.
← Didn't Know|Knew It →
Find the missing value in the table if $(x,y)$ follow $2:7$ and $x=10$.
Find the missing value in the table if $(x,y)$ follow $2:7$ and $x=10$.
Tap to reveal answer
$y=35$. Since $10÷2=5$, multiply $7×5=35$ to maintain the ratio.
$y=35$. Since $10÷2=5$, multiply $7×5=35$ to maintain the ratio.
← Didn't Know|Knew It →
Which point fits the ratio $2:5$: $(4,10)$ or $(4,12)$?
Which point fits the ratio $2:5$: $(4,10)$ or $(4,12)$?
Tap to reveal answer
$(4,10)$. Check if $\frac{4}{10}=\frac{2}{5}$; yes, so $(4,10)$ fits.
$(4,10)$. Check if $\frac{4}{10}=\frac{2}{5}$; yes, so $(4,10)$ fits.
← Didn't Know|Knew It →
Identify the point to plot when the ratio table row is $x=6$ and $y=9$.
Identify the point to plot when the ratio table row is $x=6$ and $y=9$.
Tap to reveal answer
$(6,9)$. Plot the $x$-coordinate first, then the $y$-coordinate.
$(6,9)$. Plot the $x$-coordinate first, then the $y$-coordinate.
← Didn't Know|Knew It →
What is $y$ if $y=\frac{3}{2}x$ and $x=10$ in a ratio table?
What is $y$ if $y=\frac{3}{2}x$ and $x=10$ in a ratio table?
Tap to reveal answer
$y=15$. Substitute $x=10$ into $y=\frac{3}{2}×10=15$.
$y=15$. Substitute $x=10$ into $y=\frac{3}{2}×10=15$.
← Didn't Know|Knew It →
What is the constant of proportionality $k$ if a table follows $y=kx$ and includes $(4,14)$?
What is the constant of proportionality $k$ if a table follows $y=kx$ and includes $(4,14)$?
Tap to reveal answer
$k=\frac{14}{4}=\frac{7}{2}$. Divide $y$ by $x$ to find the constant ratio.
$k=\frac{14}{4}=\frac{7}{2}$. Divide $y$ by $x$ to find the constant ratio.
← Didn't Know|Knew It →
Which ratio is larger: $3:4$ or $5:8$? (Compare using $\frac{a}{b}$.)
Which ratio is larger: $3:4$ or $5:8$? (Compare using $\frac{a}{b}$.)
Tap to reveal answer
$3:4$. Compare $\frac{3}{4}=0.75$ and $\frac{5}{8}=0.625$; $0.75>0.625$.
$3:4$. Compare $\frac{3}{4}=0.75$ and $\frac{5}{8}=0.625$; $0.75>0.625$.
← Didn't Know|Knew It →
What is the unit rate (per $1$) for the ratio $15$ dollars for $5$ notebooks?
What is the unit rate (per $1$) for the ratio $15$ dollars for $5$ notebooks?
Tap to reveal answer
$3$ dollars per $1$ notebook. Divide $15$ dollars by $5$ notebooks to find cost per notebook.
$3$ dollars per $1$ notebook. Divide $15$ dollars by $5$ notebooks to find cost per notebook.
← Didn't Know|Knew It →
What is the unit rate (per $1$) for the ratio $12$ miles in $3$ hours?
What is the unit rate (per $1$) for the ratio $12$ miles in $3$ hours?
Tap to reveal answer
$4$ miles per $1$ hour. Divide $12$ miles by $3$ hours to find miles per hour.
$4$ miles per $1$ hour. Divide $12$ miles by $3$ hours to find miles per hour.
← Didn't Know|Knew It →