Ratio and Proportion - SSAT Upper Level: Quantitative
Card 1 of 25
What is the scale factor from $8$ to $20$ in a proportional relationship?
What is the scale factor from $8$ to $20$ in a proportional relationship?
Tap to reveal answer
$\frac{5}{2}$. Divide the new value by the original: $20 \div 8 = \frac{5}{2}$, representing the proportional increase.
$\frac{5}{2}$. Divide the new value by the original: $20 \div 8 = \frac{5}{2}$, representing the proportional increase.
← Didn't Know|Knew It →
What is the ratio of boys to girls if there are $12$ boys and $18$ girls (simplest form)?
What is the ratio of boys to girls if there are $12$ boys and $18$ girls (simplest form)?
Tap to reveal answer
$2:3$. Express as $12:18$ and divide both by $6$, their greatest common divisor, to simplify.
$2:3$. Express as $12:18$ and divide both by $6$, their greatest common divisor, to simplify.
← Didn't Know|Knew It →
What is the total number of parts in the ratio $3:5:2$?
What is the total number of parts in the ratio $3:5:2$?
Tap to reveal answer
$10$ parts. Add the individual ratios $3 + 5 + 2$ to find the total divisions of the whole.
$10$ parts. Add the individual ratios $3 + 5 + 2$ to find the total divisions of the whole.
← Didn't Know|Knew It →
What is each share if $48$ is divided in the ratio $1:3$ (give both parts)?
What is each share if $48$ is divided in the ratio $1:3$ (give both parts)?
Tap to reveal answer
$12$ and $36$. Total parts are $4$; divide $48$ by $4$ to get $12$ per part, then multiply by $1$ and $3$.
$12$ and $36$. Total parts are $4$; divide $48$ by $4$ to get $12$ per part, then multiply by $1$ and $3$.
← Didn't Know|Knew It →
What is the larger share if $70$ is divided in the ratio $3:4$?
What is the larger share if $70$ is divided in the ratio $3:4$?
Tap to reveal answer
$40$. Total parts are $7$; divide $70$ by $7$ to get $10$ per part, then multiply the larger ratio by $10$.
$40$. Total parts are $7$; divide $70$ by $7$ to get $10$ per part, then multiply the larger ratio by $10$.
← Didn't Know|Knew It →
What is the value of $x$ if $x$ is $\frac{2}{5}$ of $60$?
What is the value of $x$ if $x$ is $\frac{2}{5}$ of $60$?
Tap to reveal answer
$x=24$. Multiply $60$ by the fraction $\frac{2}{5}$ to find the proportional amount.
$x=24$. Multiply $60$ by the fraction $\frac{2}{5}$ to find the proportional amount.
← Didn't Know|Knew It →
What is $x$ if $x:36=5:9$?
What is $x$ if $x:36=5:9$?
Tap to reveal answer
$x=20$. Set up the proportion $\frac{x}{36} = \frac{5}{9}$ and solve by multiplying $36$ by $\frac{5}{9}$.
$x=20$. Set up the proportion $\frac{x}{36} = \frac{5}{9}$ and solve by multiplying $36$ by $\frac{5}{9}$.
← Didn't Know|Knew It →
What is $x$ if $\frac{x-2}{6}=\frac{3}{4}$?
What is $x$ if $\frac{x-2}{6}=\frac{3}{4}$?
Tap to reveal answer
$x=\frac{13}{2}$. Cross-multiply to get $4(x-2) = 18$, solve for $x-2$, then add $2$.
$x=\frac{13}{2}$. Cross-multiply to get $4(x-2) = 18$, solve for $x-2$, then add $2$.
← Didn't Know|Knew It →
What is the new length if a $12$ cm segment is scaled by a factor of $\frac{3}{2}$?
What is the new length if a $12$ cm segment is scaled by a factor of $\frac{3}{2}$?
Tap to reveal answer
$18$ cm. Multiply the original length by the scale factor: $12 \times \frac{3}{2}$.
$18$ cm. Multiply the original length by the scale factor: $12 \times \frac{3}{2}$.
← Didn't Know|Knew It →
What is the missing value $x$ if $4$ items cost $\$10$ and $x$ items cost $$25$?
What is the missing value $x$ if $4$ items cost $\$10$ and $x$ items cost $$25$?
Tap to reveal answer
$x=10$. Set up the proportion $\frac{4}{10} = \frac{x}{25}$ for items to cost, then cross-multiply to solve.
$x=10$. Set up the proportion $\frac{4}{10} = \frac{x}{25}$ for items to cost, then cross-multiply to solve.
← Didn't Know|Knew It →
What is the speed in mph if $150$ miles are driven in $3$ hours at a constant rate?
What is the speed in mph if $150$ miles are driven in $3$ hours at a constant rate?
Tap to reveal answer
$50$ mph. Use the speed formula: distance divided by time, $150 \div 3$.
$50$ mph. Use the speed formula: distance divided by time, $150 \div 3$.
← Didn't Know|Knew It →
What is the time in hours for $240$ miles at $60$ mph (constant speed)?
What is the time in hours for $240$ miles at $60$ mph (constant speed)?
Tap to reveal answer
$4$ hours. Use the time formula: distance divided by speed, $240 \div 60$.
$4$ hours. Use the time formula: distance divided by speed, $240 \div 60$.
← Didn't Know|Knew It →
What is the percent equivalent of the ratio $3:20$?
What is the percent equivalent of the ratio $3:20$?
Tap to reveal answer
$15%$. Convert the ratio to a fraction $\frac{3}{20}$, multiply by $100$ to get the percentage.
$15%$. Convert the ratio to a fraction $\frac{3}{20}$, multiply by $100$ to get the percentage.
← Didn't Know|Knew It →
Which option is proportional to $6:15$: $2:5$, $4:9$, or $9:20$?
Which option is proportional to $6:15$: $2:5$, $4:9$, or $9:20$?
Tap to reveal answer
$2:5$. Simplify $6:15$ to $2:5$; check which option matches this reduced form.
$2:5$. Simplify $6:15$ to $2:5$; check which option matches this reduced form.
← Didn't Know|Knew It →
What is the missing number $x$ if $\frac{7}{x}=\frac{21}{60}$?
What is the missing number $x$ if $\frac{7}{x}=\frac{21}{60}$?
Tap to reveal answer
$x=20$. Cross-multiply: $7 \times 60 = 21 \times x$, then divide by $21$ to solve.
$x=20$. Cross-multiply: $7 \times 60 = 21 \times x$, then divide by $21$ to solve.
← Didn't Know|Knew It →
What does it mean to say two ratios are proportional?
What does it mean to say two ratios are proportional?
Tap to reveal answer
They are equal: $\frac{a}{b}=\frac{c}{d}$ (with $b\neq^0$, $d\neq^0$). Two ratios are proportional when they express the same relationship, meaning their values are equal under the given conditions.
They are equal: $\frac{a}{b}=\frac{c}{d}$ (with $b\neq^0$, $d\neq^0$). Two ratios are proportional when they express the same relationship, meaning their values are equal under the given conditions.
← Didn't Know|Knew It →
What is $x$ if $\frac{x}{14}=\frac{9}{21}$?
What is $x$ if $\frac{x}{14}=\frac{9}{21}$?
Tap to reveal answer
$x=6$. Cross-multiply: $x \times 21 = 14 \times 9$, then divide by $21$ to isolate $x$.
$x=6$. Cross-multiply: $x \times 21 = 14 \times 9$, then divide by $21$ to isolate $x$.
← Didn't Know|Knew It →
What is $x$ if $\frac{4}{x}=\frac{10}{25}$?
What is $x$ if $\frac{4}{x}=\frac{10}{25}$?
Tap to reveal answer
$x=10$. Cross-multiply the proportions: $4 \times 25 = 10 \times x$, then divide by $10$.
$x=10$. Cross-multiply the proportions: $4 \times 25 = 10 \times x$, then divide by $10$.
← Didn't Know|Knew It →
What value of $x$ makes the ratios proportional: $7:9=x:45$?
What value of $x$ makes the ratios proportional: $7:9=x:45$?
Tap to reveal answer
$x=35$. Set up the proportion and cross-multiply: $7 \times 45 = 9 \times x$, then solve for $x$.
$x=35$. Set up the proportion and cross-multiply: $7 \times 45 = 9 \times x$, then solve for $x$.
← Didn't Know|Knew It →
What value of $x$ makes the ratios proportional: $\frac{3}{5}=\frac{x}{20}$?
What value of $x$ makes the ratios proportional: $\frac{3}{5}=\frac{x}{20}$?
Tap to reveal answer
$x=12$. Cross-multiply to solve the proportion: $3 \times 20 = 5 \times x$, then divide by $5$.
$x=12$. Cross-multiply to solve the proportion: $3 \times 20 = 5 \times x$, then divide by $5$.
← Didn't Know|Knew It →
What is the simplest form of the ratio $18:24$?
What is the simplest form of the ratio $18:24$?
Tap to reveal answer
$3:4$. Simplify by dividing both terms by their greatest common divisor, which is $6$.
$3:4$. Simplify by dividing both terms by their greatest common divisor, which is $6$.
← Didn't Know|Knew It →
What is the unit rate for a ratio written as $a:b$?
What is the unit rate for a ratio written as $a:b$?
Tap to reveal answer
The per-1 rate: $\frac{a}{b}$ (meaning $\frac{a}{b}$ per $1$). The unit rate converts the ratio to a fraction representing the amount per single unit.
The per-1 rate: $\frac{a}{b}$ (meaning $\frac{a}{b}$ per $1$). The unit rate converts the ratio to a fraction representing the amount per single unit.
← Didn't Know|Knew It →
What is the constant of proportionality $k$ if $y$ is proportional to $x$?
What is the constant of proportionality $k$ if $y$ is proportional to $x$?
Tap to reveal answer
$k=\frac{y}{x}$, so $y=kx$. When $y$ varies directly with $x$, their ratio is constant, defining the proportional relationship.
$k=\frac{y}{x}$, so $y=kx$. When $y$ varies directly with $x$, their ratio is constant, defining the proportional relationship.
← Didn't Know|Knew It →
What is the cross-multiplication rule for $\frac{a}{b}=\frac{c}{d}$?
What is the cross-multiplication rule for $\frac{a}{b}=\frac{c}{d}$?
Tap to reveal answer
$ad=bc$ (with $b\neq^0$, $d\neq^0$). For equal ratios, the product of the means equals the product of the extremes, ensuring proportionality.
$ad=bc$ (with $b\neq^0$, $d\neq^0$). For equal ratios, the product of the means equals the product of the extremes, ensuring proportionality.
← Didn't Know|Knew It →
What is the missing term $x$ in the proportion $\frac{5}{8}=\frac{15}{x}$?
What is the missing term $x$ in the proportion $\frac{5}{8}=\frac{15}{x}$?
Tap to reveal answer
$x=24$. Cross-multiply the proportion: $5 \times x = 8 \times 15$, then solve for $x$.
$x=24$. Cross-multiply the proportion: $5 \times x = 8 \times 15$, then solve for $x$.
← Didn't Know|Knew It →