SSAT Upper Level Quantitative Flashcards: Ratio And Proportion

What this deck covers

This deck focuses on Ratio And Proportion, giving you a quick way to review the definitions, rules, and examples that matter most for SSAT Upper Level Quantitative.

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: What is the value of $x$ if $x$ is $\frac{2}{5}$ of $60$?

Answer: $x=24$. Multiply $60$ by the fraction $\frac{2}{5}$ to find the proportional amount.

Flashcard 2: What is $x$ if $\frac{4}{x}=\frac{10}{25}$?

Answer: $x=10$. Cross-multiply the proportions: $4 \times 25 = 10 \times x$, then divide by $10$.

Flashcard 3: What is $x$ if $\frac{x}{14}=\frac{9}{21}$?

Answer: $x=6$. Cross-multiply: $x \times 21 = 14 \times 9$, then divide by $21$ to isolate $x$.

Flashcard 4: What is the missing value $x$ if $4$ items cost $10 and $x$ items cost $25?

Answer: $x=10$. Set up the proportion $\frac{4}{10} = \frac{x}{25}$ for items to cost, then cross-multiply to solve.

Flashcard 5: What is the cross-multiplication rule for $\frac{a}{b}=\frac{c}{d}$?

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.

Flashcard 6: What is the scale factor from $8$ to $20$ in a proportional relationship?

Answer: $\frac{5}{2}$. Divide the new value by the original: $20 \div 8 = \frac{5}{2}$, representing the proportional increase.

Flashcard 7: What is each share if $48$ is divided in the ratio $1:3$ (give both parts)?

Answer: $12$ and $36$. Total parts are $4$; divide $48$ by $4$ to get $12$ per part, then multiply by $1$ and $3$.

Flashcard 8: What is the simplest form of the ratio $18:24$?

Answer: $3:4$. Simplify by dividing both terms by their greatest common divisor, which is $6$.

Flashcard 9: What is $x$ if $\frac{x-2}{6}=\frac{3}{4}$?

Answer: $x=\frac{13}{2}$. Cross-multiply to get $4(x-2) = 18$, solve for $x-2$, then add $2$.

Flashcard 10: What does it mean to say two ratios are proportional?

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.

Flashcard 11: What is the unit rate for a ratio written as $a:b$?

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.

Flashcard 12: What is the total number of parts in the ratio $3:5:2$?

Answer: $10$ parts. Add the individual ratios $3 + 5 + 2$ to find the total divisions of the whole.

Flashcard 13: What is the time in hours for $240$ miles at $60$ mph (constant speed)?

Answer: $4$ hours. Use the time formula: distance divided by speed, $240 \div 60$.

Flashcard 14: What is the missing number $x$ if $\frac{7}{x}=\frac{21}{60}$?

Answer: $x=20$. Cross-multiply: $7 \times 60 = 21 \times x$, then divide by $21$ to solve.

Flashcard 15: What is the constant of proportionality $k$ if $y$ is proportional to $x$?

Answer: $k=\frac{y}{x}$, so $y=kx$. When $y$ varies directly with $x$, their ratio is constant, defining the proportional relationship.

Flashcard 16: What is the larger share if $70$ is divided in the ratio $3:4$?

Answer: $40$. Total parts are $7$; divide $70$ by $7$ to get $10$ per part, then multiply the larger ratio by $10$.

Flashcard 17: What is the speed in mph if $150$ miles are driven in $3$ hours at a constant rate?

Answer: $50$ mph. Use the speed formula: distance divided by time, $150 \div 3$.

Flashcard 18: What is the new length if a $12$ cm segment is scaled by a factor of $\frac{3}{2}$?

Answer: $18$ cm. Multiply the original length by the scale factor: $12 \times \frac{3}{2}$.

Flashcard 19: What is the percent equivalent of the ratio $3:20$?

Answer: $15\%$. Convert the ratio to a fraction $\frac{3}{20}$, multiply by $100$ to get the percentage.

Flashcard 20: What value of $x$ makes the ratios proportional: $7:9=x:45$?

Answer: $x=35$. Set up the proportion and cross-multiply: $7 \times 45 = 9 \times x$, then solve for $x$.

Flashcard 21: Which option is proportional to $6:15$: $2:5$, $4:9$, or $9:20$?

Answer: $2:5$. Simplify $6:15$ to $2:5$; check which option matches this reduced form.

Flashcard 22: What is the missing term $x$ in the proportion $\frac{5}{8}=\frac{15}{x}$?

Answer: $x=24$. Cross-multiply the proportion: $5 \times x = 8 \times 15$, then solve for $x$.

Flashcard 23: What is $x$ if $x:36=5:9$?

Answer: $x=20$. Set up the proportion $\frac{x}{36} = \frac{5}{9}$ and solve by multiplying $36$ by $\frac{5}{9}$.

Flashcard 24: What value of $x$ makes the ratios proportional: $\frac{3}{5}=\frac{x}{20}$?

Answer: $x=12$. Cross-multiply to solve the proportion: $3 \times 20 = 5 \times x$, then divide by $5$.

Flashcard 25: What is the ratio of boys to girls if there are $12$ boys and $18$ girls (simplest form)?

Answer: $2:3$. Express as $12:18$ and divide both by $6$, their greatest common divisor, to simplify.