ISEE Upper Level Quantitative Reasoning Flashcards: Ratios And Comparisons

What this deck covers

This deck focuses on Ratios And Comparisons, giving you a quick way to review the definitions, rules, and examples that matter most for ISEE Upper Level Quantitative Reasoning.

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 missing number $x$ in $\frac{7}{x}=\frac{21}{30}$?

Answer: $10$. Cross-multiply to get $7 \times 30 = 21x$, then solve for $x$.

Flashcard 2: What is the scale factor from $2:5$ to $6:15$?

Answer: $3$. Each term in the first ratio is multiplied by 3 to obtain the second ratio.

Flashcard 3: What does the ratio $a:b$ mean in fraction form?

Answer: $\frac{a}{b}$. The ratio $a:b$ expresses the comparison of $a$ to $b$ as the fraction $\frac{a}{b}$.

Flashcard 4: What is the unit rate (miles per hour) for $150$ miles in $3$ hours?

Answer: $50\ \text{mph}$. Divide total miles by total hours to find the rate per hour.

Flashcard 5: What is the ratio of $3$ feet to $18$ inches in simplest form?

Answer: $2:1$. Convert 3 feet to 36 inches, then simplify 36:18 by dividing both by 18.

Flashcard 6: If the ratio of cats to dogs is $3:5$ and there are $40$ dogs, how many cats are there?

Answer: $24$. Dogs represent 5 parts equaling 40, so 1 part is 8, and cats are 3 parts.

Flashcard 7: What is the missing number $x$ in the proportion $5:8=x:40$?

Answer: $25$. Solve by cross-multiplying: $5 \times 40 = 8x$, so $x = \frac{200}{8}$.

Flashcard 8: What is the ratio of $\frac{3}{4}$ to $\frac{5}{8}$ in simplest form?

Answer: $6:5$. Divide $\frac{3}{4}$ by $\frac{5}{8}$ to get $\frac{6}{5}$, or find a common denominator to compare.

Flashcard 9: What is the ratio of shaded to total if $9$ of $12$ squares are shaded, simplified?

Answer: $3:4$. Shaded is 9 and total is 12, simplify by dividing both by 3.

Flashcard 10: Which is larger: $\frac{3}{5}$ or $\frac{5}{9}$?

Answer: $\frac{3}{5}$. Compare by cross-multiplying: $3 \times 9 = 27$ and $5 \times 5 = 25$, since 27 > 25.

Flashcard 11: What is the unit price (dollars per pound) for $9 for $3$ lb?

Answer: \3\ \text{per lb}$. Divide total cost by total pounds to find the price per pound.

Flashcard 12: What is the cross-multiplication condition for $\frac{a}{b}=\frac{c}{d}$?

Answer: $ad=bc$. Cross-multiplication checks equality by verifying if the products of numerator and opposite denominator are equal.

Flashcard 13: What is the missing number $x$ in the proportion $\frac{3}{4}=\frac{x}{20}$?

Answer: $15$. Solve by cross-multiplying or multiplying both sides by 20 and then by $\frac{3}{4}$.

Flashcard 14: Find and correct the ratio error: simplifying $18:24$ as $9:10$.

Answer: Correct: $18:24=3:4$. Simplify 18:24 by dividing both by 6, not incorrectly by 2 to get 9:12 or other errors.

Flashcard 15: If the ratio is $2:3$ and the first quantity is $14$, what is the second quantity?

Answer: $21$. The first quantity 14 is 7 times 2, so multiply 3 by 7 to find the second.

Flashcard 16: A recipe uses flour to sugar in a $5:2$ ratio. If flour is $20$ cups, how much sugar is needed?

Answer: $8\ \text{cups}$. Flour is 5 parts equaling 20 cups, so 1 part is 4 cups, and sugar is 2 parts.

Flashcard 17: If the ratio is $4:7$ and the total is $33$, what is the first quantity?

Answer: $12$. Total parts are 11, divide 33 by 11 to get 3 per part, then multiply by 4.

Flashcard 18: What is the ratio of girls to boys if there are $12$ boys and $8$ girls, simplified?

Answer: $2:3$. Girls are 8 and boys are 12, so simplify 8:12 by dividing both by 4.

Flashcard 19: What is the ratio of boys to total students if there are $12$ boys and $8$ girls?

Answer: $3:5$. Total students are 20, so simplify 12:20 by dividing both by 4.

Flashcard 20: What is the ratio of $0.6$ to $0.15$ in simplest form?

Answer: $4:1$. Divide 0.6 by 0.15 to get 4, or multiply both by 100 and simplify 60:15 by dividing by 15.

Flashcard 21: Identify the equivalent ratio to $4:9$ among $8:18$, $6:16$, and $12:20$.

Answer: $8:18$. Check equivalents: 8:18 simplifies to 4:9 by dividing by 2, while others do not.

Flashcard 22: What is the ratio of $45$ minutes to $2$ hours in simplest form?

Answer: $3:8$. Convert 2 hours to 120 minutes, then simplify 45:120 by dividing both by 15.

Flashcard 23: What is the ratio of $12$ to $18$ in simplest form?

Answer: $2:3$. Simplify by dividing both 12 and 18 by their greatest common divisor of 6.