ISEE Upper Level Quantitative Reasoning Flashcards: Comparing Rational Numbers

What this deck covers

This deck focuses on Comparing Rational Numbers, 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: Which is greater: 0.2ar{7} or rac{5}{18}?

Answer: They are equal. Dividing $5$ by $18$ yields $0.2\bar{7}$, matching the repeating decimal.

Flashcard 2: Which is greater: 0.ar{6} or rac{2}{3}?

Answer: They are equal. The repeating decimal $0.\bar{6} = 0.666\ldots$ equals $\frac{2}{3}$ exactly.

Flashcard 3: Which is greater: $1.2$ or rac{6}{5}?

Answer: They are equal. Dividing $6$ by $5$ gives exactly $1.2$, confirming equivalence.

Flashcard 4: Which is greater: 0.ar{1} or rac{1}{9}?

Answer: They are equal. The repeating decimal $0.\bar{1} = 0.111\ldots$ equals $\frac{1}{9}$ exactly.

Flashcard 5: Which is greater: 0.ar{3} or rac{1}{3}?

Answer: They are equal. The repeating decimal $0.\bar{3} = 0.333\ldots$ equals $\frac{1}{3}$ exactly.

Flashcard 6: Which is greater: rac{17}{50} or $0.34$?

Answer: They are equal. Dividing $17$ by $50$ yields exactly $0.34$, confirming equivalence.

Flashcard 7: Which is greater: $0.58$ or 58 ext{%}?

Answer: They are equal. $58\%$ converts to $0.58$, confirming both represent the same value.

Flashcard 8: Which is greater: $0.04$ or rac{1}{20}?

Answer: rac{1}{20} is greater. Converting $\frac{1}{20}$ to $0.05$ shows it exceeds $0.04$.

Flashcard 9: Which is greater: 0.ar{27} or rac{3}{11}?

Answer: They are equal. Dividing $3$ by $11$ yields $0.\bar{27}$, matching the repeating decimal.

Flashcard 10: Which is greater: $0.125$ or rac{1}{8}?

Answer: They are equal. Dividing $1$ by $8$ yields exactly $0.125$, matching the decimal value.

Flashcard 11: Which is greater: 125 ext{%} or rac{5}{4}?

Answer: They are equal. Converting $125\%$ to $1.25$ matches $\frac{5}{4} = 1.25$.

Flashcard 12: Which is greater: -rac{5}{4} or $-1.1$?

Answer: $-1.1$ is greater. Converting $-\frac{5}{4} = -1.25$ shows $-1.1 > -1.25$ on the number line.

Flashcard 13: Which is greater: rac{5}{12} or rac{2}{5}?

Answer: rac{5}{12} is greater. Cross-multiplying gives $5 \times 5 = 25$ and $2 \times 12 = 24$, so $25 > 24$ implies $\frac{5}{12} > \frac{2}{5}$.

Flashcard 14: What must you do to an inequality when multiplying both sides by a negative number?

Answer: Reverse the inequality sign. This preserves the inequality's direction, as negative multipliers reverse the order of numbers on the number line.

Flashcard 15: Which is greater: -40 ext{%} or -rac{3}{8}?

Answer: -rac{3}{8} is greater. Converting $-40\%$ to $-0.4$ and $-\frac{3}{8} = -0.375$ shows $-0.375 > -0.4$.

Flashcard 16: Which is greater: rac{9}{4} or $2.2$?

Answer: rac{9}{4} is greater. Dividing $9$ by $4$ yields $2.25$, which is larger than $2.2$.

Flashcard 17: Which is greater: $0.6$ or rac{3}{5}?

Answer: They are equal. Converting $\frac{3}{5}$ to a decimal yields $0.6$, confirming both values are identical.

Flashcard 18: Which is greater: -rac{2}{3} or $-0.7$?

Answer: -rac{2}{3} is greater. On the number line, $-\frac{2}{3} \approx -0.666$ is to the right of $-0.7$, making it larger.

Flashcard 19: Which is greater: rac{11}{20} or rac{3}{5}?

Answer: rac{3}{5} is greater. Converting to decimals shows $\frac{11}{20} = 0.55$ and $\frac{3}{5} = 0.6$, confirming $0.6 > 0.55$.

Flashcard 20: Which is greater: rac{1}{6} or $0.16$?

Answer: rac{1}{6} is greater. Converting $\frac{1}{6}$ to approximately $0.1667$ shows it exceeds $0.16$.

Flashcard 21: Which is greater: rac{13}{25} or $0.53$?

Answer: $0.53$ is greater. Converting $\frac{13}{25}$ to $0.52$ shows $0.53 > 0.52$.