SSAT Upper Level Quantitative Flashcards: Comparing Rational Forms

What this deck covers

This deck focuses on Comparing Rational Forms, 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 quickest method to compare \frac{a}{b} and \frac{c}{d} for positive $b,d$?

Answer: Compare $ad$ and $bc$ (cross-multiply). Cross-multiplication determines the relationship without converting to decimals or finding common denominators, as $ad > bc$ implies $\frac{a}{b} > \frac{c}{d}$.

Flashcard 2: Which is greater: \frac{-7}{8} or -0.9?

Answer: $-\frac{7}{8}$. Approximating $-\frac{7}{8} = -0.875$, which has a smaller magnitude than $-0.9$, placing it higher on the number line.

Flashcard 3: Which is greater: \frac{5}{6} or 83\%?

Answer: $\frac{5}{6}$. Converting $83\%$ to $0.83$ and $\frac{5}{6} \approx 0.8333$ shows the fraction exceeds it slightly.

Flashcard 4: Which is greater: 0.\overline{6} or \frac{2}{3}?

Answer: They are equal. Converting $0.\overline{6}$ using the formula for repeating decimals yields exactly $\frac{2}{3}$.

Flashcard 5: Which is smaller: \frac{1}{4} or 25\%?

Answer: They are equal. Converting $25\%$ to $\frac{25}{100} = \frac{1}{4}$ shows both are identical.

Flashcard 6: What is the rule to convert a terminating decimal to a fraction?

Answer: Write over $10^n$ and simplify. The number of decimal places determines the power of $10$ in the denominator, allowing simplification to the equivalent fraction.

Flashcard 7: What is the comparison result: \frac{2}{5} \square 40\%?

Answer: $=$. Both $\frac{2}{5} = 0.4$ and $40\% = 0.4$ represent the same value.

Flashcard 8: Which is greater: \frac{3}{4} or 0.7?

Answer: $\frac{3}{4}$. Converting the fraction to $0.75$ shows it exceeds $0.7$ on the number line.

Flashcard 9: Which is greater: -\frac{3}{5} or -0.55?

Answer: $-0.55$. Since $|-0.55| < |-0.6|$, $-0.55$ is positioned to the right of $-\frac{3}{5} \approx -0.6$ on the number line.

Flashcard 10: Which is less: -\frac{5}{6} or -0.8?

Answer: $-\frac{5}{6}$. Approximating $-\frac{5}{6} \approx -0.833$, which is less than $-0.8$ since it is further left on the number line.

Flashcard 11: Which is less: \frac{9}{20} or 0.46?

Answer: $\frac{9}{20}$. Converting $\frac{9}{20} = 0.45$ reveals it is smaller than $0.46$ by $0.01$.

Flashcard 12: What is the sign rule when comparing two negative rational numbers?

Answer: The number with the smaller absolute value is greater. For negative numbers, the one closer to zero (smaller magnitude) is larger on the number line.

Flashcard 13: What is 0.\overline{3} written as a fraction in simplest form?

Answer: $\frac{1}{3}$. The repeating decimal $0.\overline{3}$ represents an infinite series summing to $\frac{1}{3}$.

Flashcard 14: Which is greater: \frac{4}{9} or 0.44\overline{4}?

Answer: They are equal. Dividing $4$ by $9$ produces the repeating decimal $0.\overline{4}$, matching the given form.

Flashcard 15: Which is greater: 0.375 or \frac{3}{10}?

Answer: $0.375$. Expressing $\frac{3}{10} = 0.3$ shows $0.375$ is larger due to the higher tenths and hundredths digits.

Flashcard 16: Which is greater: \frac{11}{12} or 0.91?

Answer: $\frac{11}{12}$. Converting yields $\frac{11}{12} \approx 0.9167 > 0.91$, due to the higher hundredths place.

Flashcard 17: Which is greater: \frac{13}{15} or 0.86\overline{6}?

Answer: They are equal. Dividing $13$ by $15$ yields $0.8\overline{6}$, exactly matching the given decimal.

Flashcard 18: Which is greater: 0.125 or \frac{1}{9}?

Answer: $0.125$. Comparing decimals, $0.125 > 0.\overline{1} \approx 0.111$, as the former has a higher tenths digit.

Flashcard 19: Identify the larger number: \frac{5}{8} or 0.62.

Answer: $\frac{5}{8}$. Dividing $5$ by $8$ yields $0.625$, which is greater than $0.62$.

Flashcard 20: Which is greater: 37.5\% or \frac{3}{8}?

Answer: They are equal. Expressing $37.5\%$ as $\frac{37.5}{100} = \frac{3}{8}$ confirms their equivalence.

Flashcard 21: What fraction is equal to 0.\overline{12} in simplest form?

Answer: $\frac{4}{33}$. Applying the conversion method for two-digit repeating decimals results in the simplified fraction $\frac{4}{33}$.