ISEE Lower Level Quantitative Reasoning Flashcards: Comparing Fractions

What this deck covers

This deck focuses on Comparing Fractions, giving you a quick way to review the definitions, rules, and examples that matter most for ISEE Lower 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 option is greatest:
frac{14}{27} or
frac{1}{2}?

Answer: $\frac{14}{27}$. Cross-multiplying yields $14 \times 2 = 28 > 1 \times 27 = 27$, so $\frac{14}{27}$ is greater.

Flashcard 2: Which option is greatest:
frac{12}{25} or
frac{5}{11}?

Answer: $\frac{12}{25}$. Cross-multiplying shows $12 \times 11 = 132 > 5 \times 25 = 125$, confirming $\frac{12}{25}$ is greater.

Flashcard 3: Which option is greatest:
frac{8}{9} or
frac{15}{16}?

Answer: $\frac{15}{16}$. Cross-multiplying results in $8 \times 16 = 128 < 15 \times 9 = 135$, confirming $\frac{15}{16}$ is greater.

Flashcard 4: Which option is greatest:
frac{3}{10} or
frac{7}{20}?

Answer: $\frac{7}{20}$. Converting to twentieths yields $\frac{3}{10} = \frac{6}{20} < \frac{7}{20}$, or cross-multiplying $3 \times 20 = 60 < 7 \times 10 = 70$.

Flashcard 5: Which option is greatest:
frac{2}{9} or
frac{1}{4}?

Answer: $\frac{1}{4}$. Cross-multiplying gives $2 \times 4 = 8 < 1 \times 9 = 9$, indicating $\frac{1}{4}$ is greater.

Flashcard 6: Which option is greatest:
frac{7}{15} or
frac{9}{20}?

Answer: $\frac{7}{15}$. Cross-multiplying results in $7 \times 20 = 140 > 9 \times 15 = 135$, indicating $\frac{7}{15}$ is greater.

Flashcard 7: Which option is greatest:
frac{10}{21} or
frac{1}{2}?

Answer: $\frac{1}{2}$. Cross-multiplying yields $10 \times 2 = 20 < 1 \times 21 = 21$, so $\frac{1}{2}$ is greater.

Flashcard 8: Which option is greatest:
frac{9}{14} or
frac{5}{7}?

Answer: $\frac{5}{7}$. Cross-multiplying gives $9 \times 7 = 63 < 5 \times 14 = 70$, confirming $\frac{5}{7}$ is greater.

Flashcard 9: Which option is greatest:
frac{5}{14} or
frac{3}{7}?

Answer: $\frac{3}{7}$. Converting to fourteenths gives $\frac{3}{7} = \frac{6}{14} > \frac{5}{14}$, or cross-multiplying $5 \times 7 = 35 < 3 \times 14 = 42$.

Flashcard 10: Which option is greatest:
frac{1}{2} or
frac{4}{9}?

Answer: $\frac{1}{2}$. Cross-multiplying yields $1 \times 9 = 9 > 4 \times 2 = 8$, so $\frac{1}{2}$ is greater.

Flashcard 11: Which option is greatest:
frac{6}{11} or
frac{7}{13}?

Answer: $\frac{6}{11}$. Cross-multiplying shows $6 \times 13 = 78 > 7 \times 11 = 77$, indicating $\frac{6}{11}$ is greater.

Flashcard 12: Which option is greatest:
frac{4}{9} or
frac{4}{11}?

Answer: $\frac{4}{9}$. With the same numerator, $\frac{4}{9}$ is greater because its smaller denominator divides the whole into fewer parts, making each part larger.

Flashcard 13: Which option is greatest:
frac{3}{7} or
frac{5}{7}?

Answer: $\frac{5}{7}$. With the same denominator, $\frac{5}{7}$ is greater because its numerator is larger, representing more sevenths.

Flashcard 14: Which option is greatest:
frac{7}{12} or
frac{5}{8}?

Answer: $\frac{5}{8}$. Cross-multiplying yields $7 \times 8 = 56 < 5 \times 12 = 60$, confirming $\frac{5}{8}$ is greater.

Flashcard 15: Which option is greatest:
frac{2}{3} or
frac{3}{5}?

Answer: $\frac{2}{3}$. Cross-multiplying gives $2 \times 5 = 10 > 3 \times 3 = 9$, so $\frac{2}{3}$ is greater.

Flashcard 16: What method compares
frac{a}{b} and
frac{c}{d} by comparing $ad$ and $bc$ (with $b,d>0$)?

Answer: Cross-multiply: compare $ad$ and $bc$. This method determines which fraction is larger by comparing the cross products $ad$ and $bc$, where if $ad > bc$ then $\frac{a}{b} > \frac{c}{d}$ for positive denominators.

Flashcard 17: What is the rule for comparing
frac{a}{b} and
frac{c}{b} when denominators are equal and $b>0$?

Answer: Greater numerator gives the greater fraction. When denominators are identical and positive, the fraction with the larger numerator represents a greater value since it takes a bigger portion of the same whole.

Flashcard 18: What is the rule for comparing
frac{a}{b} and
frac{a}{d} when numerators are equal and $b,d>0$?

Answer: Smaller denominator gives the greater fraction. When numerators are identical and denominators positive, the fraction with the smaller denominator is larger because the whole is divided into fewer parts.

Flashcard 19: Which option is greatest:
frac{5}{6} or
frac{6}{7}?

Answer: $\frac{6}{7}$. Cross-multiplying shows $5 \times 7 = 35 < 6 \times 6 = 36$, so $\frac{6}{7}$ is greater.

Flashcard 20: Which option is greatest:
frac{9}{10} or
frac{17}{20}?

Answer: $\frac{9}{10}$. Converting to twentieths gives $\frac{9}{10} = \frac{18}{20} > \frac{17}{20}$, or cross-multiplying $9 \times 20 = 180 > 17 \times 10 = 170$.

Flashcard 21: Which option is greatest:
frac{11}{15} or
frac{3}{4}?

Answer: $\frac{3}{4}$. Cross-multiplying results in $11 \times 4 = 44 < 3 \times 15 = 45$, indicating $\frac{3}{4}$ is greater.

Flashcard 22: Which option is greatest:
frac{13}{18} or
frac{7}{9}?

Answer: $\frac{7}{9}$. Cross-multiplying gives $13 \times 9 = 117 < 7 \times 18 = 126$, so $\frac{7}{9}$ is greater.

Flashcard 23: Which option is greatest:
frac{4}{5} or
frac{13}{15}?

Answer: $\frac{13}{15}$. Cross-multiplying shows $4 \times 15 = 60 < 13 \times 5 = 65$, so $\frac{13}{15}$ is greater.

Flashcard 24: Which option is greatest:
frac{5}{12} or
frac{3}{8}?

Answer: $\frac{5}{12}$. Cross-multiplying yields $5 \times 8 = 40 > 3 \times 12 = 36$, confirming $\frac{5}{12}$ is greater.