ISEE Middle 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 Middle 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 symbol makes the statement true: $\frac{7}{10}\ \Box\ \frac{2}{3}$?

Answer: $>$. Cross-multiplying gives $7 \cdot 3 = 21 > 2 \cdot 10 = 20$, so $7/10 > 2/3$.

Flashcard 2: Which number is greater: $\frac{3}{4}$ or $\frac{5}{7}$?

Answer: $\frac{3}{4}$. Cross-multiplying yields $3 \cdot 7 = 21 > 5 \cdot 4 = 20$, confirming $3/4 > 5/7$.

Flashcard 3: Which symbol makes the statement true: $-\frac{7}{5}\ \Box\ -1.35$?

Answer: $<$. Since $-7/5 = -1.4 < -1.35$, the more negative value is smaller.

Flashcard 4: Which symbol makes the statement true: $1.25\ \Box\ \frac{5}{4}$?

Answer: $=$. Both express the same value, as $5/4 = 1.25$.

Flashcard 5: Which number is greater: $1\frac{1}{3}$ or $\frac{4}{3}$?

Answer: $=$. Converting $1\frac{1}{3} = 4/3$ shows both are identical.

Flashcard 6: Which number is least: $0.2$, $\frac{1}{6}$, or $0.18$?

Answer: $\frac{1}{6}$. Comparing decimals: $1/6 \approx 0.1667 < 0.18 < 0.2$, making $1/6$ the smallest.

Flashcard 7: Which symbol makes the statement true: $0.333\ldots\ \Box\ \frac{1}{3}$?

Answer: $=$. The repeating decimal $0.333\ldots$ is the exact decimal form of $1/3$.

Flashcard 8: Which symbol makes the statement true: $\frac{11}{20}\ \Box\ 0.55$?

Answer: $=$. Dividing $11 \div 20 = 0.55$ confirms equivalence.

Flashcard 9: Which symbol makes the statement true: $\frac{5}{8}\ \Box\ 0.6$?

Answer: $>$. Converting $5/8 = 0.625$ reveals it exceeds $0.6$ by $0.025$.

Flashcard 10: What is the rule for comparing two positive fractions $\frac{a}{b}$ and $\frac{c}{d}$ using cross products?

Answer: Compare $ad$ and $bc$; if $ad>bc$ then $\frac{a}{b}>\frac{c}{d}$. Cross-multiplying compares $a/b$ and $c/d$ by checking if $a \cdot d > b \cdot c$, preserving the inequality for positive denominators.

Flashcard 11: What is the rule for comparing $\frac{a}{b}$ and $\frac{c}{d}$ when $b$ and $d$ are the same positive number?

Answer: Compare numerators: if $a>c$ then $\frac{a}{b}>\frac{c}{b}$. With identical positive denominators, the fraction with the larger numerator represents a greater value since it divides a bigger quantity by the same amount.

Flashcard 12: Which symbol makes the statement true: $\frac{3}{5}\ \Box\ 0.62$?

Answer: $<$. Converting $3/5 = 0.6$ shows it is less than $0.62$ by $0.02$.

Flashcard 13: Which number is greater: $-\frac{5}{6}$ or $-0.8$?

Answer: $-0.8$. Comparing $-5/6 \approx -0.833 < -0.8$, the less negative value is greater.

Flashcard 14: What is the rule for comparing any negative number to any positive number?

Answer: Any negative number is less than any positive number. Negative numbers lie to the left of positive numbers on the number line, making them smaller regardless of magnitude.

Flashcard 15: Which symbol makes the statement true: $0.7\ \Box\ \frac{2}{3}$?

Answer: $>$. Converting to decimals shows $0.7 > 0.666\ldots$, as $2/3 \approx 0.666\ldots$.

Flashcard 16: Which number is greater: $\frac{4}{9}$ or $0.45$?

Answer: $0.45$. Since $4/9 \approx 0.444 < 0.45$, the decimal is larger.

Flashcard 17: Which number is greater: $\frac{13}{25}$ or $0.5$?

Answer: $\frac{13}{25}$. Converting $13/25 = 0.52$ shows it exceeds $0.5$ by $0.02$.

Flashcard 18: Which symbol makes the statement true: $0.666\ldots\ \Box\ \frac{2}{3}$?

Answer: $=$. The repeating decimal $0.666\ldots$ equals $2/3$ precisely.

Flashcard 19: Which symbol makes the statement true: $\frac{3}{8}\ \Box\ 0.375$?

Answer: $=$. Dividing $3 \div 8 = 0.375$ verifies exact equality.

Flashcard 20: What is the rule for comparing $\frac{a}{b}$ and $\frac{a}{d}$ when the numerators match and denominators are positive?

Answer: Smaller denominator gives larger value: if $b<d$ then $\frac{a}{b}>\frac{a}{d}$. For positive denominators and identical numerators, a smaller denominator results in a larger fraction as it divides the numerator into fewer parts.

Flashcard 21: Which number is greater: $2.05$ or $2\frac{1}{20}$?

Answer: $=$. Converting $2\frac{1}{20} = 2.05$ confirms equivalence.

Flashcard 22: What is the rule for comparing negative numbers $-x$ and $-y$ where $x$ and $y$ are positive?

Answer: Reverse the comparison: if $x>y$ then $-x<-y$. Multiplying both sides of an inequality by -1 reverses the direction, so the negative of a larger positive is smaller.

Flashcard 23: Which symbol makes the statement true: $\frac{9}{16}\ \Box\ 0.56$?

Answer: $>$. Converting $9/16 = 0.5625$ exceeds $0.56$ slightly.

Flashcard 24: Which symbol makes the statement true: $-0.4\ \Box\ -\frac{3}{8}$?

Answer: $<$. On the number line, $-0.4$ is left of $-0.375$, confirming $-0.4 < -3/8$.

Flashcard 25: Which symbol makes the statement true: $-\frac{9}{4}\ \Box\ -2.2$?

Answer: $<$. Converting $-9/4 = -2.25$ places it left of $-2.2$ on the number line.