SSAT Upper Level Quantitative Flashcards: Ordering Rational Numbers

What this deck covers

This deck focuses on Ordering Rational Numbers, 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: Which inequality is true: $\frac{2}{3}\ \square\ \frac{3}{5}$?

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

Flashcard 2: Which number is the greatest: $-\frac{7}{3}$, $-2.2$, $-\frac{9}{4}$, $-2$?

Answer: $-2$. Among negatives, $-2$ is the least negative, thus the greatest.

Flashcard 3: What rule compares two fractions with the same denominator, such as $\frac{a}{d}$ and $\frac{b}{d}$ where $d>0$?

Answer: Compare numerators: larger numerator gives larger fraction. When denominators are identical and positive, the fraction with the larger numerator is greater.

Flashcard 4: Which inequality is true: $\frac{5}{12}\ \square\ \frac{7}{12}$?

Answer: $\frac{5}{12} < \frac{7}{12}$. With the same denominator, the fraction with the smaller numerator is lesser.

Flashcard 5: What is the correct order from least to greatest: $\frac{1}{2}$, $0.49$, $\frac{3}{5}$?

Answer: $0.49 < \frac{1}{2} < \frac{3}{5}$. Converting to decimals: 0.49 < 0.5 < 0.6 confirms the order.

Flashcard 6: Which number is the least: $-2$, $\frac{1}{3}$, $-\frac{5}{2}$, $0$?

Answer: $-\frac{5}{2}$. $-\frac{5}{2} = -2.5$ is the most negative, hence the smallest among the options.

Flashcard 7: What method compares $\frac{a}{b}$ and $\frac{c}{d}$ efficiently when $b,d>0$?

Answer: Cross-multiply: compare $ad$ and $bc$. Cross-multiplication compares $ad$ and $bc$ to determine which fraction is larger without common denominators.

Flashcard 8: What rule determines which integer is greater when comparing a positive and a negative integer?

Answer: Any positive integer is greater than any negative integer. On the number line, positive integers are to the right of all negative integers, hence greater.

Flashcard 9: Which symbol makes the statement true: $5\ \square\ -12$?

Answer: $>$. Positive numbers are always greater than negative numbers on the number line.

Flashcard 10: Which is greater: $-0.4$ or $-0.35$?

Answer: $-0.35$. -0.35 is to the right of -0.4 on the number line, making it greater.

Flashcard 11: Which symbol makes the statement true: $| -9 |\ \square\ | -4 |$?

Answer: $>$. $|-9| = 9 > 4 = |-4|$, as absolute values are compared.

Flashcard 12: What is the definition of absolute value for an integer $a$?

Answer: $|a|$ is the distance from $0$ on the number line. Absolute value measures the non-negative distance of $a$ from zero on the number line.

Flashcard 13: What is the median of the set $\left\{-1,\ 2,\ -3,\ 4,\ 0\right\}$?

Answer: $0$. Ordering the set as $-3, -1, 0, 2, 4$ places 0 in the middle.

Flashcard 14: What is the correct order from least to greatest: $-\frac{2}{3}$, $-0.6$, $-\frac{5}{8}$?

Answer: $-\frac{2}{3} < -\frac{5}{8} < -0.6$. Converting to decimals: $-0.667 < -0.625 < -0.6$ shows increasing order.

Flashcard 15: What is the decimal value of $\frac{1}{8}$?

Answer: $0.125$. Dividing 1 by 8 results in 0.125.

Flashcard 16: What is the decimal value of $\frac{3}{4}$?

Answer: $0.75$. Dividing 3 by 4 yields 0.75.

Flashcard 17: What rule compares two fractions with the same numerator, such as $\frac{n}{a}$ and $\frac{n}{b}$ where $a,b>0$?

Answer: Smaller denominator gives larger fraction. For positive denominators and identical numerators, a smaller denominator yields a larger fraction.

Flashcard 18: Which statement is correct for decimals and fractions: $0.6\ \square\ \frac{3}{5}$?

Answer: $0.6 = \frac{3}{5}$. Dividing 3 by 5 gives exactly 0.6, making them equal.

Flashcard 19: What happens to an inequality when both sides are multiplied by a negative number?

Answer: The inequality sign reverses direction. To preserve the inequality's truth, the direction reverses when multiplying by a negative.

Flashcard 20: Which is greater: $0.07$ or $0.7$?

Answer: $0.7$. 0.7 represents 7 tenths, which is greater than 0.07 or 7 hundredths.

Flashcard 21: Which inequality is true: $\frac{3}{8}\ \square\ \frac{3}{10}$?

Answer: $\frac{3}{8} > \frac{3}{10}$. With equal numerators, the fraction with the smaller denominator is larger.

Flashcard 22: Which inequality is true: $-\frac{4}{7}\ \square\ -\frac{3}{7}$?

Answer: $-\frac{4}{7} < -\frac{3}{7}$. With the same denominator, the more negative fraction (larger absolute numerator) is smaller.

Flashcard 23: What rule determines which integer is greater when comparing two negative integers?

Answer: The integer with the smaller absolute value is greater. For negative integers, the one closer to zero, with smaller absolute value, is greater on the number line.

Flashcard 24: Which symbol makes the statement true: $-7\ \square\ -3$?

Answer: $<$. Since $-7$ is to the left of $-3$ on the number line, $-7$ is less than $-3$.