Ordering Rational Numbers - SSAT Upper Level Quantitative

1. Which inequality is true: $\frac{2}{3}\ \square\ \frac{3}{5}$?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

   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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    $0.75$. Dividing 3 by 4 yields 0.75.

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

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

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

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

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

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

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

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

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

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

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

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

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

    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.

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

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

Study these flashcards