Ordering Rational Numbers - SSAT Upper Level: Quantitative
Card 1 of 24
What method compares $\frac{a}{b}$ and $\frac{c}{d}$ efficiently when $b,d>0$?
What method compares $\frac{a}{b}$ and $\frac{c}{d}$ efficiently when $b,d>0$?
Tap to reveal answer
Cross-multiply: compare $ad$ and $bc$. Cross-multiplication compares $ad$ and $bc$ to determine which fraction is larger without common denominators.
Cross-multiply: compare $ad$ and $bc$. Cross-multiplication compares $ad$ and $bc$ to determine which fraction is larger without common denominators.
← Didn't Know|Knew It →
Which inequality is true: $\frac{2}{3}\ \square\ \frac{3}{5}$?
Which inequality is true: $\frac{2}{3}\ \square\ \frac{3}{5}$?
Tap to reveal answer
$\frac{2}{3} > \frac{3}{5}$. Cross-multiplying yields $2 \times 5 = 10 > 3 \times 3 = 9$, so $\frac{2}{3}$ is greater.
$\frac{2}{3} > \frac{3}{5}$. Cross-multiplying yields $2 \times 5 = 10 > 3 \times 3 = 9$, so $\frac{2}{3}$ is greater.
← Didn't Know|Knew It →
Which inequality is true: $-\frac{4}{7}\ \square\ -\frac{3}{7}$?
Which inequality is true: $-\frac{4}{7}\ \square\ -\frac{3}{7}$?
Tap to reveal answer
$-\frac{4}{7} < -\frac{3}{7}$. With the same denominator, the more negative fraction (larger absolute numerator) is smaller.
$-\frac{4}{7} < -\frac{3}{7}$. With the same denominator, the more negative fraction (larger absolute numerator) is smaller.
← Didn't Know|Knew It →
What happens to an inequality when both sides are multiplied by a negative number?
What happens to an inequality when both sides are multiplied by a negative number?
Tap to reveal answer
The inequality sign reverses direction. To preserve the inequality's truth, the direction reverses when multiplying by a negative.
The inequality sign reverses direction. To preserve the inequality's truth, the direction reverses when multiplying by a negative.
← Didn't Know|Knew It →
Which is greater: $-0.4$ or $-0.35$?
Which is greater: $-0.4$ or $-0.35$?
Tap to reveal answer
$-0.35$. -0.35 is to the right of -0.4 on the number line, making it greater.
$-0.35$. -0.35 is to the right of -0.4 on the number line, making it greater.
← Didn't Know|Knew It →
What is the decimal value of $\frac{1}{8}$?
What is the decimal value of $\frac{1}{8}$?
Tap to reveal answer
$0.125$. Dividing 1 by 8 results in 0.125.
$0.125$. Dividing 1 by 8 results in 0.125.
← Didn't Know|Knew It →
What is the correct order from least to greatest: $\frac{1}{2}$, $0.49$, $\frac{3}{5}$?
What is the correct order from least to greatest: $\frac{1}{2}$, $0.49$, $\frac{3}{5}$?
Tap to reveal answer
$0.49 < \frac{1}{2} < \frac{3}{5}$. Converting to decimals: 0.49 < 0.5 < 0.6 confirms the order.
$0.49 < \frac{1}{2} < \frac{3}{5}$. Converting to decimals: 0.49 < 0.5 < 0.6 confirms the order.
← Didn't Know|Knew It →
What is the correct order from least to greatest: $-\frac{2}{3}$, $-0.6$, $-\frac{5}{8}$?
What is the correct order from least to greatest: $-\frac{2}{3}$, $-0.6$, $-\frac{5}{8}$?
Tap to reveal answer
$-\frac{2}{3} < -\frac{5}{8} < -0.6$. Converting to decimals: $-0.667 < -0.625 < -0.6$ shows increasing order.
$-\frac{2}{3} < -\frac{5}{8} < -0.6$. Converting to decimals: $-0.667 < -0.625 < -0.6$ shows increasing order.
← Didn't Know|Knew It →
Which symbol makes the statement true: $| -9 |\ \square\ | -4 |$?
Which symbol makes the statement true: $| -9 |\ \square\ | -4 |$?
Tap to reveal answer
$>$. $|-9| = 9 > 4 = |-4|$, as absolute values are compared.
$>$. $|-9| = 9 > 4 = |-4|$, as absolute values are compared.
← Didn't Know|Knew It →
What is the median of the set $\left\{-1,\ 2,\ -3,\ 4,\ 0\right\}$?
What is the median of the set $\left\{-1,\ 2,\ -3,\ 4,\ 0\right\}$?
Tap to reveal answer
$0$. Ordering the set as $-3, -1, 0, 2, 4$ places 0 in the middle.
$0$. Ordering the set as $-3, -1, 0, 2, 4$ places 0 in the middle.
← Didn't Know|Knew It →
Which symbol makes the statement true: $5\ \square\ -12$?
Which symbol makes the statement true: $5\ \square\ -12$?
Tap to reveal answer
$>$. Positive numbers are always greater than negative numbers on the number line.
$>$. Positive numbers are always greater than negative numbers on the number line.
← Didn't Know|Knew It →
Which symbol makes the statement true: $-7\ \square\ -3$?
Which symbol makes the statement true: $-7\ \square\ -3$?
Tap to reveal answer
$<$. Since $-7$ is to the left of $-3$ on the number line, $-7$ is less than $-3$.
$<$. Since $-7$ is to the left of $-3$ on the number line, $-7$ is less than $-3$.
← Didn't Know|Knew It →
What is the definition of absolute value for an integer $a$?
What is the definition of absolute value for an integer $a$?
Tap to reveal 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.
$|a|$ is the distance from $0$ on the number line. Absolute value measures the non-negative distance of $a$ from zero on the number line.
← Didn't Know|Knew It →
What rule determines which integer is greater when comparing two negative integers?
What rule determines which integer is greater when comparing two negative integers?
Tap to reveal 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.
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.
← Didn't Know|Knew It →
Which statement is correct for decimals and fractions: $0.6\ \square\ \frac{3}{5}$?
Which statement is correct for decimals and fractions: $0.6\ \square\ \frac{3}{5}$?
Tap to reveal answer
$0.6 = \frac{3}{5}$. Dividing 3 by 5 gives exactly 0.6, making them equal.
$0.6 = \frac{3}{5}$. Dividing 3 by 5 gives exactly 0.6, making them equal.
← Didn't Know|Knew It →
Which is greater: $0.07$ or $0.7$?
Which is greater: $0.07$ or $0.7$?
Tap to reveal answer
$0.7$. 0.7 represents 7 tenths, which is greater than 0.07 or 7 hundredths.
$0.7$. 0.7 represents 7 tenths, which is greater than 0.07 or 7 hundredths.
← Didn't Know|Knew It →
What rule determines which integer is greater when comparing a positive and a negative integer?
What rule determines which integer is greater when comparing a positive and a negative integer?
Tap to reveal 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.
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.
← Didn't Know|Knew It →
What is the decimal value of $\frac{3}{4}$?
What is the decimal value of $\frac{3}{4}$?
Tap to reveal answer
$0.75$. Dividing 3 by 4 yields 0.75.
$0.75$. Dividing 3 by 4 yields 0.75.
← Didn't Know|Knew It →
What rule compares two fractions with the same numerator, such as $\frac{n}{a}$ and $\frac{n}{b}$ where $a,b>0$?
What rule compares two fractions with the same numerator, such as $\frac{n}{a}$ and $\frac{n}{b}$ where $a,b>0$?
Tap to reveal answer
Smaller denominator gives larger fraction. For positive denominators and identical numerators, a smaller denominator yields a larger fraction.
Smaller denominator gives larger fraction. For positive denominators and identical numerators, a smaller denominator yields a larger fraction.
← Didn't Know|Knew It →
What rule compares two fractions with the same denominator, such as $\frac{a}{d}$ and $\frac{b}{d}$ where $d>0$?
What rule compares two fractions with the same denominator, such as $\frac{a}{d}$ and $\frac{b}{d}$ where $d>0$?
Tap to reveal answer
Compare numerators: larger numerator gives larger fraction. When denominators are identical and positive, the fraction with the larger numerator is greater.
Compare numerators: larger numerator gives larger fraction. When denominators are identical and positive, the fraction with the larger numerator is greater.
← Didn't Know|Knew It →
Which inequality is true: $\frac{3}{8}\ \square\ \frac{3}{10}$?
Which inequality is true: $\frac{3}{8}\ \square\ \frac{3}{10}$?
Tap to reveal answer
$\frac{3}{8} > \frac{3}{10}$. With equal numerators, the fraction with the smaller denominator is larger.
$\frac{3}{8} > \frac{3}{10}$. With equal numerators, the fraction with the smaller denominator is larger.
← Didn't Know|Knew It →
Which inequality is true: $\frac{5}{12}\ \square\ \frac{7}{12}$?
Which inequality is true: $\frac{5}{12}\ \square\ \frac{7}{12}$?
Tap to reveal answer
$\frac{5}{12} < \frac{7}{12}$. With the same denominator, the fraction with the smaller numerator is lesser.
$\frac{5}{12} < \frac{7}{12}$. With the same denominator, the fraction with the smaller numerator is lesser.
← Didn't Know|Knew It →
Which number is the least: $-2$, $\frac{1}{3}$, $-\frac{5}{2}$, $0$?
Which number is the least: $-2$, $\frac{1}{3}$, $-\frac{5}{2}$, $0$?
Tap to reveal answer
$-\frac{5}{2}$. $-\frac{5}{2} = -2.5$ is the most negative, hence the smallest among the options.
$-\frac{5}{2}$. $-\frac{5}{2} = -2.5$ is the most negative, hence the smallest among the options.
← Didn't Know|Knew It →
Which number is the greatest: $-\frac{7}{3}$, $-2.2$, $-\frac{9}{4}$, $-2$?
Which number is the greatest: $-\frac{7}{3}$, $-2.2$, $-\frac{9}{4}$, $-2$?
Tap to reveal answer
$-2$. Among negatives, $-2$ is the least negative, thus the greatest.
$-2$. Among negatives, $-2$ is the least negative, thus the greatest.
← Didn't Know|Knew It →