Comparing Rational Numbers - ISEE Upper Level: Quantitative Reasoning
Card 1 of 21
Which is greater: $ rac{9}{4}$ or $2.2$?
Which is greater: $ rac{9}{4}$ or $2.2$?
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$ rac{9}{4}$ is greater. Dividing $9$ by $4$ yields $2.25$, which is larger than $2.2$.
$ rac{9}{4}$ is greater. Dividing $9$ by $4$ yields $2.25$, which is larger than $2.2$.
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Which is greater: $0.ar{6}$ or $ rac{2}{3}$?
Which is greater: $0.ar{6}$ or $ rac{2}{3}$?
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They are equal. The repeating decimal $0.\bar{6} = 0.666\ldots$ equals $\frac{2}{3}$ exactly.
They are equal. The repeating decimal $0.\bar{6} = 0.666\ldots$ equals $\frac{2}{3}$ exactly.
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Which is greater: $1.2$ or $ rac{6}{5}$?
Which is greater: $1.2$ or $ rac{6}{5}$?
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They are equal. Dividing $6$ by $5$ gives exactly $1.2$, confirming equivalence.
They are equal. Dividing $6$ by $5$ gives exactly $1.2$, confirming equivalence.
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Which is greater: $0.125$ or $ rac{1}{8}$?
Which is greater: $0.125$ or $ rac{1}{8}$?
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They are equal. Dividing $1$ by $8$ yields exactly $0.125$, matching the decimal value.
They are equal. Dividing $1$ by $8$ yields exactly $0.125$, matching the decimal value.
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Which is greater: $ rac{11}{20}$ or $ rac{3}{5}$?
Which is greater: $ rac{11}{20}$ or $ rac{3}{5}$?
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$ rac{3}{5}$ is greater. Converting to decimals shows $\frac{11}{20} = 0.55$ and $\frac{3}{5} = 0.6$, confirming $0.6 > 0.55$.
$ rac{3}{5}$ is greater. Converting to decimals shows $\frac{11}{20} = 0.55$ and $\frac{3}{5} = 0.6$, confirming $0.6 > 0.55$.
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Which is greater: $ rac{5}{12}$ or $ rac{2}{5}$?
Which is greater: $ rac{5}{12}$ or $ rac{2}{5}$?
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$ rac{5}{12}$ is greater. Cross-multiplying gives $5 \times 5 = 25$ and $2 \times 12 = 24$, so $25 > 24$ implies $\frac{5}{12} > \frac{2}{5}$.
$ rac{5}{12}$ is greater. Cross-multiplying gives $5 \times 5 = 25$ and $2 \times 12 = 24$, so $25 > 24$ implies $\frac{5}{12} > \frac{2}{5}$.
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Which is greater: $- rac{2}{3}$ or $-0.7$?
Which is greater: $- rac{2}{3}$ or $-0.7$?
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$- rac{2}{3}$ is greater. On the number line, $-\frac{2}{3} \approx -0.666$ is to the right of $-0.7$, making it larger.
$- rac{2}{3}$ is greater. On the number line, $-\frac{2}{3} \approx -0.666$ is to the right of $-0.7$, making it larger.
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Which is greater: $0.6$ or $ rac{3}{5}$?
Which is greater: $0.6$ or $ rac{3}{5}$?
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They are equal. Converting $\frac{3}{5}$ to a decimal yields $0.6$, confirming both values are identical.
They are equal. Converting $\frac{3}{5}$ to a decimal yields $0.6$, confirming both values are identical.
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What must you do to an inequality when multiplying both sides by a negative number?
What must you do to an inequality when multiplying both sides by a negative number?
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Reverse the inequality sign. This preserves the inequality's direction, as negative multipliers reverse the order of numbers on the number line.
Reverse the inequality sign. This preserves the inequality's direction, as negative multipliers reverse the order of numbers on the number line.
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Which is greater: $ rac{1}{6}$ or $0.16$?
Which is greater: $ rac{1}{6}$ or $0.16$?
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$ rac{1}{6}$ is greater. Converting $\frac{1}{6}$ to approximately $0.1667$ shows it exceeds $0.16$.
$ rac{1}{6}$ is greater. Converting $\frac{1}{6}$ to approximately $0.1667$ shows it exceeds $0.16$.
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Which is greater: $0.2ar{7}$ or $ rac{5}{18}$?
Which is greater: $0.2ar{7}$ or $ rac{5}{18}$?
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They are equal. Dividing $5$ by $18$ yields $0.2\bar{7}$, matching the repeating decimal.
They are equal. Dividing $5$ by $18$ yields $0.2\bar{7}$, matching the repeating decimal.
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Which is greater: $ rac{17}{50}$ or $0.34$?
Which is greater: $ rac{17}{50}$ or $0.34$?
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They are equal. Dividing $17$ by $50$ yields exactly $0.34$, confirming equivalence.
They are equal. Dividing $17$ by $50$ yields exactly $0.34$, confirming equivalence.
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Which is greater: $ rac{13}{25}$ or $0.53$?
Which is greater: $ rac{13}{25}$ or $0.53$?
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$0.53$ is greater. Converting $\frac{13}{25}$ to $0.52$ shows $0.53 > 0.52$.
$0.53$ is greater. Converting $\frac{13}{25}$ to $0.52$ shows $0.53 > 0.52$.
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Which is greater: $0.58$ or $58 ext{%}$?
Which is greater: $0.58$ or $58 ext{%}$?
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They are equal. $58%$ converts to $0.58$, confirming both represent the same value.
They are equal. $58%$ converts to $0.58$, confirming both represent the same value.
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Which is greater: $-40 ext{%}$ or $- rac{3}{8}$?
Which is greater: $-40 ext{%}$ or $- rac{3}{8}$?
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$- rac{3}{8}$ is greater. Converting $-40%$ to $-0.4$ and $-\frac{3}{8} = -0.375$ shows $-0.375 > -0.4$.
$- rac{3}{8}$ is greater. Converting $-40%$ to $-0.4$ and $-\frac{3}{8} = -0.375$ shows $-0.375 > -0.4$.
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Which is greater: $125 ext{%}$ or $ rac{5}{4}$?
Which is greater: $125 ext{%}$ or $ rac{5}{4}$?
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They are equal. Converting $125%$ to $1.25$ matches $\frac{5}{4} = 1.25$.
They are equal. Converting $125%$ to $1.25$ matches $\frac{5}{4} = 1.25$.
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Which is greater: $0.ar{27}$ or $ rac{3}{11}$?
Which is greater: $0.ar{27}$ or $ rac{3}{11}$?
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They are equal. Dividing $3$ by $11$ yields $0.\bar{27}$, matching the repeating decimal.
They are equal. Dividing $3$ by $11$ yields $0.\bar{27}$, matching the repeating decimal.
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Which is greater: $0.ar{1}$ or $ rac{1}{9}$?
Which is greater: $0.ar{1}$ or $ rac{1}{9}$?
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They are equal. The repeating decimal $0.\bar{1} = 0.111\ldots$ equals $\frac{1}{9}$ exactly.
They are equal. The repeating decimal $0.\bar{1} = 0.111\ldots$ equals $\frac{1}{9}$ exactly.
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Which is greater: $0.ar{3}$ or $ rac{1}{3}$?
Which is greater: $0.ar{3}$ or $ rac{1}{3}$?
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They are equal. The repeating decimal $0.\bar{3} = 0.333\ldots$ equals $\frac{1}{3}$ exactly.
They are equal. The repeating decimal $0.\bar{3} = 0.333\ldots$ equals $\frac{1}{3}$ exactly.
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Which is greater: $0.04$ or $ rac{1}{20}$?
Which is greater: $0.04$ or $ rac{1}{20}$?
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$ rac{1}{20}$ is greater. Converting $\frac{1}{20}$ to $0.05$ shows it exceeds $0.04$.
$ rac{1}{20}$ is greater. Converting $\frac{1}{20}$ to $0.05$ shows it exceeds $0.04$.
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Which is greater: $- rac{5}{4}$ or $-1.1$?
Which is greater: $- rac{5}{4}$ or $-1.1$?
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$-1.1$ is greater. Converting $-\frac{5}{4} = -1.25$ shows $-1.1 > -1.25$ on the number line.
$-1.1$ is greater. Converting $-\frac{5}{4} = -1.25$ shows $-1.1 > -1.25$ on the number line.
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