Comparing Rational Forms - SSAT Upper Level: Quantitative
Card 1 of 21
Which is greater: $\frac{11}{12}$ or $0.91$?
Which is greater: $\frac{11}{12}$ or $0.91$?
Tap to reveal answer
$\frac{11}{12}$. Converting yields $\frac{11}{12} \approx 0.9167 > 0.91$, due to the higher hundredths place.
$\frac{11}{12}$. Converting yields $\frac{11}{12} \approx 0.9167 > 0.91$, due to the higher hundredths place.
← Didn't Know|Knew It →
What is the comparison result: $\frac{2}{5}$ $\square$ $40%$?
What is the comparison result: $\frac{2}{5}$ $\square$ $40%$?
Tap to reveal answer
$=$. Both $\frac{2}{5} = 0.4$ and $40% = 0.4$ represent the same value.
$=$. Both $\frac{2}{5} = 0.4$ and $40% = 0.4$ represent the same value.
← Didn't Know|Knew It →
Which is greater: $\frac{5}{6}$ or $83%$?
Which is greater: $\frac{5}{6}$ or $83%$?
Tap to reveal answer
$\frac{5}{6}$. Converting $83%$ to $0.83$ and $\frac{5}{6} \approx 0.8333$ shows the fraction exceeds it slightly.
$\frac{5}{6}$. Converting $83%$ to $0.83$ and $\frac{5}{6} \approx 0.8333$ shows the fraction exceeds it slightly.
← Didn't Know|Knew It →
Which is greater: $37.5%$ or $\frac{3}{8}$?
Which is greater: $37.5%$ or $\frac{3}{8}$?
Tap to reveal answer
They are equal. Expressing $37.5%$ as $\frac{37.5}{100} = \frac{3}{8}$ confirms their equivalence.
They are equal. Expressing $37.5%$ as $\frac{37.5}{100} = \frac{3}{8}$ confirms their equivalence.
← Didn't Know|Knew It →
Which is smaller: $\frac{1}{4}$ or $25%$?
Which is smaller: $\frac{1}{4}$ or $25%$?
Tap to reveal answer
They are equal. Converting $25%$ to $\frac{25}{100} = \frac{1}{4}$ shows both are identical.
They are equal. Converting $25%$ to $\frac{25}{100} = \frac{1}{4}$ shows both are identical.
← Didn't Know|Knew It →
Which is greater: $\frac{13}{15}$ or $0.86\overline{6}$?
Which is greater: $\frac{13}{15}$ or $0.86\overline{6}$?
Tap to reveal answer
They are equal. Dividing $13$ by $15$ yields $0.8\overline{6}$, exactly matching the given decimal.
They are equal. Dividing $13$ by $15$ yields $0.8\overline{6}$, exactly matching the given decimal.
← Didn't Know|Knew It →
Which is greater: $\frac{-7}{8}$ or $-0.9$?
Which is greater: $\frac{-7}{8}$ or $-0.9$?
Tap to reveal answer
$-\frac{7}{8}$. Approximating $-\frac{7}{8} = -0.875$, which has a smaller magnitude than $-0.9$, placing it higher on the number line.
$-\frac{7}{8}$. Approximating $-\frac{7}{8} = -0.875$, which has a smaller magnitude than $-0.9$, placing it higher on the number line.
← Didn't Know|Knew It →
Which is less: $\frac{9}{20}$ or $0.46$?
Which is less: $\frac{9}{20}$ or $0.46$?
Tap to reveal answer
$\frac{9}{20}$. Converting $\frac{9}{20} = 0.45$ reveals it is smaller than $0.46$ by $0.01$.
$\frac{9}{20}$. Converting $\frac{9}{20} = 0.45$ reveals it is smaller than $0.46$ by $0.01$.
← Didn't Know|Knew It →
Which is greater: $0.375$ or $\frac{3}{10}$?
Which is greater: $0.375$ or $\frac{3}{10}$?
Tap to reveal answer
$0.375$. Expressing $\frac{3}{10} = 0.3$ shows $0.375$ is larger due to the higher tenths and hundredths digits.
$0.375$. Expressing $\frac{3}{10} = 0.3$ shows $0.375$ is larger due to the higher tenths and hundredths digits.
← Didn't Know|Knew It →
What is the rule to convert a terminating decimal to a fraction?
What is the rule to convert a terminating decimal to a fraction?
Tap to reveal answer
Write over $10^n$ and simplify. The number of decimal places determines the power of $10$ in the denominator, allowing simplification to the equivalent fraction.
Write over $10^n$ and simplify. The number of decimal places determines the power of $10$ in the denominator, allowing simplification to the equivalent fraction.
← Didn't Know|Knew It →
Which is greater: $\frac{4}{9}$ or $0.44\overline{4}$?
Which is greater: $\frac{4}{9}$ or $0.44\overline{4}$?
Tap to reveal answer
They are equal. Dividing $4$ by $9$ produces the repeating decimal $0.\overline{4}$, matching the given form.
They are equal. Dividing $4$ by $9$ produces the repeating decimal $0.\overline{4}$, matching the given form.
← Didn't Know|Knew It →
What fraction is equal to $0.\overline{12}$ in simplest form?
What fraction is equal to $0.\overline{12}$ in simplest form?
Tap to reveal answer
$\frac{4}{33}$. Applying the conversion method for two-digit repeating decimals results in the simplified fraction $\frac{4}{33}$.
$\frac{4}{33}$. Applying the conversion method for two-digit repeating decimals results in the simplified fraction $\frac{4}{33}$.
← Didn't Know|Knew It →
Which is greater: $0.\overline{6}$ or $\frac{2}{3}$?
Which is greater: $0.\overline{6}$ or $\frac{2}{3}$?
Tap to reveal answer
They are equal. Converting $0.\overline{6}$ using the formula for repeating decimals yields exactly $\frac{2}{3}$.
They are equal. Converting $0.\overline{6}$ using the formula for repeating decimals yields exactly $\frac{2}{3}$.
← Didn't Know|Knew It →
What is the sign rule when comparing two negative rational numbers?
What is the sign rule when comparing two negative rational numbers?
Tap to reveal answer
The number with the smaller absolute value is greater. For negative numbers, the one closer to zero (smaller magnitude) is larger on the number line.
The number with the smaller absolute value is greater. For negative numbers, the one closer to zero (smaller magnitude) is larger on the number line.
← Didn't Know|Knew It →
Which is greater: $-\frac{3}{5}$ or $-0.55$?
Which is greater: $-\frac{3}{5}$ or $-0.55$?
Tap to reveal answer
$-0.55$. Since $|-0.55| < |-0.6|$, $-0.55$ is positioned to the right of $-\frac{3}{5} \approx -0.6$ on the number line.
$-0.55$. Since $|-0.55| < |-0.6|$, $-0.55$ is positioned to the right of $-\frac{3}{5} \approx -0.6$ on the number line.
← Didn't Know|Knew It →
What is $0.\overline{3}$ written as a fraction in simplest form?
What is $0.\overline{3}$ written as a fraction in simplest form?
Tap to reveal answer
$\frac{1}{3}$. The repeating decimal $0.\overline{3}$ represents an infinite series summing to $\frac{1}{3}$.
$\frac{1}{3}$. The repeating decimal $0.\overline{3}$ represents an infinite series summing to $\frac{1}{3}$.
← Didn't Know|Knew It →
Which is greater: $0.125$ or $\frac{1}{9}$?
Which is greater: $0.125$ or $\frac{1}{9}$?
Tap to reveal answer
$0.125$. Comparing decimals, $0.125 > 0.\overline{1} \approx 0.111$, as the former has a higher tenths digit.
$0.125$. Comparing decimals, $0.125 > 0.\overline{1} \approx 0.111$, as the former has a higher tenths digit.
← Didn't Know|Knew It →
What is the quickest method to compare $\frac{a}{b}$ and $\frac{c}{d}$ for positive $b,d$?
What is the quickest method to compare $\frac{a}{b}$ and $\frac{c}{d}$ for positive $b,d$?
Tap to reveal answer
Compare $ad$ and $bc$ (cross-multiply). Cross-multiplication determines the relationship without converting to decimals or finding common denominators, as $ad > bc$ implies $\frac{a}{b} > \frac{c}{d}$.
Compare $ad$ and $bc$ (cross-multiply). Cross-multiplication determines the relationship without converting to decimals or finding common denominators, as $ad > bc$ implies $\frac{a}{b} > \frac{c}{d}$.
← Didn't Know|Knew It →
Which is greater: $\frac{3}{4}$ or $0.7$?
Which is greater: $\frac{3}{4}$ or $0.7$?
Tap to reveal answer
$\frac{3}{4}$. Converting the fraction to $0.75$ shows it exceeds $0.7$ on the number line.
$\frac{3}{4}$. Converting the fraction to $0.75$ shows it exceeds $0.7$ on the number line.
← Didn't Know|Knew It →
Which is less: $-\frac{5}{6}$ or $-0.8$?
Which is less: $-\frac{5}{6}$ or $-0.8$?
Tap to reveal answer
$-\frac{5}{6}$. Approximating $-\frac{5}{6} \approx -0.833$, which is less than $-0.8$ since it is further left on the number line.
$-\frac{5}{6}$. Approximating $-\frac{5}{6} \approx -0.833$, which is less than $-0.8$ since it is further left on the number line.
← Didn't Know|Knew It →
Identify the larger number: $\frac{5}{8}$ or $0.62$.
Identify the larger number: $\frac{5}{8}$ or $0.62$.
Tap to reveal answer
$\frac{5}{8}$. Dividing $5$ by $8$ yields $0.625$, which is greater than $0.62$.
$\frac{5}{8}$. Dividing $5$ by $8$ yields $0.625$, which is greater than $0.62$.
← Didn't Know|Knew It →