Comparing Fractions
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SSAT Middle Level: Quantitative › Comparing Fractions
Which is farther: $5/6$ mile or $8/9$ mile?
$5/6$ is larger because 6 is smaller.
$5/6$ mile is larger.
They are equal distances.
$8/9$ mile is larger.
Explanation
This question tests middle school mathematics skills: comparing fractions to determine which is greater. Comparing fractions involves understanding that a larger numerator or smaller denominator can affect the fraction's size. Key principle: fractions represent parts of a whole, and understanding their size relative to each other is crucial. In this scenario, students compare 5/6 mile and 8/9 mile to determine which is farther. The correct choice B states that 8/9 mile is larger because cross-multiplying shows 59=45 < 86=48, so 5/6 < 8/9. This demonstrates understanding of how numerators and denominators affect fraction size. A common distractor, D, fails because it incorrectly assumes a smaller denominator means a larger fraction without comparing properly. This often happens when students do not consider the role of the denominator. To help students: Use visual aids like fraction strips or pie charts to illustrate comparisons. Practice comparing fractions with similar numerators or denominators to develop a deeper understanding. Watch for: students relying solely on numerators or denominators without considering the whole fraction.
Which runner goes farther: $5/8$ mile or $3/4$ mile?
They are equal distances.
$5/8$ mile is larger.
$5/8$ is larger because 8 is bigger.
$3/4$ mile is larger.
Explanation
This question tests middle school mathematics skills: comparing fractions to determine which is greater. Comparing fractions involves understanding that a larger numerator or smaller denominator can affect the fraction's size. Key principle: fractions represent parts of a whole, and understanding their size relative to each other is crucial. In this scenario, students compare 5/8 mile and 3/4 mile to determine which runner goes farther. The correct choice B states that 3/4 mile is larger because cross-multiplying shows 54=20 < 38=24, so 5/8 < 3/4. This demonstrates understanding of how numerators and denominators affect fraction size. A common distractor, D, fails because it incorrectly assumes a larger denominator means a larger fraction without comparing properly. This often happens when students do not consider the role of the denominator. To help students: Use visual aids like fraction strips or pie charts to illustrate comparisons. Practice comparing fractions with similar numerators or denominators to develop a deeper understanding. Watch for: students relying solely on numerators or denominators without considering the whole fraction.
Which is larger: $2/5$ of the budget or $3/8$ of the budget?
They are equal shares.
$3/8$ is the larger share.
$2/5$ is the larger share.
$3/8$ is larger because 3 is bigger.
Explanation
This question tests middle school mathematics skills: comparing fractions to determine which is greater. Comparing fractions involves understanding that a larger numerator or smaller denominator can affect the fraction's size. Key principle: fractions represent parts of a whole, and understanding their size relative to each other is crucial. In this scenario, students compare 2/5 and 3/8 of a budget to determine which is larger. The correct choice B states that 2/5 is the larger share because cross-multiplying shows 35=15 < 28=16, so 3/8 < 2/5. This demonstrates understanding of how numerators and denominators affect fraction size. A common distractor, D, fails because it focuses only on numerators without considering denominators. This often happens when students do not consider the role of the denominator. To help students: Use visual aids like fraction strips or pie charts to illustrate comparisons. Practice comparing fractions with similar numerators or denominators to develop a deeper understanding. Watch for: students relying solely on numerators or denominators without considering the whole fraction.
Which is longer: $4/7$ hour studying or $3/5$ hour gaming?
$4/7$ is larger because 4 is bigger.
They are equal times.
$3/5$ hour is larger.
$4/7$ hour is larger.
Explanation
This question tests middle school mathematics skills: comparing fractions to determine which is greater. Comparing fractions involves understanding that a larger numerator or smaller denominator can affect the fraction's size. Key principle: fractions represent parts of a whole, and understanding their size relative to each other is crucial. In this scenario, students compare 4/7 hour and 3/5 hour to determine which is longer. The correct choice B states that 3/5 hour is larger because cross-multiplying shows 45=20 < 37=21, so 4/7 < 3/5. This demonstrates understanding of how numerators and denominators affect fraction size. A common distractor, D, fails because it focuses only on numerators without considering denominators. This often happens when students do not consider the role of the denominator. To help students: Use visual aids like fraction strips or pie charts to illustrate comparisons. Practice comparing fractions with similar numerators or denominators to develop a deeper understanding. Watch for: students relying solely on numerators or denominators without considering the whole fraction.
Which is more time: $2/3$ hour or $5/8$ hour?
$5/8$ hour is larger.
$2/3$ hour is larger.
They are equal times.
$5/8$ is larger because 5 is bigger.
Explanation
This question tests middle school mathematics skills: comparing fractions to determine which is greater. Comparing fractions involves understanding that a larger numerator or smaller denominator can affect the fraction's size. Key principle: fractions represent parts of a whole, and understanding their size relative to each other is crucial. In this scenario, students compare 2/3 hour and 5/8 hour to determine which is more time. The correct choice B states that 2/3 hour is larger because cross-multiplying shows 53=15 < 28=16, so 5/8 < 2/3. This demonstrates understanding of how numerators and denominators affect fraction size. A common distractor, D, fails because it focuses only on numerators without considering denominators. This often happens when students do not consider the role of the denominator. To help students: Use visual aids like fraction strips or pie charts to illustrate comparisons. Practice comparing fractions with similar numerators or denominators to develop a deeper understanding. Watch for: students relying solely on numerators or denominators without considering the whole fraction.
Which is larger: $7/10$ of funds or $2/3$ of funds?
$2/3$ is the larger share.
$7/10$ is the larger share.
$2/3$ is larger because 3 is smaller.
They are equal shares.
Explanation
This question tests middle school mathematics skills: comparing fractions to determine which is greater. Comparing fractions involves understanding that a larger numerator or smaller denominator can affect the fraction's size. Key principle: fractions represent parts of a whole, and understanding their size relative to each other is crucial. In this scenario, students compare 7/10 and 2/3 of funds to determine which is larger. The correct choice B states that 7/10 is the larger share because cross-multiplying shows 210=20 < 73=21, so 2/3 < 7/10. This demonstrates understanding of how numerators and denominators affect fraction size. A common distractor, D, fails because it incorrectly assumes a smaller denominator means a larger fraction without comparing properly. This often happens when students do not consider the role of the denominator. To help students: Use visual aids like fraction strips or pie charts to illustrate comparisons. Practice comparing fractions with similar numerators or denominators to develop a deeper understanding. Watch for: students relying solely on numerators or denominators without considering the whole fraction.
Which is larger: $8/9$ of the supplies or $7/10$ of supplies?
$8/9$ is the larger share.
$7/10$ is the larger share.
They are equal shares.
$7/10$ is larger because 10 is bigger.
Explanation
This question tests middle school mathematics skills: comparing fractions to determine which is greater. Comparing fractions involves understanding that a larger numerator or smaller denominator can affect the fraction's size. Key principle: fractions represent parts of a whole, and understanding their size relative to each other is crucial. In this scenario, students compare 8/9 and 7/10 of supplies to determine which is larger. The correct choice B states that 8/9 is the larger share because cross-multiplying shows 79=63 < 810=80, so 7/10 < 8/9. This demonstrates understanding of how numerators and denominators affect fraction size. A common distractor, D, fails because it incorrectly assumes a larger denominator means a larger fraction without comparing properly. This often happens when students do not consider the role of the denominator. To help students: Use visual aids like fraction strips or pie charts to illustrate comparisons. Practice comparing fractions with similar numerators or denominators to develop a deeper understanding. Watch for: students relying solely on numerators or denominators without considering the whole fraction.
Which share is larger: $5/6$ for equipment or $3/4$ for snacks?
$3/4$ is the larger share.
$3/4$ is larger because 4 is smaller.
$5/6$ is the larger share.
They are equal shares.
Explanation
This question tests middle school mathematics skills: comparing fractions to determine which is greater. Comparing fractions involves understanding that a larger numerator or smaller denominator can affect the fraction's size. Key principle: fractions represent parts of a whole, and understanding their size relative to each other is crucial. In this scenario, students compare 5/6 and 3/4 to determine which share is larger. The correct choice B states that 5/6 is the larger share because cross-multiplying shows 36=18 < 54=20, so 3/4 < 5/6. This demonstrates understanding of how numerators and denominators affect fraction size. A common distractor, D, fails because it incorrectly assumes a smaller denominator means a larger fraction without comparing properly. This often happens when students do not consider the role of the denominator. To help students: Use visual aids like fraction strips or pie charts to illustrate comparisons. Practice comparing fractions with similar numerators or denominators to develop a deeper understanding. Watch for: students relying solely on numerators or denominators without considering the whole fraction.
Which is more butter: $5/6$ cup or $3/4$ cup?
$5/6$ cup is larger.
$3/4$ cup is larger.
$3/4$ is larger because 4 is smaller.
They are equal amounts.
Explanation
This question tests middle school mathematics skills: comparing fractions to determine which is greater. Comparing fractions involves understanding that a larger numerator or smaller denominator can affect the fraction's size. Key principle: fractions represent parts of a whole, and understanding their size relative to each other is crucial. In this scenario, students compare 5/6 cup and 3/4 cup to determine which is more butter. The correct choice B states that 5/6 cup is larger because cross-multiplying shows 36=18 < 54=20, so 3/4 < 5/6. This demonstrates understanding of how numerators and denominators affect fraction size. A common distractor, D, fails because it incorrectly assumes a smaller denominator means a larger fraction without comparing properly. This often happens when students do not consider the role of the denominator. To help students: Use visual aids like fraction strips or pie charts to illustrate comparisons. Practice comparing fractions with similar numerators or denominators to develop a deeper understanding. Watch for: students relying solely on numerators or denominators without considering the whole fraction.
Which is more time: $3/8$ hour or $4/9$ hour?
$3/8$ hour is larger.
$4/9$ hour is larger.
They are equal times.
$3/8$ is larger because 8 is smaller.
Explanation
This question tests middle school mathematics skills: comparing fractions to determine which is greater. Comparing fractions involves understanding that a larger numerator or smaller denominator can affect the fraction's size. Key principle: fractions represent parts of a whole, and understanding their size relative to each other is crucial. In this scenario, students compare 3/8 hour and 4/9 hour to determine which is more time. The correct choice B states that 4/9 hour is larger because cross-multiplying shows 39=27 < 48=32, so 3/8 < 4/9. This demonstrates understanding of how numerators and denominators affect fraction size. A common distractor, D, fails because it incorrectly assumes a smaller denominator means a larger fraction without comparing properly. This often happens when students do not consider the role of the denominator. To help students: Use visual aids like fraction strips or pie charts to illustrate comparisons. Practice comparing fractions with similar numerators or denominators to develop a deeper understanding. Watch for: students relying solely on numerators or denominators without considering the whole fraction.