Question:
The fractions
\(\dfrac{42}{491}, \ \dfrac{30}{313}, \ \text{and} \ \dfrac{35}{367}\)
are arranged in ascending order of magnitude as:
The fractions
\(\dfrac{42}{491}, \ \dfrac{30}{313}, \ \text{and} \ \dfrac{35}{367}\)
are arranged in ascending order of magnitude as:
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When comparing fractions with different denominators, cross multiplication avoids converting to decimals. Always keep the multiplication consistent across comparisons.
Updated On: Aug 14, 2025
- \(\dfrac{35}{367}, \ \dfrac{30}{313}, \ \dfrac{42}{491}\)
- \(\dfrac{42}{491}, \ \dfrac{35}{367}, \ \dfrac{30}{313}\)
- \(\dfrac{30}{313}, \ \dfrac{35}{367}, \ \dfrac{42}{491}\)
- \(\dfrac{42}{491}, \ \dfrac{30}{313}, \ \dfrac{35}{367}\)
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The Correct Option is B
Solution and Explanation
Step 1: Compare \(\frac{42}{491}\) and \(\frac{35}{367}\) using cross multiplication.
We compare \(42 \times 367 = 15414\) and \(35 \times 491 = 17185\).
Since \(15414<17185\), \(\frac{42}{491}<\frac{35}{367}\).
Step 2: Compare \(\frac{35}{367}\) and \(\frac{30}{313}\).
We compare \(35 \times 313 = 10955\) and \(30 \times 367 = 11010\).
Since \(10955<11010\), \(\frac{35}{367}<\frac{30}{313}\).
Step 3: Final order.
From the above comparisons: \(\frac{42}{491}<\frac{35}{367}<\frac{30}{313}\). \[ \boxed{\frac{42}{491}, \ \frac{35}{367}, \ \frac{30}{313}} \]
We compare \(42 \times 367 = 15414\) and \(35 \times 491 = 17185\).
Since \(15414<17185\), \(\frac{42}{491}<\frac{35}{367}\).
Step 2: Compare \(\frac{35}{367}\) and \(\frac{30}{313}\).
We compare \(35 \times 313 = 10955\) and \(30 \times 367 = 11010\).
Since \(10955<11010\), \(\frac{35}{367}<\frac{30}{313}\).
Step 3: Final order.
From the above comparisons: \(\frac{42}{491}<\frac{35}{367}<\frac{30}{313}\). \[ \boxed{\frac{42}{491}, \ \frac{35}{367}, \ \frac{30}{313}} \]
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