Which of the following fraction is greater than 1/3?

Q: Which of the following fraction is greater than 1/3?

To determine which fraction is greater than $ \frac{1}{3} $, we need to compare each option with $ \frac{1}{3} $. 1. **Option 1: $ \frac{27}{82} $** - To compare $ \frac{27}{82} $ with $ \frac{1}{3} $, we find a common denominator or cross-multiply: - Cross-multiplying: $ 27 \times 3 = 81 $ and $ 1 \times 82 = 82 $. - Since 81 is less than 82, $ \frac{27}{82} $ is less than $ \frac{1}{3} $. 2. **Option 2: $ \frac{20}{61} $** - Cross-multiplying: $ 20 \times 3 = 60 $ and $ 1 \times 61 = 61 $. - Since 60 is less than 61, $ \frac{20}{61} $ is less than $ \frac{1}{3} $. 3. **Option 3: $ \frac{16}{45} $** - Cross-multiplying: $ 16 \times 3 = 48 $ and $ 1 \times 45 = 45 $. - Since 48 is greater than 45, $ \frac{16}{45} $ is greater than $ \frac{1}{3} $. - This confirms that Option 3 is indeed greater than $ \frac{1}{3} $. 4. **Option 4: $ \frac{51}{154} $** - Cross-multiplying: $ 51 \times 3 = 153 $ and $ 1 \times 154 = 154 $. - Since 153 is less than 154, $ \frac{51}{154} $ is less than $ \frac{1}{3} $. In conclusion, Option 3 ($ \frac{16}{45} $) is the only fraction that is greater than $ \frac{1}{3} $. The other options are all less than $ \frac{1}{3} $, which supports the given correct answer.

Question

Accepted Answer

To determine which fraction is greater than $ \frac{1}{3} $, we need to compare each option with $ \frac{1}{3} $.

1. **Option 1: $ \frac{27}{82} $**
   - To compare $ \frac{27}{82} $ with $ \frac{1}{3} $, we find a common denominator or cross-multiply:
   - Cross-multiplying: $ 27 \times 3 = 81 $ and $ 1 \times 82 = 82 $.
   - Since 81 is less than 82, $ \frac{27}{82} $ is less than $ \frac{1}{3} $.

2. **Option 2: $ \frac{20}{61} $**
   - Cross-multiplying: $ 20 \times 3 = 60 $ and $ 1 \times 61 = 61 $.
   - Since 60 is less than 61, $ \frac{20}{61} $ is less than $ \frac{1}{3} $.

3. **Option 3: $ \frac{16}{45} $**
   - Cross-multiplying: $ 16 \times 3 = 48 $ and $ 1 \times 45 = 45 $.
   - Since 48 is greater than 45, $ \frac{16}{45} $ is greater than $ \frac{1}{3} $.
   - This confirms that Option 3 is indeed greater than $ \frac{1}{3} $.

4. **Option 4: $ \frac{51}{154} $**
   - Cross-multiplying: $ 51 \times 3 = 153 $ and $ 1 \times 154 = 154 $.
   - Since 153 is less than 154, $ \frac{51}{154} $ is less than $ \frac{1}{3} $.

In conclusion, Option 3 ($ \frac{16}{45} $) is the only fraction that is greater than $ \frac{1}{3} $. The other options are all less than $ \frac{1}{3} $, which supports the given correct answer.