Question : Which of the following statements is true?
Option 1: $1 \frac{1}{2} + 17 \frac{3}{4} - 5 \frac{1}{5} - 2 \frac{1}{10} = \frac{239}{20}$
Option 2: $\frac{9}{1078}>\frac{11}{1127} >\frac{12}{1219}$
Option 3: $\frac{149}{151} > \frac{153}{155} > \frac{157}{159}$
Option 4: None
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Correct Answer: $1 \frac{1}{2} + 17 \frac{3}{4} - 5 \frac{1}{5} - 2 \frac{1}{10} = \frac{239}{20}$
Solution :
1. $1 \frac{1}{2} + 17 \frac{3}{4} - 5 \frac{1}{5} - 2 \frac{1}{10} = \frac{239}{20}$
$\frac{3}{2} + \frac{71}{4} - \frac{26}{5} - \frac{21}{10} = \frac{239}{20}$
Simplifying the left side, we get:
$\frac{239}{20} = \frac{239}{20}$
This is true.
2. $\frac{9}{1078}>\frac{11}{1127} >\frac{12}{1219}$
For this, we can cross-multiply to compare the fractions:
$9×1127 > 11×1078$
$10143 > 11858$
This is false.
3. $\frac{149}{151} > \frac{153}{155} > \frac{157}{159}$
Again, we can cross-multiply to compare the fractions:
$149×155 > 153×151$
$23095 > 23103$
This is false.
Hence, the correct answer is '$1 \frac{1}{2} + 17 \frac{3}{4} - 5 \frac{1}{5} - 2 \frac{1}{10} = \frac{239}{20}$'.
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