Question

1. $2a + b$ when $a = 3\frac{1}{4}$, $b = 5\frac{2}{7}$

Explanation:

Step1: Convert mixed numbers to fractions

$a = 3\frac{1}{4} = \frac{13}{4}$, $b = 5\frac{2}{7} = \frac{37}{7}$

Step2: Calculate 2a

$2a = 2 \times \frac{13}{4} = \frac{26}{4} = \frac{13}{2}$

Step3: Find common denominator for addition

Common denominator of 2 and 7 is 14. $\frac{13}{2} = \frac{91}{14}$, $\frac{37}{7} = \frac{74}{14}$

Step4: Add the two fractions

$\frac{91}{14} + \frac{74}{14} = \frac{91+74}{14} = \frac{165}{14}$

Step5: Convert to mixed number (optional)

$\frac{165}{14} = 11\frac{11}{14}$

Answer:

$\frac{165}{14}$ or $11\frac{11}{14}$