Question - Calculation of Average of Two Numbers
Solution:
The given problem is to find the value of $$\frac{a + b}{2}$$.First, we'll calculate the value of $$a$$ and $$b$$ separately and then find $$\frac{a + b}{2}$$.$$a = 4\frac{1}{2} + 1\frac{1}{2}$$$$a = \frac{9}{2} + \frac{3}{2}$$ (converting mixed fractions to improper fractions)$$a = \frac{9 + 3}{2}$$$$a = \frac{12}{2}$$$$a = 6$$ (simplifying the fraction)$$b = 6\frac{1}{2} + 1\frac{3}{4}$$$$b = \frac{13}{2} + \frac{7}{4}$$ (converting mixed fractions to improper fractions)To add these fractions, they must have a common denominator. The least common denominator for 2 and 4 is 4.$$b = \frac{26}{4} + \frac{7}{4}$$ (making the denominators the same)$$b = \frac{26 + 7}{4}$$$$b = \frac{33}{4}$$ (simplifying the fraction)Now, let's calculate $$\frac{a + b}{2}$$.$$\frac{a + b}{2} = \frac{6 + \frac{33}{4}}{2}$$First, express 6 as a fraction with a denominator of 4 to be able to add it to $$\frac{33}{4}$$.$$\frac{6}{1} = \frac{24}{4}$$Now, add the fractions:$$\frac{a + b}{2} = \frac{\frac{24}{4} + \frac{33}{4}}{2}$$$$\frac{a + b}{2} = \frac{24 + 33}{4 \cdot 2}$$$$\frac{a + b}{2} = \frac{57}{8}$$So the value of $$\frac{a + b}{2}$$ is $$\frac{57}{8}$$.
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