Question

3
what is the value of \\(\frac{1}{2} - 4(\frac{1}{4} - \frac{3}{5}) + \frac{5}{8}\\)?

• a \\(\frac{7}{8}\\)
• b \\(1\frac{1}{8}\\)
• c \\(2\frac{21}{40}\\)
• d \\(2\frac{41}{80}\\)

Explanation:

Step1: Simplify the parentheses

First, we simplify the expression inside the parentheses: $\frac{1}{4} - \frac{3}{5}$. To subtract these fractions, we find a common denominator, which is 20. So we have $\frac{1\times5}{4\times5} - \frac{3\times4}{5\times4} = \frac{5}{20} - \frac{12}{20} = -\frac{7}{20}$.

Step2: Multiply by 4

Next, we multiply this result by 4: $4\times(-\frac{7}{20}) = -\frac{28}{20} = -\frac{7}{5}$.

Step3: Rewrite the original expression

Now we rewrite the original expression with the simplified parts: $\frac{1}{2} - (-\frac{7}{5}) + \frac{5}{8}$. Subtracting a negative is the same as adding the positive, so this becomes $\frac{1}{2} + \frac{7}{5} + \frac{5}{8}$.

Step4: Find a common denominator

To add these fractions, we find a common denominator. The least common multiple of 2, 5, and 8 is 40. So we convert each fraction:

• $\frac{1}{2} = \frac{1\times20}{2\times20} = \frac{20}{40}$
• $\frac{7}{5} = \frac{7\times8}{5\times8} = \frac{56}{40}$
• $\frac{5}{8} = \frac{5\times5}{8\times5} = \frac{25}{40}$

Step5: Add the fractions

Now we add them together: $\frac{20}{40} + \frac{56}{40} + \frac{25}{40} = \frac{20 + 56 + 25}{40} = \frac{101}{40}$.

Step6: Convert to mixed number

Finally, we convert $\frac{101}{40}$ to a mixed number: $101 \div 40 = 2$ with a remainder of 21, so $\frac{101}{40} = 2\frac{21}{40}$.

Answer:

C. $2\frac{21}{40}$