Question

1. \\(\frac{a}{b} - c + d\\)\\(\frac{7}{8}\left(-\frac{7}{16}\

ight) - 0.8 + \frac{1}{4}\\)

Explanation:

Step1: Simplify the fraction multiplication

First, calculate \(\frac{7}{8} \times (-\frac{7}{16})\). The formula for multiplying fractions is \(\frac{m}{n} \times \frac{p}{q} = \frac{m \times p}{n \times q}\), so here we have \(\frac{7 \times (-7)}{8 \times 16} = -\frac{49}{128}\).

Step2: Convert decimals to fractions

Next, convert \(0.8\) to a fraction. \(0.8=\frac{8}{10}=\frac{4}{5}\), and \(\frac{1}{4}\) remains as it is. Now the expression becomes \(-\frac{49}{128}-\frac{4}{5}+\frac{1}{4}\).

Step3: Find a common denominator

The common denominator of 128, 5, and 4 is 640. Convert each fraction:
\(-\frac{49}{128}=-\frac{49\times5}{128\times5}=-\frac{245}{640}\)
\(-\frac{4}{5}=-\frac{4\times128}{5\times128}=-\frac{512}{640}\)
\(\frac{1}{4}=\frac{1\times160}{4\times160}=\frac{160}{640}\)

Step4: Combine the fractions

Now add the fractions together: \(-\frac{245}{640}-\frac{512}{640}+\frac{160}{640}=\frac{-245 - 512+160}{640}=\frac{-597}{640}\)

Answer:

\(-\frac{597}{640}\)