Even with fractions, we still use the order of operations. The acronym to remember this is PEMDAS. First is parentheses, then exponents, multiplication/division, addition/subtraction.
The given problem is \(\frac{1}{5}( 3\frac{1}{2}* \frac{4}{7} - \frac{11}{14}) + \frac{3}{28}\).
First we simplify what's in the parentheses. PEMDAS then applies in the parentheses, and since they are no further parentheses or exponents, we look at multiplication/division and multiply. First let's have all improper fractions.
\(\frac{1}{5}( 3\frac{1}{2}* \frac{4}{7} - \frac{11}{14}) + \frac{3}{28} \\ = \frac{1}{5}( \frac{7}{2}* \frac{4}{7} - \frac{11}{14}) + \frac{3}{28}\).
Next multiply the fractions: numerator with numerator and denominator with denominator.
\(\frac{1}{5}( \frac{7}{2}* \frac{4}{7} - \frac{11}{14}) + \frac{3}{28} \\\\
= \frac{1}{5}( \frac{28}{14} - \frac{11}{14}) + \frac{3}{28}\)
Next in the parentheses is addition/subtraction.
\(\frac{1}{5}( \frac{28}{14} - \frac{11}{14}) + \frac{3}{28} \\\\
= \frac{1}{5} ( \frac{17}{14}) + \frac{3}{28}\)
Now apply PEMDAS again, and since there are no parentheses or exponents to simplify, we multiply.
\(\frac{1}{5} ( \frac{17}{14}) + \frac{3}{28} \\\\
= \frac{17}{70} + \frac{3}{28}\)
Finally find a common denominator and add.
\(\frac{17}{70} + \frac{3}{28} \\\\
= \frac{34}{140} + \frac{15}{140} \\\\
= \frac{49}{140} = \frac{7}{20}\)
