Chapter 4, Problem 9MS

To determine

To simplify expression $\frac{7}{8}-\left(-\frac{1}{4}+\frac{1}{2}\right)$

Answer to Problem 9MS

  $\frac{5}{8}$

Explanation of Solution

Given information:

The expression, $\frac{7}{8}-\left(-\frac{1}{4}+\frac{1}{2}\right)$

Concept used:

For Order of Operation, we will use PEMDAS rule.

Symbols are representing:

P − parenthesis, E − exponent, M − multiplication,

D − division, A − addition and S − subtraction.

• If grouping symbols such as parenthesis are present, simplify expressions within those first, starting with the innermost set.
• Evaluate exponential expressions or absolute values in order from left to right.
• Multiply or divide in order from left to right.
• Add or subtract in order from left to right.

If there is no grouping symbols or no exponents, we multiply or divide and then add or subtract in the order from left to right.

Calculation:

To simplify the expression $\frac{7}{8}-\left(-\frac{1}{4}+\frac{1}{2}\right)$ , first subtract the fractions inside the parenthesis by taking the Least Common Denominator (LCD) and then simplify further by subtracting the resulting fractions as shown below,

  $\begin{array}{c}\frac{7}{8}-\left(-\frac{1}{4}+\frac{1}{2}\right)=\frac{7}{8}-\left(-\frac{1}{4}+\frac{1}{2}\cdot \frac{2}{2}\right)\\ =\frac{7}{8}-\left(-\frac{1}{4}+\frac{2}{4}\right)\\ =\frac{7}{8}-\left(\frac{-1+2}{4}\right)\\ =\frac{7}{8}-\left(\frac{1}{4}\right)\\ =\frac{7}{8}-\frac{1}{4}\cdot \frac{2}{2}\\ =\frac{7}{8}-\frac{2}{8}\\ =\frac{7-2}{8}\\ =\frac{5}{8}\end{array}$

Thus, the given expression simplifies to $\frac{5}{8}$ .