Question

Use pemdas.
4 + 4/ -7 + 5 - 10 + (-1)/8 + (-1)²

Answer 1

To solve the expression using the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)), we first identify and calculate any exponents, then proceed with addition and subtraction while taking care of the division.

Let's break down the expression step by step:

1. The expression is:
\[
4 + \frac{4}{-7} + 5 - 10 + \frac{-1}{8} + (-1)^2
\]

2. Calculate the exponent:
\[
(-1)^2 = 1
\]

3. Substitute back into the expression:
\[
4 + \frac{4}{-7} + 5 - 10 + \frac{-1}{8} + 1
\]

4. Now, calculate the divisions:
\[
\frac{4}{-7} = -\frac{4}{7}
\]
\[
\frac{-1}{8} = -\frac{1}{8}
\]

5. Substitute these values back into the expression:
\[
4 - \frac{4}{7} + 5 - 10 - \frac{1}{8} + 1
\]

6. Now combine the whole numbers first:
\[
4 + 5 - 10 + 1 = 0
\]

7. Substitute this back:
\[
0 - \frac{4}{7} - \frac{1}{8}
\]

8. Now, find a common denominator to combine the fractions. The common denominator between 7 and 8 is 56:
\[
-\frac{4}{7} = -\frac{4 \times 8}{7 \times 8} = -\frac{32}{56}
\]
\[
-\frac{1}{8} = -\frac{1 \times 7}{8 \times 7} = -\frac{7}{56}
\]

9. Now combine the fractions:
\[
-\frac{32}{56} - \frac{7}{56} = -\frac{32 + 7}{56} = -\frac{39}{56}
\]

So, the simplified result of the expression is:
\[
-\frac{39}{56}
\]