Question #85951

Jan 26, 2017

$1 + 4 \left(1 + 1 - 4 \times {\pi}^{0}\right) - 7 \div 6 = - \frac{49}{6} = - 8 \frac{1}{6}$

Explanation:

Assuming ${\pi}^{\circ}$ is intended as ${\pi}^{0}$ ($\pi$ to the power of $0$), we will follow the order of operations: First, anything inside of parentheses. Next, any exponents. Then any multiplication or division, going left to right. Finally, any addition or subtraction, going left to right. With that,

Complete any operations within parentheses

$1 + 4 \textcolor{red}{\left(1 + 1 - 4 \times {\pi}^{0}\right)} - 7 \div 6$

Evaluate any exponents.

$= 1 + 4 \textcolor{red}{\text{(")1+1-4xxcolor(blue)(pi^0)color(red)(")}} - 7 \div 6$

Any nonzero number to the power $0$ is $1$.

$= 1 + 4 \textcolor{red}{\text{(")1+1-4xx1color(red)(")}} - 7 \div 6$

Evaluate any multiplication or division, going left to right.

$= 1 + 4 \textcolor{red}{\text{(")1+1-color(blue)(4xx1)color(red)(")}} - 7 \div 6$

$= 1 + 4 \textcolor{red}{\text{(")1+1-4color(red)(")}} - 7 \div 6$

Evaluate any addition or subtraction, going left to right.

$= 1 + 4 \textcolor{red}{\text{(")color(blue)(1+1)-4color(red)(")}} - 7 \div 6$

$= 1 + 4 \textcolor{red}{\text{(")color(blue)(2-4)color(red)(")}} - 7 \div 6$

$= 1 + 4 \left(- 2\right) - 7 \div 6$

All operations within parentheses have been evaluated. No further parentheses or exponents remain, so evaluate any multiplication or division, going left to right.

$= 1 + \textcolor{red}{4 \left(- 2\right)} - 7 \div 6$

$= 1 + \left(- 8\right) - \textcolor{red}{7 \div 6}$

$= 1 + \left(- 8\right) - \frac{7}{6}$

Evaluate any addition or subtraction, going left to right.

$= \textcolor{red}{1 + \left(- 8\right)} - \frac{7}{6}$

$= \textcolor{red}{- 7 - \frac{7}{6}}$

$= - \frac{49}{6}$

$= - 8 \frac{1}{6}$

Jan 26, 2017

$- 8.167$ or as a fraction:

$- 8 \frac{1}{6}$

Explanation:

Remember what you learned with BEDMAS
The order is Brackets, Exponent, Divide, Multiply, Add and Subtract.
Knowing that,

$1 + 4 \left(1 + 1 - 4 \times {\pi}^{0}\right) - 7 \div 6$

We start with the bracket. We calculate everything that is inside the bracket. There is an exponent, therefore we do that first. Then the multiplication then the addition and then subtraction.

$1 + 4 \left(1 + 1 - 4 \times 1\right) - 7 \div 6 \text{ }$ (anything to the power of 0 = 1)
$1 + 4 \left(1 + 1 - 4\right) - 7 \div 6 \text{ }$ (4x1=4)
$1 + 4 \left(- 2\right) - 7 \div 6 \text{ }$ (1+1-4 = -2)

Since the bracket is almost completely done, we have to remember that when two numbers are connected by a bracket, that means that you multiply them. Then to finish off the problem, you do the Dividing and multiplication. you then end the problem by adding and subtract your problem and you are done.

$1 + 4 \times \left(- 2\right) - 7 \div 6$

$1 - 8 - 1.167$

$- 8.167$ is your final answer

Mar 6, 2017

$- 8 \frac{1}{6}$

Explanation:

Note that there are 3 terms. We will need to simplify each term to a single answer and add or subtract in the last line.

$\textcolor{b l u e}{1} + \textcolor{red}{4 \left(1 + 1 - 4 \times {\pi}^{0}\right)} \textcolor{g r e e n}{- 7 \div 6}$

In the second term we will start inside the brackets.

$\text{ "color(blue)(1)+4(1+1-4xxcolor(red)(pi^0)) color(green)(-7 div 6)" } \leftarrow \textcolor{red}{{x}^{0} = 1}$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . .} \downarrow$
$= \textcolor{b l u e}{1} + 4 \left(1 + 1 - 4 \times \textcolor{red}{1}\right) \textcolor{g r e e n}{- \frac{7}{6}} \text{ } \leftarrow$ multiply $4 \times 1 = 4$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots .} \downarrow$
$= \textcolor{b l u e}{1} \text{ "+4(1+1-color(red)(4))" } \textcolor{g r e e n}{- 1 \frac{1}{6}}$

$= \textcolor{b l u e}{1} + 4 \left(\textcolor{red}{- 2}\right) \textcolor{g r e e n}{- 1 \frac{1}{6}} \text{ }$( simplify $1 + 1 - 4 = - 2$)

$= \textcolor{b l u e}{1} \textcolor{red}{- 8} \textcolor{g r e e n}{- 1 \frac{1}{6}}$

The three terms can now be added or subtracted

$1 - 9 \frac{1}{6}$

$= - 8 \frac{1}{6}$

Note that a fraction answer is more accurate because it does not require any rounding.