# How do you evaluate 3- ( 1- ( - \frac { 11} { 2} ) )?

Sep 7, 2017

$- 3.5$

#### Explanation:

Use "PEMDAS"

Parenthesis
Exponents
Multiplication/Division

We begin by working within the parenthesis

$3 - \left(1 - \left(- \frac{11}{2}\right)\right)$

We see we have $\left(1 - \left(- \frac{11}{2}\right)\right)$ We can rewrite this as

$1 - \left(- \frac{11}{2}\right) \to 1 - - 5.5 \to 1 + 5.5$

And evaluate to get $6.5$

Our expression is now

$3 - 6.5$

Which equates to $- 3.5$

Sep 7, 2017

3-(1-(-11/2))=color(teal)(-7/2

#### Explanation:

A different approach, without writing fractions as decimals.

$3 - \left(1 - \left(- \frac{11}{2}\right)\right)$

Simplify the parentheses.

$3 - \left(1 + \frac{11}{2}\right)$

Any whole number, $n$, has a denominator of $1$: $n = \frac{n}{1}$.

Rewrite.

$\frac{3}{1} - \left(\frac{1}{1} + \frac{11}{2}\right)$

The common denominator is $2$. Multiply the numerators and denominators of $\frac{3}{1} \mathmr{and} \frac{1}{1}$ by $\frac{\textcolor{m a \ge n t a}{2}}{\textcolor{m a \ge n t a}{2}}$ to get equivalent fractions with $2$ as the denominator.

$\frac{3}{1} \times \frac{\textcolor{m a \ge n t a}{2}}{\textcolor{m a \ge n t a}{2}} - \left(\frac{1}{1} \times \frac{\textcolor{m a \ge n t a}{2}}{\textcolor{m a \ge n t a}{2}} + \frac{11}{2}\right)$

Simplify.

$\frac{6}{2} - \left(\frac{2}{2} + \frac{11}{2}\right)$

Simplify the parentheses.

$\frac{6}{2} - \left(\frac{13}{2}\right)$

Subtract.

$- \frac{7}{2}$