# How do you evaluate  ( 4+ 3} / { 4^ { 2} + 4- 6}?

Oct 6, 2017

$0.5 \mathmr{and} \frac{1}{2}$

#### Explanation:

The giant bar can be rewritten as a division sign with parentheses.

So your question is the same as:

$\left(4 + 3\right) \div \left({4}^{2} + 4 - 6\right)$

Use order of operations:
Parentheses
Exponents
Multiplication
Division
Subtraction

First parentheses:

$7 \div \left({4}^{2} + 4 - 6\right)$

This second set of parentheses has exponents, so we do that first before the addition and subtraction:

$7 \div \left(16 + 4 - 6\right) = 7 \div \left(20 - 6\right) = 7 \div \left(14\right)$

Finally we finish with division:

$7 \div 14 = \frac{1}{2} = 0.5$

Oct 6, 2017

$\frac{1}{2}$

#### Explanation:

It's best to evaluate the top and bottom separately:

The numerator is $7$

The denominator is $16 + 4 - 6 = 14$

So your difficult looking fraction is nothing more than $\frac{7}{14}$, which if you reduce, is equivalent to $\frac{1}{2}$.