# How do you evaluate (2+ 3) ^ { 2} - 4\times 5\div 3?

Mar 15, 2018

Using PEMDAS, you can calculate the solution to be $18 \frac{1}{3}$

#### Explanation:

Remember that PEMDAS defines the order of operations for all arithmetic. PEMDAS stands for:

Parentheses
Exponents
Multiplication
Division
Subtraction

So starting from the top of the acronym, we evaluate the terms inside of the parentheses:

$2 + 3 = 5$

Making our expression:

${5}^{2} - 4 \times 5 \div 3$

Now, we work on exponents. The only exponent here is the ${5}^{2}$ term, and that evaluates to: ${5}^{2} = 25$. Let's put that in the expression:

$25 - 4 \times 5 \div 3$

We're now at multiplication and division. we have one multiplication and one division exercise to do, let's combine them! Since the 4, 5, and 3 are all together, you can re-write that expression like so:

$4 \times 5 \div 3 \Rightarrow \frac{4 \times 5}{3} \Rightarrow \frac{20}{3}$

What I did here was that instead of dividing by 3, I multiplied by its inverse, $\frac{1}{3}$. This way, I was able to do both multiplications at the same time!

Finally, We'll skip addition (there's no addition in this expression!) and go straight to subtraction:

$25 - \frac{20}{3}$

Let's raise the 25 so it's a function of thirds, making the arithmetic slightly easier. We'll then put that modified fraction into the expression:

$25 \cdot \frac{3}{3} = \frac{75}{3} \Rightarrow \frac{75}{3} - \frac{20}{3} = \frac{55}{3}$

Now we have a solution as an improper fraction, $\frac{55}{3}$. Let's make it a mixed fraction to finish things off:

$\frac{55}{3} = \textcolor{red}{18 \frac{1}{3}}$

Mar 16, 2018

$18 \frac{1}{3}$

#### Explanation:

In any expression with multiple operations, identify the individual terms first:

$\textcolor{b l u e}{{\left(2 + 3\right)}^{2}} \textcolor{g r e e n}{- 4 \times 5 \div 3} \text{ } \leftarrow$ there are two terms.
$\textcolor{w h i t e}{\times} \downarrow \textcolor{w h i t e}{\times \times} \downarrow$
$= \textcolor{b l u e}{{\left(5\right)}^{2}} \textcolor{g r e e n}{\text{ } - 20 \div 3}$
$\textcolor{w h i t e}{\times} \downarrow \textcolor{w h i t e}{\times \times \times} \downarrow$
$= \textcolor{b l u e}{25} \textcolor{g r e e n}{\text{ "-" } \frac{20}{3}}$

$= 25 - 6 \frac{2}{3}$

$= 19 - \frac{2}{3}$

$= 18 \frac{1}{3}$