Question

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

Answer 1

Using PEMDAS, you can calculate the solution to be `18 1/3`

Explanation:

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

Parentheses
Exponents
Multiplication
Division
Addition
Subtraction

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

`2+3=5`

Making our expression:

`5^2-4xx5-: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:

`25-4xx5-: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:

`4xx5-:3 rArr (4xx5)/3 rArr 20/3`

What I did here was that instead of dividing by 3, I multiplied by its inverse, `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:

`25-20/3`

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*3/3=75/3 rArr 75/3-20/3=55/3`

Now we have a solution as an improper fraction, `55/3`. Let's make it a mixed fraction to finish things off:

`55/3=color(red)(18 1/3)`

Answer 2

`18 1/3`

Explanation:

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

`color(blue)((2+3)^2)color(green)( -4xx5 div3)" "larr` there are two terms.
`color(white)(xx)darrcolor(white)(xxxx)darr`
`=color(blue)((5)^2)color(green)(" "-20 div3)`
`color(white)(xx)darrcolor(white)(xxxxxx)darr`
`=color(blue)(25)color(green)(" "-" "20/3)`

`=25-6 2/3`

`= 19- 2/3`

`=18 1/3`