How do you evaluate (2+ 3) ^ { 2} - 4\times 5\div 3(2+3)24×5÷3?

2 Answers
Mar 15, 2018

Using PEMDAS, you can calculate the solution to be 18 1/31813

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=52+3=5

Making our expression:

5^2-4xx5-:3524×5÷3

Now, we work on exponents. The only exponent here is the 5^252 term, and that evaluates to: 5^2=2552=25. Let's put that in the expression:

25-4xx5-:3254×5÷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 20/34×5÷34×53203

What I did here was that instead of dividing by 3, I multiplied by its inverse, 1/313. 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:

25-20/325203

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=55/32533=753753203=553

Now we have a solution as an improper fraction, 55/3553. Let's make it a mixed fraction to finish things off:

55/3=color(red)(18 1/3)553=1813

Mar 16, 2018

18 1/31813

Explanation:

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

color(blue)((2+3)^2)color(green)( -4xx5 div3)" "larr(2+3)24×5÷3 there are two terms.
color(white)(xx)darrcolor(white)(xxxx)darr×××
=color(blue)((5)^2)color(green)(" "-20 div3)=(5)2 20÷3
color(white)(xx)darrcolor(white)(xxxxxx)darr××××
=color(blue)(25)color(green)(" "-" "20/3)=25 203

=25-6 2/3=25623

= 19- 2/3=1923

=18 1/3=1813