Question

calculate the following expressionusing the order of operations. show all steps( do not combine more than two numbers together at a time) and write your answer as a mixed fraction if neccessary. show all steps for answer

(7/15 +125/9)2 - 16 multiplies* 0.25 divides 2

Answer 1

Answer: $204\frac{2}{5}$

Step-by-step explanation:

Given the following expression:

$(\frac{7}{15}+\frac{125}{9})^2-16(\frac{0.25}{2})$

You can follow these steps in order to solve the exercise:

1. You need to solve the operations inside the parentheses:

- Add the fractions. Since they have different denominators, you have to find the Least Comon Denominator (LCD):

$15=3*5\\9=3*3=3^2\\LCD=5*3^2=45$

- Solve the division divididing the numerator 0.25 by the denominator 2.

Then, you get:

$(\frac{(3)(7)+(5)(125)}{45})^2-16(\frac{0.25}{2})\\\\(\frac{646}{45})^2-16(0.125)$

2. Solve the exponent:

$\(\frac{417,316}{2,025}-16(0.125)$

3. Solve the multiplication:

$\(\frac{417,316}{2,025}-2$

4. Solve the subtraction:

$\(\frac{417,316-(2,025)(2)}{2,025}=\frac{413,266}{2,025}\approx204.08$

5. Since :

$0.8=\frac{2}{5}$

You can write the result as a mixed fraction:

$=204\frac{2}{5}$