Question

Evaluate.
16 ÷ (2 + 1/2) ^2
A) 2 14/25
B) 4 1/4
C) 6 2/5
D) 8 1/4

Answer 1

Answer:

$\bold{2\frac{14}{25}}$

Step-by-step explanation:

Follow the PEMDAS order of operations

P = Parenthesis

E = Exponents

M = Multiplication

D = Division

A = Addition

S = Subtraction

Step 1: Parenthesis

The first operation is parenthesis "()", and we have parenthesis so we solve the parenthesis first.

$16\div(2+\frac{1}{2})^2\\\\=\frac{16}{\left(2+\frac{1}{2}\right)^2}$

$\underline{\mathrm{Solve}}\\\\(2+\frac{1}{2})\\\\=2+\frac{1}{2}\\\\=2\frac{1}{2}$

$\frac{16}{\left(2\frac{1}{2}\right)^2}$

Step 2: Exponents

The Exponent is the tiny number on top of a bigger number. For example, we have $2\frac{1}{2}^\bold{2}$, and the bolded part is the exponent. And the number there is how many times you will multiply the bigger number to itself. So we can simplify:

$(2\frac{1}{2})^2\\\\=2\frac{1}{2}\times2\frac{1}{2}\\\\=6\frac{1}{4}$

$\frac{16}{6\frac{1}{4}}$

Step 3: Division

We don't have any multiplication, so we skip to the next operation in the order. Division:

$\frac{16}{6\frac{1}{4}}=2\frac{14}{25}\\\\\bold{2\frac{14}{25}}$