GED Math - Order of Operations

Simplify the following expression:

Explanation

Remember the order of operations: PEMDAS

Start by simplifying what is found in the parentheses:

Next, simplify the exponents.

Next, take care of any multiplication and division.

Finally, add and subtract.

Evaluate: $\frac{a+ b^{2}}{b }$

$8 \frac{1}{3}$

$9\frac{2}{3}$

Explanation

Substitute and 9 for and in the expression:

$\frac{a+ b^{2}}{b }$

$=\frac{-6+ 9^{2}}{9 }$

Evaluate the numerator first. Since exponentiation takes precedence over addition in the order of operations, square 9 first:

$=\frac{-6+(9 \times 9) }{9 }$

$=\frac{-6+81 }{9 }$

Now, add as follows:

$=\frac{+(81-6) }{9 }$

$= \frac{75}{9}$

This fraction can be simplified by dividing both halves by 3:

$= \frac{75 \div 3 }{9 \div 3 }$

$= \frac{25 }{3 }$

Divide 25 by 3 to restate this as a mixed fraction:

$25 \div 3 = 8 \textup{ R }1$ , so

$\frac{25 }{3 } =\textbf{8} \frac{\textbf{1}}{\textbf{3}}$ ,

the correct value.

Suppose the values of all of the variables in the expression

$a - b \div c \cdot d +e$

are known. In order to evaluate this expression, what would be the first step?

Division

Addition

Subtraction

Multiplication

Explanation

In the absence of grouping symbols, the first operations that should be carried out are exponentiations, of which there are none here.

The next operations to be carried out are the multiplications and divisions, from left to right. The division is to the left, so it is executed first.

In order to calculate

$250 - 200 \div \left (6+4 \right )^{2}$

what step must you take first?

Adding six and four

Subtracting two hundred from two hundred fifty

Dividing two hundred by six

Squaring four

Explanation

By the order of operations, the operation(s) within grouping symbols - here, the addition of six and four - must be carried out first.

Simplify the following expression:

Explanation

Simplify the following expression:

Recall PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. This is our order of operations, the order we need to go in when simplifying mathematical expressions.

Let's begin with parentheses. We need to simplify the innermost parentheses first:

Next, we need to simplify the exponent on the 4.

Now, we went through a lot there, but basically, by simplifying the 4 squared and then subtracting it from 16, we made the inside of our parentheses "0". When we multiplied the 4 through, everything within the parentheses canceled out, leaving us with just 12.

So, our answer is 12

Jeff went to the casino with $1,000 in his pocket. He lost $400 of it playing blackjack, won $900 playing craps, then left the casino. How much money did he leave with?

Do not use a calculator.