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Chapter 2: Problem 33

Simplify using the order of operations. $$12+(14-16)^{2} \div(-4)$$

Short Answer

Expert verified
11

Step by step solution

01

Identify the expression inside the parentheses

First, look at the expression inside the parentheses: \ \(14 - 16\).
02

Simplify the expression inside the parentheses

Perform the subtraction inside the parentheses: \ \(14 - 16 = -2\).
03

Square the result from the parentheses

Next, square the result from step 2: \ \((-2)^2 = 4\).
04

Divide by the given number

Now, divide the squared result by -4: \ \(4 \div (-4) = -1\).
05

Add to the initial number

Finally, add the result from step 4 to 12: \ \(12 + (-1) = 11\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

parentheses in math
In mathematics, parentheses serve to group parts of an expression that should be treated as a single unit. They help clarify which operations should be performed first.
According to the order of operations, expressions inside parentheses (parentheses....) have priority over other operations.
For example, in the expression (14 - 16), the subtraction must be performed before dealing with any external operations.
simplifying expressions
Simplifying expressions involves performing operations in such a way that the expression becomes easier to understand or work with.
The idea is to reduce it to its simplest form without changing its value.
In the given problem, we started with the expression (14 - 16), which simplifies to -2.
As you can see, operations within parentheses are taken care of first.
squaring numbers
Squaring a number means multiplying the number by itself.
This is denoted by an exponent of 2.
For example, (-2)^2 means -2 multiplied by -2, which equals 4.
It's a crucial step in our example where we squared -2 to get 4.
division
Division is the process of determining how many times one number is contained within another.
It鈥檚 represented by the symbol \(\textdiv\).
In our problem, we divided 4 by -4 resulting in -1.
This part is often straightforward, but always remember to include the correct sign for the result.
addition in algebra
Addition in algebra follows the same basic rules as in arithmetic but can often involve variables. In our problem, we simply added -1 to 12.
When performing addition, always combine like terms to simplify equations effectively.
In this case, we combined 12 and -1 to get our final result, 11.

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Most popular questions from this chapter

Rank the numbers from least to greatest. If \(d\) represents a negative number, then what is the sign of \(-(-d) ?\)

Perform the indicated operation. $$\frac{0}{-5}$$

Jeff's balance in his checking account was 2036 dollar at the beginning of the week. During the week, he wrote two checks, made two deposits, and made one ATM withdrawal. What is his ending balance? $$\begin{array}{l|r} \hline \text { Check } & -\$ 150 \\ \hline \text { Check } & -\$ 25 \\ \hline \text { Paycheck (deposit) } & \$ 480 \\ \hline \text { ATM } & -\$ 200 \\ \hline \text { Cash (deposit) } & \$ 80 \\ \hline \end{array}$$

Translate the English phrase to a mathematical expression. Then simplify. \(-108\) divided by \(-4\)

Translate each English phrase to a mathematical expression. Then simplify. 320 decreased by \(-20\)
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