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Chapter 5: Problem 86

Use the order of operations to find the value of each expression. \(3-7(-1)-6\)

Short Answer

Expert verified
The value of the expression \(3-7(-1)-6\) is -10.

Step by step solution

01

Perform operations within parentheses

Look for operations within parentheses. In this case, there is \(-1\) inside the parentheses. Since it鈥檚 already a single number, no action is needed inside the parentheses.
02

Perform multiplication

After dealing with the parentheses, the next step in the order of operations is multiplication or division. Here we encounter multiplication, \(-7 * -1\), which equals to 7.
03

Perform Subtraction

The final step is to perform subtraction. The expression now reads as \(3 - 7 - 6 \). Subtraction is done from left to right, so first subtract 7 from 3 to get -4. Then subtract 6 from -4 to get -10.

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Key Concepts

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

Understanding Mathematical Expressions
Mathematical expressions are combinations of numbers, variables, and operations (like addition or multiplication) that represent a value. They do not have an equal sign, unlike equations, which show two expressions are equal. Instead, expressions tell us instructions about how to calculate or transform the numbers involved.
For example, in the expression \(3-7(-1)-6\), instructions are embedded in both the operators (subtraction and multiplication) and the presence of parentheses. Practicing these can help in understanding how to solve mathematical problems correctly.
The Role of Multiplication in Expressions
Multiplication is a core arithmetic operation that combines groups of equal sizes. In expressions like \(-7(-1)\), multiplication acts as a form of addition but with repeated groups. Here, multiplying
  • Two negative numbers (-7 and -1) results in a positive number. When two negative signs interact, they produce a positive product, which is 7.
  • For clear understanding, remember that multiplying two negatives always results in a positive.
This basic rule is fundamental when working with algebraic or arithmetic expressions.
Subtraction in Math: Simplifying Differences
Subtraction, or taking away, is the process used to find the difference between numbers. It's conceptually the opposite of addition. In our example, the expression simplifies through subtraction: once after multiplication is complete, we subtract from left to right.
  • Start with 3, subtract 7 to get -4.
  • Then, subtract 6 from -4 to get -10.
Subtraction must be executed from left to right, as per the order of operations, making it crucial to practice how to correctly apply it following other operations.
Working with Parentheses in Math
Parentheses are symbols used to group parts of mathematical expressions, indicating operations should be performed first, overriding the typical order. They help clarify which operations take priority and ensure expressions are solved accurately. In the noted expression, \(-1\) is within parentheses, though no direct calculations are needed within.
  • Parentheses cue that any operations inside should be done before others.
  • They help manage complex operations by organizing which mathematical steps to prioritize.
Grasping the utility of parentheses is essential for handling intricate expressions and ensuring correct solutions.

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Most popular questions from this chapter

Write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for \(a_{n}\) to find \(a_{7}\), the seventh term of the sequence. \(5,-1, \frac{1}{5},-\frac{1}{25}, \ldots\)

Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{20}\), when \(a_{1}=2, r=2\).

Write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for \(a_{n}\) to find \(a_{7}\), the seventh term of the sequence. \(0.0004,-0.004,0.04,-0.4, \ldots\)

What is a geometric sequence? Give an example with your description.

Determine whether each statement makes sense or does not make sense, and explain your reasoning. The sequence for the number of seats per row in our movie theater as the rows move toward the back is arithmetic with \(d=1\) so people don't block the view of those in the row behind them.
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