Problem 109 In the following exercises, simp... [FREE SOLUTION]

Chapter 1: Problem 109

In the following exercises, simplify using the order of operations. $$ 2^{3}-12 \div(9-5) $$

Short Answer

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Step by step solution

Evaluate Expressions Within Parentheses

First, solve the expression within the parentheses. Here we have (9-5) which is equal to 4. So the expression becomes 2^3 - 12 梅 4.

Perform Exponentiation

Next, evaluate the exponent. 2^3 = 8. So the expression now is 8 - 12 梅 4.

Perform Division

Perform the division operation next. 12 梅 4 = 3. So the expression becomes 8 - 3.

Perform Subtraction

Finally, perform the subtraction operation. 8 - 3 = 5.

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Key Concepts

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

Evaluating Expressions

Evaluating expressions is a critical skill in algebra and mathematics in general. This involves simplifying an expression to its simplest form. To do this, you need to apply the order of operations correctly. The order of operations is a rule that defines the sequence in which different operations should be performed to correctly evaluate an expression. Remember PEMDAS:

Parentheses
Exponents
Multiplication and Division (from left to right)
Addition and Subtraction (from left to right)

Following these rules ensures that everyone can get the same correct result when evaluating an expression.

Exponentiation

Exponentiation is a way to raise a number to a certain power. In the expression, our exponentiation is shown by the term $2^3$. This means that we multiply 2 by itself three times:

$2 \times 2 \times 2 = 8$.

Exponentiation must come after evaluating expressions within parentheses but before performing multiplication, division, addition, or subtraction. It is essential to write out each step when you're learning, so you don't skip any operations.

Division

Division is one of the four fundamental arithmetic operations. In our simplified expression (after parentheses and exponentiation), we have 8 - $12 梅 4$. Our focus now is on division.
When you divide 12 by 4, you get 3, so the expression now simplifies to 8 - 3. Here, division is performed before subtraction because that is the correct sequence according to PEMDAS rules. Always remember to perform division and multiplication from left to right, as they appear in the expression.

Subtraction

Finally, subtraction is the last operation we perform. Our simplified expression is now 8 - 3.

Subtraction means taking away or deducting a value from another. So, when you subtract 3 from 8, you get 5. This is our final simplified answer.
Keeping the order clear helps in double-checking your work and ensures accuracy in your results. So the full answer to the original problem is 5.

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91影视

In the following exercises, simplify using the order of operations. $$ 2^{3}-12 \div(9-5) $$

Short Answer

Step by step solution

Evaluate Expressions Within Parentheses

Perform Exponentiation

Perform Division

Perform Subtraction

Key Concepts

Evaluating Expressions

Exponentiation

Division

Subtraction

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