Simplify The Expression Using The Order Of Operations:$\[ 8^3 - 2 \left( \frac{3+30}{3} \right) \\]

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Introduction

The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. It is a crucial concept in mathematics, and it helps us to simplify complex expressions. In this article, we will simplify the given expression using the order of operations.

The Order of Operations

The order of operations is a mnemonic device that helps us to remember the order in which we should perform operations. It is often remembered using the acronym PEMDAS, which stands for:

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next.
  3. Multiplication and Division: Evaluate multiplication and division operations from left to right.
  4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

The Given Expression

The given expression is:

83−2(3+303){ 8^3 - 2 \left( \frac{3+30}{3} \right) }

Step 1: Evaluate the Exponential Expression

The first step is to evaluate the exponential expression, which is 838^3. This means that we need to raise 8 to the power of 3.

83=8×8×8=512{ 8^3 = 8 \times 8 \times 8 = 512 }

Step 2: Evaluate the Expression Inside the Parentheses

The next step is to evaluate the expression inside the parentheses, which is 3+303\frac{3+30}{3}. This means that we need to add 3 and 30, and then divide the result by 3.

3+303=333=11{ \frac{3+30}{3} = \frac{33}{3} = 11 }

Step 3: Multiply 2 by the Result

Now that we have evaluated the expression inside the parentheses, we can multiply 2 by the result.

2×11=22{ 2 \times 11 = 22 }

Step 4: Subtract 22 from 512

Finally, we can subtract 22 from 512 to get the final result.

512−22=490{ 512 - 22 = 490 }

Conclusion

In this article, we simplified the given expression using the order of operations. We evaluated the exponential expression, the expression inside the parentheses, multiplied 2 by the result, and finally subtracted 22 from 512 to get the final result. The order of operations is a crucial concept in mathematics, and it helps us to simplify complex expressions.

Frequently Asked Questions

Q: What is the order of operations?

A: The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. It is often remembered using the acronym PEMDAS.

Q: What is PEMDAS?

A: PEMDAS is a mnemonic device that helps us to remember the order in which we should perform operations. It stands for:

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next.
  3. Multiplication and Division: Evaluate multiplication and division operations from left to right.
  4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I simplify an expression using the order of operations?

A: To simplify an expression using the order of operations, follow these steps:

  1. Evaluate any exponential expressions.
  2. Evaluate any expressions inside parentheses.
  3. Multiply and divide operations from left to right.
  4. Finally, evaluate any addition and subtraction operations from left to right.

References

Further Reading

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Introduction

In our previous article, we simplified the expression 83−2(3+303)8^3 - 2 \left( \frac{3+30}{3} \right) using the order of operations. In this article, we will answer some frequently asked questions about simplifying expressions using the order of operations.

Q&A

Q: What is the order of operations?

A: The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. It is often remembered using the acronym PEMDAS.

Q: What does PEMDAS stand for?

A: PEMDAS stands for:

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next.
  3. Multiplication and Division: Evaluate multiplication and division operations from left to right.
  4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I simplify an expression using the order of operations?

A: To simplify an expression using the order of operations, follow these steps:

  1. Evaluate any exponential expressions.
  2. Evaluate any expressions inside parentheses.
  3. Multiply and divide operations from left to right.
  4. Finally, evaluate any addition and subtraction operations from left to right.

Q: What if I have multiple operations with the same precedence?

A: If you have multiple operations with the same precedence, you should evaluate them from left to right. For example, if you have the expression 3×2+4÷23 \times 2 + 4 \div 2, you should evaluate the multiplication and division operations from left to right, and then evaluate the addition operation.

Q: Can I use the order of operations to simplify expressions with fractions?

A: Yes, you can use the order of operations to simplify expressions with fractions. For example, if you have the expression 12×3+14÷2\frac{1}{2} \times 3 + \frac{1}{4} \div 2, you should evaluate the multiplication and division operations from left to right, and then evaluate the addition operation.

Q: How do I simplify expressions with negative numbers?

A: To simplify expressions with negative numbers, you should follow the same steps as you would with positive numbers. For example, if you have the expression −3×2+4÷2-3 \times 2 + 4 \div 2, you should evaluate the multiplication and division operations from left to right, and then evaluate the addition operation.

Q: Can I use the order of operations to simplify expressions with decimals?

A: Yes, you can use the order of operations to simplify expressions with decimals. For example, if you have the expression 3.5×2+4.2÷23.5 \times 2 + 4.2 \div 2, you should evaluate the multiplication and division operations from left to right, and then evaluate the addition operation.

Conclusion

In this article, we answered some frequently asked questions about simplifying expressions using the order of operations. We covered topics such as the order of operations, PEMDAS, simplifying expressions with fractions, negative numbers, and decimals. By following the steps outlined in this article, you should be able to simplify complex expressions using the order of operations.

Further Reading

References