Calculate The Following Expression:$ 8 + 10 \div 2 - 4 \cdot 2 $

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**Calculating the Expression: A Step-by-Step Guide** =====================================================

Understanding the Order of Operations

When it comes to calculating mathematical expressions, it's essential to follow the order of operations. This ensures that we perform the calculations in the correct order, avoiding any potential errors. The order of operations 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.

Breaking Down the Expression

Now that we've covered the order of operations, let's break down the given expression:

$ 8 + 10 \div 2 - 4 \cdot 2 $

To calculate this expression, we'll follow the order of operations:

Step 1: Evaluate Expressions Inside Parentheses

There are no expressions inside parentheses in this case, so we can move on to the next step.

Step 2: Evaluate Exponents

There are no exponential expressions in this case, so we can move on to the next step.

Step 3: Evaluate Multiplication and Division

We have two multiplication and division operations in this expression:

  • $ 10 \div 2 $
  • $ 4 \cdot 2 $

Let's evaluate these operations:

  • $ 10 \div 2 = 5 $
  • $ 4 \cdot 2 = 8 $

So, the expression now becomes:

$ 8 + 5 - 8 $

Step 4: Evaluate Addition and Subtraction

Now that we've evaluated the multiplication and division operations, we can move on to the addition and subtraction operations:

  • $ 8 + 5 = 13 $
  • $ 13 - 8 = 5 $

And that's the final result!

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. The acronym PEMDAS is often used to remember the order of operations:

  1. Parentheses
  2. Exponents
  3. Multiplication and Division
  4. Addition and Subtraction

Q: How do I evaluate expressions inside parentheses?

A: To evaluate expressions inside parentheses, simply perform the operations inside the parentheses first. For example, if we have the expression $ (2 + 3) \cdot 4 $, we would first evaluate the expression inside the parentheses: $ 2 + 3 = 5 $, and then multiply the result by 4: $ 5 \cdot 4 = 20 $.

Q: What is the difference between multiplication and division?

A: Multiplication and division are both operations that involve numbers, but they have different effects on the result. Multiplication involves adding a number a certain number of times, while division involves finding the result of a number being divided by another number.

Q: Can you give an example of how to evaluate an expression using the order of operations?

A: Let's consider the expression $ 12 + 3 \cdot 2 - 8 $. To evaluate this expression, we would follow the order of operations:

  1. Evaluate the multiplication operation: $ 3 \cdot 2 = 6 $
  2. Add 12 and 6: $ 12 + 6 = 18 $
  3. Subtract 8 from 18: $ 18 - 8 = 10 $

And that's the final result!

Q: What if I have a fraction in my expression?

A: If you have a fraction in your expression, you can simply evaluate it as you would any other number. For example, if you have the expression $ 12 + \frac1}{2} - 8 $, you would first evaluate the fraction $ \frac{1{2} = 0.5 $, and then perform the addition and subtraction operations: $ 12 + 0.5 - 8 = 4.5 $.

Q: Can I use a calculator to evaluate expressions?

A: Yes, you can use a calculator to evaluate expressions. However, it's essential to understand the order of operations and how to evaluate expressions manually, as this will help you to avoid errors and develop a deeper understanding of mathematical concepts.

Q: What if I have a decimal in my expression?

A: If you have a decimal in your expression, you can simply evaluate it as you would any other number. For example, if you have the expression $ 12 + 3.5 - 8 $, you would first perform the addition and subtraction operations: $ 12 + 3.5 = 15.5 $, and then subtract 8: $ 15.5 - 8 = 7.5 $.

Q: Can I use a calculator to evaluate expressions with decimals?

A: Yes, you can use a calculator to evaluate expressions with decimals. However, it's essential to understand how to evaluate expressions manually, as this will help you to avoid errors and develop a deeper understanding of mathematical concepts.

Q: What if I have a negative number in my expression?

A: If you have a negative number in your expression, you can simply evaluate it as you would any other number. For example, if you have the expression $ 12 - 8 $, you would first subtract 8 from 12: $ 12 - 8 = 4 $.

Q: Can I use a calculator to evaluate expressions with negative numbers?

A: Yes, you can use a calculator to evaluate expressions with negative numbers. However, it's essential to understand how to evaluate expressions manually, as this will help you to avoid errors and develop a deeper understanding of mathematical concepts.

Q: What if I have a mixed expression with addition, subtraction, multiplication, and division?

A: If you have a mixed expression with addition, subtraction, multiplication, and division, you can simply follow the order of operations:

  1. Evaluate expressions inside parentheses
  2. Evaluate exponents
  3. Evaluate multiplication and division operations from left to right
  4. Evaluate addition and subtraction operations from left to right

For example, if you have the expression $ 12 + 3 \cdot 2 - 8 \div 2 $, you would first evaluate the multiplication and division operations: $ 3 \cdot 2 = 6 $ and $ 8 \div 2 = 4 $, and then perform the addition and subtraction operations: $ 12 + 6 - 4 = 14 $.

Q: Can I use a calculator to evaluate mixed expressions?

A: Yes, you can use a calculator to evaluate mixed expressions. However, it's essential to understand the order of operations and how to evaluate expressions manually, as this will help you to avoid errors and develop a deeper understanding of mathematical concepts.

Q: What if I have a complex expression with multiple operations?

A: If you have a complex expression with multiple operations, you can simply follow the order of operations:

  1. Evaluate expressions inside parentheses
  2. Evaluate exponents
  3. Evaluate multiplication and division operations from left to right
  4. Evaluate addition and subtraction operations from left to right

For example, if you have the expression $ 12 + 3 \cdot 2 - 8 \div 2 + 4 \cdot 3 - 2 $, you would first evaluate the multiplication and division operations: $ 3 \cdot 2 = 6 $, $ 8 \div 2 = 4 $, and $ 4 \cdot 3 = 12 $, and then perform the addition and subtraction operations: $ 12 + 6 - 4 + 12 - 2 = 24 $.

Q: Can I use a calculator to evaluate complex expressions?

A: Yes, you can use a calculator to evaluate complex expressions. However, it's essential to understand the order of operations and how to evaluate expressions manually, as this will help you to avoid errors and develop a deeper understanding of mathematical concepts.

Q: What if I have a fraction in my complex expression?

A: If you have a fraction in your complex expression, you can simply evaluate it as you would any other number. For example, if you have the expression $ 12 + \frac1}{2} \cdot 3 - 8 \div 2 + 4 \cdot 3 - 2 $, you would first evaluate the fraction $ \frac{1{2} \cdot 3 = 1.5 $, and then perform the addition and subtraction operations: $ 12 + 1.5 - 4 + 12 - 2 = 19.5 $.

Q: Can I use a calculator to evaluate complex expressions with fractions?

A: Yes, you can use a calculator to evaluate complex expressions with fractions. However, it's essential to understand how to evaluate expressions manually, as this will help you to avoid errors and develop a deeper understanding of mathematical concepts.

Q: What if I have a decimal in my complex expression?

A: If you have a decimal in your complex expression, you can simply evaluate it as you would any other number. For example, if you have the expression $ 12 + 3.5 \cdot 2 - 8 \div 2 + 4 \cdot 3 - 2 $, you would first evaluate the multiplication and division operations: $ 3.5 \cdot 2 = 7 $ and $ 8 \div 2 = 4 $, and then perform the addition and subtraction operations: $ 12 + 7 -