Simplify The Expression:${ 7 - { (-4 \times 2) - (8 - 6) } }$

Introduction

Mathematical expressions can be complex and overwhelming, especially when they involve multiple operations and parentheses. In this article, we will simplify the expression $7 - \{ (-4 \times 2) - (8 - 6) \}$, breaking it down into manageable steps and providing a clear understanding of the mathematical concepts involved.

Understanding the Expression

The given expression is $7 - \{ (-4 \times 2) - (8 - 6) \}$. To simplify this expression, we need to follow the order of operations (PEMDAS):

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.

Step 1: Evaluate Expressions Inside Parentheses

The first step is to evaluate the expressions inside the parentheses. We have two sets of parentheses: $(-4 \times 2)$ and $(8 - 6)$.

Evaluating $(-4 \times 2)$

To evaluate $(-4 \times 2)$, we multiply $-4$ by $2$. This gives us:

$$(-4 \times 2) = -8$$

Evaluating $(8 - 6)$

To evaluate $(8 - 6)$, we subtract $6$ from $8$. This gives us:

$$(8 - 6) = 2$$

Step 2: Substitute the Values Back into the Original Expression

Now that we have evaluated the expressions inside the parentheses, we can substitute the values back into the original expression:

$$7 - \{ (-8) - 2 \}$$

Step 3: Evaluate the Expression Inside the Curly Brackets

The next step is to evaluate the expression inside the curly brackets. We have $(-8) - 2$.

Evaluating $(-8) - 2$

To evaluate $(-8) - 2$, we subtract $2$ from $-8$. This gives us:

$$(-8) - 2 = -10$$

Step 4: Substitute the Value Back into the Original Expression

Now that we have evaluated the expression inside the curly brackets, we can substitute the value back into the original expression:

$$7 - (-10)$$

Step 5: Evaluate the Final Expression

The final step is to evaluate the expression $7 - (-10)$. To do this, we need to remember that subtracting a negative number is the same as adding a positive number.

Evaluating $7 - (-10)$

To evaluate $7 - (-10)$, we add $10$ to $7$. This gives us:

$$7 - (-10) = 17$$

Conclusion

In this article, we simplified the expression $7 - \{ (-4 \times 2) - (8 - 6) \}$ by following the order of operations (PEMDAS). We evaluated the expressions inside the parentheses, substituted the values back into the original expression, evaluated the expression inside the curly brackets, and finally evaluated the final expression. The simplified expression is $17$.

Frequently Asked Questions

• Q: What is the order of operations (PEMDAS)? A: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The acronym PEMDAS stands for:
  • Parentheses
  • Exponents
  • Multiplication and Division
  • Addition and Subtraction
• Q: How do I evaluate expressions inside parentheses? A: To evaluate expressions inside parentheses, we need to follow the order of operations (PEMDAS). We start by evaluating any exponential expressions, then any multiplication and division operations, and finally any addition and subtraction operations.
• Q: How do I evaluate expressions with curly brackets? A: To evaluate expressions with curly brackets, we need to follow the order of operations (PEMDAS). We start by evaluating any expressions inside the curly brackets, then substitute the value back into the original expression.

Final Thoughts

Simplifying mathematical expressions can be a challenging task, but by following the order of operations (PEMDAS) and breaking down the expression into manageable steps, we can make it easier to understand and evaluate. In this article, we simplified the expression $7 - \{ (-4 \times 2) - (8 - 6) \}$, providing a clear understanding of the mathematical concepts involved.

Introduction

In our previous article, we simplified the expression $7 - \{ (-4 \times 2) - (8 - 6) \}$ by following the order of operations (PEMDAS). In this article, we will provide a Q&A guide to help you understand and evaluate mathematical expressions.

Q&A Guide

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The acronym PEMDAS stands for: + Parentheses + Exponents + Multiplication and Division + Addition and Subtraction

Q: How do I evaluate expressions inside parentheses?

A: To evaluate expressions inside parentheses, you need to follow the order of operations (PEMDAS). You start by evaluating any exponential expressions, then any multiplication and division operations, and finally any addition and subtraction operations.

Q: How do I evaluate expressions with curly brackets?

A: To evaluate expressions with curly brackets, you need to follow the order of operations (PEMDAS). You start by evaluating any expressions inside the curly brackets, then substitute the value back into the original expression.

Q: What is the difference between subtraction and negative numbers?

A: When you see a negative number in an expression, it means you need to change the sign of the number. For example, $-5$ means $-5$ is the same as $-1 \times 5$. When you see a subtraction operation, it means you need to subtract one number from another. For example, $5 - 3$ means $5$ minus $3$.

Q: How do I evaluate expressions with multiple operations?

A: To evaluate expressions with multiple operations, you need to follow the order of operations (PEMDAS). You start by evaluating any expressions inside parentheses, then any exponential expressions, then any multiplication and division operations, and finally any addition and subtraction operations.

Q: What is the difference between multiplication and division?

A: Multiplication and division are both operations that involve numbers, but they have different meanings. Multiplication means adding a number a certain number of times, while division means sharing a number into equal groups.

Q: How do I evaluate expressions with fractions?

A: To evaluate expressions with fractions, you need to follow the order of operations (PEMDAS). You start by evaluating any expressions inside parentheses, then any exponential expressions, then any multiplication and division operations, and finally any addition and subtraction operations.

Q: What is the difference between addition and subtraction?

A: Addition and subtraction are both operations that involve numbers, but they have different meanings. Addition means combining two or more numbers, while subtraction means finding the difference between two numbers.

Q: How do I evaluate expressions with decimals?

A: To evaluate expressions with decimals, you need to follow the order of operations (PEMDAS). You start by evaluating any expressions inside parentheses, then any exponential expressions, then any multiplication and division operations, and finally any addition and subtraction operations.

Conclusion

In this article, we provided a Q&A guide to help you understand and evaluate mathematical expressions. We covered topics such as the order of operations (PEMDAS), evaluating expressions inside parentheses, and evaluating expressions with multiple operations. We also covered topics such as the difference between subtraction and negative numbers, the difference between multiplication and division, and the difference between addition and subtraction.

Frequently Asked Questions

• Q: What is the order of operations (PEMDAS)? A: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when we have multiple operations in an expression.
• Q: How do I evaluate expressions inside parentheses? A: To evaluate expressions inside parentheses, you need to follow the order of operations (PEMDAS).
• Q: How do I evaluate expressions with curly brackets? A: To evaluate expressions with curly brackets, you need to follow the order of operations (PEMDAS).
• Q: What is the difference between subtraction and negative numbers? A: When you see a negative number in an expression, it means you need to change the sign of the number.
• Q: How do I evaluate expressions with multiple operations? A: To evaluate expressions with multiple operations, you need to follow the order of operations (PEMDAS).

Final Thoughts

Evaluating mathematical expressions can be a challenging task, but by following the order of operations (PEMDAS) and breaking down the expression into manageable steps, we can make it easier to understand and evaluate. In this article, we provided a Q&A guide to help you understand and evaluate mathematical expressions. We covered topics such as the order of operations (PEMDAS), evaluating expressions inside parentheses, and evaluating expressions with multiple operations. We also covered topics such as the difference between subtraction and negative numbers, the difference between multiplication and division, and the difference between addition and subtraction.