Evaluate The Expression: $ \{[-15-(-3+2)] \times 3\} \div 6 $

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Introduction

In this article, we will evaluate the given mathematical expression step by step. The expression is $ {[-15-(-3+2)] \times 3} \div 6 $. We will use the order of operations (PEMDAS) to simplify the expression and find the final result.

Understanding the Order of Operations

Before we start evaluating the expression, it's essential to understand the order of operations. PEMDAS is a mnemonic device that helps us remember the order of operations:

  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.

Evaluating the Expression

Now that we understand the order of operations, let's start evaluating the expression step by step.

Step 1: Evaluate the Expression Inside the Parentheses

The expression inside the parentheses is −3+2-3+2. We will evaluate this expression first.

−3+2=−1-3+2 = -1

So, the expression becomes:

$ {[-15-(-1)] \times 3} \div 6 $

Step 2: Evaluate the Expression Inside the Parentheses Again

The expression inside the parentheses is −15−(−1)-15-(-1). We will evaluate this expression next.

−15−(−1)=−15+1=−14-15-(-1) = -15+1 = -14

So, the expression becomes:

$ {-14 \times 3} \div 6 $

Step 3: Multiply -14 and 3

Now, we will multiply −14-14 and 33.

−14×3=−42-14 \times 3 = -42

So, the expression becomes:

$ {-42} \div 6 $

Step 4: Divide -42 by 6

Finally, we will divide −42-42 by 66.

−42÷6=−7-42 \div 6 = -7

So, the final result of the expression is −7-7.

Conclusion

In this article, we evaluated the given mathematical expression step by step using the order of operations (PEMDAS). We started by evaluating the expressions inside the parentheses, then multiplied and divided the numbers, and finally added and subtracted the numbers. The final result of the expression is −7-7.

Frequently Asked Questions

  • What is the order of operations? 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 order of operations is PEMDAS: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
  • How do I evaluate an expression using the order of operations? To evaluate an expression using the order of operations, follow these steps:
  1. Evaluate any expressions inside parentheses.
  2. Evaluate any exponential expressions.
  3. Evaluate any multiplication and division operations from left to right.
  4. Finally, evaluate any addition and subtraction operations from left to right.

Tips and Tricks

  • Always follow the order of operations when evaluating expressions.
  • Use parentheses to group numbers and operations together.
  • Exponential expressions should be evaluated before multiplication and division operations.
  • Multiplication and division operations should be evaluated from left to right.
  • Addition and subtraction operations should be evaluated from left to right.

Further Reading

  • For more information on the order of operations, see the Khan Academy article on PEMDAS.
  • For more practice problems on evaluating expressions using the order of operations, see the Mathway website.

References

Introduction

Evaluating mathematical expressions can be a challenging task, especially when dealing with complex expressions that involve multiple operations. In this article, we will answer some of the most frequently asked questions about evaluating mathematical expressions.

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 order of operations is PEMDAS: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

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

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

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

Q: What is the difference between multiplication and division?

A: Multiplication and division are both operations that involve numbers, but they have different rules. Multiplication involves multiplying two or more numbers together, while division involves dividing one number by another.

Q: How do I evaluate an expression with multiple operations?

A: To evaluate an expression with multiple operations, follow the order of operations. First, evaluate any expressions inside parentheses, then evaluate any exponential expressions, followed by any multiplication and division operations, and finally evaluate 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 rules. Addition involves adding two or more numbers together, while subtraction involves subtracting one number from another.

Q: How do I evaluate an expression with negative numbers?

A: To evaluate an expression with negative numbers, follow the same rules as you would for positive numbers. When multiplying or dividing negative numbers, the result will be negative. When adding or subtracting negative numbers, the result will be positive.

Q: What is the difference between a fraction and a decimal?

A: A fraction is a way of expressing a part of a whole, while a decimal is a way of expressing a number as a sum of powers of 10. Fractions and decimals can be converted to each other using division.

Q: How do I evaluate an expression with fractions and decimals?

A: To evaluate an expression with fractions and decimals, follow the same rules as you would for positive numbers. When multiplying or dividing fractions and decimals, the result will be a fraction or decimal. When adding or subtracting fractions and decimals, the result will be a fraction or decimal.

Q: What is the difference between a variable and a constant?

A: A variable is a symbol that represents a value that can change, while a constant is a value that does not change.

Q: How do I evaluate an expression with variables and constants?

A: To evaluate an expression with variables and constants, follow the same rules as you would for positive numbers. When multiplying or dividing variables and constants, the result will be a variable or constant. When adding or subtracting variables and constants, the result will be a variable or constant.

Q: What is the difference between a linear equation and a quadratic equation?

A: A linear equation is an equation that involves a linear expression, while a quadratic equation is an equation that involves a quadratic expression.

Q: How do I evaluate an expression with linear and quadratic equations?

A: To evaluate an expression with linear and quadratic equations, follow the same rules as you would for positive numbers. When multiplying or dividing linear and quadratic equations, the result will be a linear or quadratic equation. When adding or subtracting linear and quadratic equations, the result will be a linear or quadratic equation.

Conclusion

Evaluating mathematical expressions can be a challenging task, but by following the order of operations and understanding the rules of arithmetic, you can evaluate expressions with confidence. Remember to always follow the order of operations, and to evaluate expressions with fractions, decimals, variables, and constants using the same rules as you would for positive numbers.

Frequently Asked Questions

  • What is the order of operations?
  • How do I evaluate an expression using the order of operations?
  • What is the difference between multiplication and division?
  • How do I evaluate an expression with multiple operations?
  • What is the difference between addition and subtraction?
  • How do I evaluate an expression with negative numbers?
  • What is the difference between a fraction and a decimal?
  • How do I evaluate an expression with fractions and decimals?
  • What is the difference between a variable and a constant?
  • How do I evaluate an expression with variables and constants?
  • What is the difference between a linear equation and a quadratic equation?
  • How do I evaluate an expression with linear and quadratic equations?

Tips and Tricks

  • Always follow the order of operations when evaluating expressions.
  • Use parentheses to group numbers and operations together.
  • Exponential expressions should be evaluated before multiplication and division operations.
  • Multiplication and division operations should be evaluated from left to right.
  • Addition and subtraction operations should be evaluated from left to right.
  • Fractions and decimals can be converted to each other using division.
  • Variables and constants can be evaluated using the same rules as positive numbers.

Further Reading

  • For more information on evaluating mathematical expressions, see the Khan Academy article on PEMDAS.
  • For more practice problems on evaluating expressions, see the Mathway website.

References