Simplify The Expression: ${ -5 \times (-3 + 7) + 20 \div (-4) }$

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Introduction

In this article, we will simplify the given mathematical expression step by step. The expression is: ${ -5 \times (-3 + 7) + 20 \div (-4) }$. We will use the order of operations (PEMDAS) to simplify the expression.

Understanding 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 acronym 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.

Step 1: Evaluate the Expression Inside the Parentheses

The expression inside the parentheses is: ${ -3 + 7 }$. We will evaluate this expression first.

−3+7=4{ -3 + 7 = 4 }

So, the expression becomes: ${ -5 \times 4 + 20 \div (-4) }$.

Step 2: Multiply -5 and 4

Next, we will multiply -5 and 4.

−5×4=−20{ -5 \times 4 = -20 }

So, the expression becomes: ${ -20 + 20 \div (-4) }$.

Step 3: Divide 20 by -4

Next, we will divide 20 by -4.

20÷(−4)=−5{ 20 \div (-4) = -5 }

So, the expression becomes: ${ -20 + (-5) }$.

Step 4: Add -20 and -5

Finally, we will add -20 and -5.

−20+(−5)=−25{ -20 + (-5) = -25 }

Therefore, the simplified expression is: ${ -25 }$.

Conclusion

In this article, we simplified the given mathematical expression step by step using the order of operations (PEMDAS). We evaluated the expression inside the parentheses, multiplied -5 and 4, divided 20 by -4, and finally added -20 and -5. The simplified expression is: ${ -25 }$.

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. The acronym PEMDAS stands for: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Q: How do I evaluate expressions inside parentheses?

A: To evaluate expressions inside parentheses, we simply perform the operations inside the parentheses first.

Q: How do I multiply and divide numbers?

A: To multiply and divide numbers, we follow the order of operations. We multiply and divide numbers from left to right.

Q: How do I add and subtract numbers?

A: To add and subtract numbers, we follow the order of operations. We add and subtract numbers from left to right.

Glossary of Terms

PEMDAS

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

Parentheses

Parentheses are used to group numbers and operations together. We evaluate expressions inside parentheses first.

Exponents

Exponents are used to indicate repeated multiplication. For example, 232^3 means 2×2×22 \times 2 \times 2.

Multiplication and Division

Multiplication and division are operations that are performed from left to right.

Addition and Subtraction

Addition and subtraction are operations that are performed from left to right.

References

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 stands for: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Q: How do I evaluate expressions inside parentheses?

A: To evaluate expressions inside parentheses, we simply perform the operations inside the parentheses first.

Q: What is the difference between multiplication and division?

A: Multiplication and division are both operations that are performed from left to right. However, multiplication involves multiplying two or more numbers together, while division involves dividing one number by another.

Q: How do I add and subtract numbers?

A: To add and subtract numbers, we follow the order of operations. We add and subtract numbers from left to right.

Q: What is the difference between addition and subtraction?

A: Addition and subtraction are both operations that are performed from left to right. However, addition involves combining two or more numbers together, while subtraction involves finding the difference between two numbers.

Q: How do I simplify a mathematical expression?

A: To simplify a mathematical expression, we follow the order of operations. We evaluate expressions inside parentheses first, then perform any exponential operations, followed by multiplication and division, and finally addition and subtraction.

Q: What is the importance of simplifying mathematical expressions?

A: Simplifying mathematical expressions is important because it helps us to:

  • Evaluate expressions more easily
  • Avoid errors
  • Understand the underlying math concepts
  • Solve problems more efficiently

Q: How do I know when to use parentheses?

A: We use parentheses to group numbers and operations together when we need to evaluate an expression in a specific order. For example, if we have the expression 2+3×42 + 3 \times 4, we would use parentheses to group the multiplication operation first, like this: (2+3)×4(2 + 3) \times 4.

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

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

Q: How do I simplify an expression with variables?

A: To simplify an expression with variables, we follow the same steps as before. We evaluate expressions inside parentheses first, then perform any exponential operations, followed by multiplication and division, and finally addition and subtraction.

Q: What is the importance of understanding the order of operations?

A: Understanding the order of operations is important because it helps us to:

  • Evaluate expressions correctly
  • Avoid errors
  • Understand the underlying math concepts
  • Solve problems more efficiently

Q: How do I practice simplifying mathematical expressions?

A: To practice simplifying mathematical expressions, try the following:

  • Start with simple expressions and work your way up to more complex ones
  • Use online resources or math apps to practice simplifying expressions
  • Work with a partner or tutor to get help and feedback
  • Practice regularly to build your skills and confidence

Conclusion

Simplifying mathematical expressions is an important skill that can help us to evaluate expressions correctly, avoid errors, and understand the underlying math concepts. By following the order of operations and practicing regularly, we can become more confident and proficient in simplifying mathematical expressions.