Simplify The Expression:$\[ \frac{22-\left(3^2+4\right)}{12 \div 4} \\]

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Introduction

In mathematics, simplifying expressions is a crucial skill that helps us solve problems efficiently. It involves reducing complex expressions to their simplest form, making it easier to understand and work with. In this article, we will simplify the given expression: 22−(32+4)12÷4\frac{22-\left(3^2+4\right)}{12 \div 4}. We will break down the expression into smaller parts, apply the order of operations, and simplify each step until we arrive at the final answer.

Understanding the Expression

The given expression is a fraction with a numerator and a denominator. The numerator is 22−(32+4)22-\left(3^2+4\right), and the denominator is 12÷412 \div 4. To simplify the 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 expression inside the parentheses is 32+43^2+4. To evaluate this expression, we need to follow the order of operations:

  1. Exponents: Evaluate the exponential expression 323^2 first.
  2. Addition: Add the result to 4.

32=93^2 = 9

9+4=139 + 4 = 13

So, the expression inside the parentheses simplifies to 13.

Step 2: Simplify the Numerator

Now that we have evaluated the expression inside the parentheses, we can simplify the numerator:

22−(32+4)=22−13=922 - (3^2 + 4) = 22 - 13 = 9

Step 3: Simplify the Denominator

The denominator is 12÷412 \div 4. To simplify this expression, we can divide 12 by 4:

12÷4=312 \div 4 = 3

Step 4: Simplify the Fraction

Now that we have simplified the numerator and the denominator, we can simplify the fraction:

22−(32+4)12÷4=93\frac{22-\left(3^2+4\right)}{12 \div 4} = \frac{9}{3}

Step 5: Final Simplification

The fraction 93\frac{9}{3} can be simplified further by dividing both the numerator and the denominator by their greatest common divisor, which is 3:

93=3\frac{9}{3} = 3

Therefore, the simplified expression is 3.

Conclusion

Simplifying expressions is an essential skill in mathematics that helps us solve problems efficiently. By following the order of operations and simplifying each step, we can arrive at the final answer. In this article, we simplified the expression 22−(32+4)12÷4\frac{22-\left(3^2+4\right)}{12 \div 4} and arrived at the final answer of 3.

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 order of operations is:

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

Q: How do I simplify a fraction?

A: To simplify a fraction, we need to find the greatest common divisor (GCD) of the numerator and the denominator and divide both numbers by the GCD.

Q: What is the greatest common divisor (GCD)?

A: The greatest common divisor (GCD) of two numbers is the largest number that divides both numbers without leaving a remainder.

Final Answer

The final answer is 3.

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Introduction

In our previous article, we simplified the expression 22−(32+4)12÷4\frac{22-\left(3^2+4\right)}{12 \div 4} and arrived at the final answer of 3. In this article, we will provide a Q&A guide to help you understand the concepts and techniques used to simplify the expression.

Q&A Guide

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:

  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 a fraction?

A: To simplify a fraction, you need to find the greatest common divisor (GCD) of the numerator and the denominator and divide both numbers by the GCD.

Q: What is the greatest common divisor (GCD)?

A: The greatest common divisor (GCD) of two numbers is the largest number that divides both numbers without leaving a remainder.

Q: How do I evaluate expressions inside parentheses?

A: To evaluate expressions inside parentheses, you need to follow the order of operations:

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

Q: What is the difference between a numerator and a denominator?

A: The numerator is the number on top of a fraction, and the denominator is the number on the bottom of a fraction.

Q: How do I simplify a fraction with a variable in the numerator or denominator?

A: To simplify a fraction with a variable in the numerator or denominator, you need to follow the same steps as before:

  1. Simplify the numerator and denominator separately.
  2. Find the GCD of the numerator and denominator.
  3. Divide both numbers by the GCD.

Q: What is the final answer to the expression 22−(32+4)12÷4\frac{22-\left(3^2+4\right)}{12 \div 4}?

A: The final answer to the expression 22−(32+4)12÷4\frac{22-\left(3^2+4\right)}{12 \div 4} is 3.

Tips and Tricks

Tip 1: Always follow the order of operations

When simplifying an expression, always follow the order of operations to ensure that you are performing the operations in the correct order.

Tip 2: Simplify the numerator and denominator separately

When simplifying a fraction, simplify the numerator and denominator separately before finding the GCD.

Tip 3: Use a calculator to check your answer

If you are unsure about your answer, use a calculator to check your work.

Conclusion

Simplifying expressions is an essential skill in mathematics that helps us solve problems efficiently. By following the order of operations and simplifying each step, we can arrive at the final answer. In this article, we provided a Q&A guide to help you understand the concepts and techniques used to simplify the expression 22−(32+4)12÷4\frac{22-\left(3^2+4\right)}{12 \div 4}.

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 order of operations is:

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

Q: How do I simplify a fraction?

A: To simplify a fraction, you need to find the greatest common divisor (GCD) of the numerator and the denominator and divide both numbers by the GCD.

Q: What is the greatest common divisor (GCD)?

A: The greatest common divisor (GCD) of two numbers is the largest number that divides both numbers without leaving a remainder.

Final Answer

The final answer is 3.