Evaluate The Expression:${ \left(\frac{q}{2} + \frac{s}{2}\right) \div \frac{11}{2} \div \frac{1}{6} }$

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Introduction

In this article, we will delve into the world of mathematics and evaluate a given expression. The expression in question is (q2+s2)÷112÷16\left(\frac{q}{2} + \frac{s}{2}\right) \div \frac{11}{2} \div \frac{1}{6}. We will break down the expression into smaller parts, simplify it, and finally arrive at the solution.

Understanding the Expression

The given expression involves several mathematical operations, including addition, division, and multiplication. To evaluate 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.

Breaking Down the Expression

Let's break down the expression into smaller parts:

(q2+s2)÷112÷16\left(\frac{q}{2} + \frac{s}{2}\right) \div \frac{11}{2} \div \frac{1}{6}

We can start by evaluating the expression inside the parentheses:

q2+s2\frac{q}{2} + \frac{s}{2}

This expression involves adding two fractions with the same denominator (2). We can combine the fractions by adding their numerators:

q+s2\frac{q + s}{2}

Now, let's rewrite the original expression using the simplified expression inside the parentheses:

q+s2÷112÷16\frac{q + s}{2} \div \frac{11}{2} \div \frac{1}{6}

Simplifying the Expression

To simplify the expression, we need to follow the order of operations. We will start by evaluating the division operations from left to right.

q+s2÷112\frac{q + s}{2} \div \frac{11}{2}

We can rewrite this expression as a multiplication operation by inverting the second fraction:

q+s2×211\frac{q + s}{2} \times \frac{2}{11}

Now, let's simplify the expression by multiplying the fractions:

(q+s)×22×11\frac{(q + s) \times 2}{2 \times 11}

We can cancel out the common factor of 2 in the numerator and denominator:

q+s11\frac{q + s}{11}

Now, let's rewrite the original expression using the simplified expression:

q+s11÷16\frac{q + s}{11} \div \frac{1}{6}

Final Simplification

To simplify the expression, we need to follow the order of operations. We will start by evaluating the division operation:

q+s11÷16\frac{q + s}{11} \div \frac{1}{6}

We can rewrite this expression as a multiplication operation by inverting the second fraction:

q+s11×61\frac{q + s}{11} \times \frac{6}{1}

Now, let's simplify the expression by multiplying the fractions:

(q+s)×611×1\frac{(q + s) \times 6}{11 \times 1}

We can simplify the expression by canceling out the common factor of 1 in the denominator:

6(q+s)11\frac{6(q + s)}{11}

Conclusion

In this article, we evaluated the expression (q2+s2)÷112÷16\left(\frac{q}{2} + \frac{s}{2}\right) \div \frac{11}{2} \div \frac{1}{6}. We broke down the expression into smaller parts, simplified it, and finally arrived at the solution. The final simplified expression is 6(q+s)11\frac{6(q + s)}{11}.

Frequently Asked Questions

Q: What is the order of operations in mathematics?

A: The order of operations in mathematics is PEMDAS: Parentheses, Exponents, Multiplication and Division, and 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 denominator and divide both numbers by the GCD.

Q: What is the difference between multiplication and division?

A: Multiplication is the process of adding a number a certain number of times, while division is the process of sharing a certain number of items into equal groups.

Final Thoughts

Evaluating mathematical expressions can be a challenging task, but with practice and patience, you can become proficient in simplifying complex expressions. Remember to follow the order of operations and simplify fractions by finding the greatest common divisor. With these skills, you can tackle even the most complex mathematical problems.

Additional Resources

References

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Introduction

Evaluating mathematical expressions can be a challenging task, but with practice and patience, you can become proficient in simplifying complex expressions. In this article, we will answer some frequently asked questions about evaluating mathematical expressions.

Q&A

Q: What is the order of operations in mathematics?

A: The order of operations in mathematics is PEMDAS: Parentheses, Exponents, Multiplication and Division, and 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 denominator and divide both numbers by the GCD.

Q: What is the difference between multiplication and division?

A: Multiplication is the process of adding a number a certain number of times, while division is the process of sharing a certain number of items into equal groups.

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

A: To evaluate an expression with multiple operations, you need to follow the order of operations. First, evaluate any expressions inside parentheses, then evaluate any exponential expressions, followed by multiplication and division operations from left to right, and finally addition and subtraction operations from left to right.

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, you need to combine like terms by adding or subtracting the coefficients of the variables.

Q: What is the difference between a rational expression and an irrational expression?

A: A rational expression is an expression that can be written as a fraction, while an irrational expression is an expression that cannot be written as a fraction.

Q: How do I simplify a rational expression?

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

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

A: A linear expression is an expression that can be written in the form ax + b, while a quadratic expression is an expression that can be written in the form ax^2 + bx + c.

Q: How do I simplify a quadratic expression?

A: To simplify a quadratic expression, you need to factor the expression, if possible, and then simplify the resulting expression.

Conclusion

Evaluating mathematical expressions can be a challenging task, but with practice and patience, you can become proficient in simplifying complex expressions. By following the order of operations and simplifying fractions, you can tackle even the most complex mathematical problems. Remember to combine like terms, simplify rational expressions, and factor quadratic expressions to arrive at the solution.

Additional Resources

References