Evaluate:${ \left(\frac{-1}{2}\right) - \frac{2}{5} - \frac{2}{3} }$Provide An Answer As A Reduced Fraction Or Mixed Number.

Introduction

When evaluating expressions involving fractions, it's essential to follow the order of operations, which includes simplifying the expression by finding a common denominator and then performing the arithmetic operations. In this case, we need to evaluate the expression $\left(\frac{-1}{2}\right) - \frac{2}{5} - \frac{2}{3}$ and provide the answer as a reduced fraction or mixed number.

Step 1: Find a Common Denominator

To add or subtract fractions, we need to have a common denominator. The least common multiple (LCM) of 2, 5, and 3 is 30. We can rewrite each fraction with a denominator of 30.

Rewrite Fractions with a Common Denominator

$\frac{-1}{2} = \frac{-1 \times 15}{2 \times 15} = \frac{-15}{30}$

$\frac{2}{5} = \frac{2 \times 6}{5 \times 6} = \frac{12}{30}$

$\frac{2}{3} = \frac{2 \times 10}{3 \times 10} = \frac{20}{30}$

Step 2: Subtract the Fractions

Now that we have a common denominator, we can subtract the fractions.

$\left(\frac{-1}{2}\right) - \frac{2}{5} - \frac{2}{3} = \frac{-15}{30} - \frac{12}{30} - \frac{20}{30}$

Step 3: Combine the Fractions

We can combine the fractions by adding or subtracting the numerators.

$\frac{-15}{30} - \frac{12}{30} - \frac{20}{30} = \frac{-15 - 12 - 20}{30}$

Step 4: Simplify the Fraction

Now, we can simplify the fraction by dividing the numerator and denominator by their greatest common divisor (GCD).

$\frac{-15 - 12 - 20}{30} = \frac{-47}{30}$

Step 5: Reduce the Fraction

We can reduce the fraction by dividing the numerator and denominator by their GCD.

$\frac{-47}{30} = \frac{-47 \div 1}{30 \div 1} = \frac{-47}{30}$

Conclusion

The final answer is $\frac{-47}{30}$, which is a reduced fraction. We can also express this as a mixed number by dividing the numerator by the denominator and writing the remainder as the new numerator.

$\frac{-47}{30} = -1\frac{17}{30}$

Therefore, the final answer is $\boxed{-1\frac{17}{30}}$.

Final Answer

The final answer is $\boxed{-1\frac{17}{30}}$.

Introduction

In our previous article, we evaluated the expression $\left(\frac{-1}{2}\right) - \frac{2}{5} - \frac{2}{3}$ and provided the answer as a reduced fraction or mixed number. In this article, we will answer some frequently asked questions related to the evaluation of this expression.

Q&A

Q: What is the least common multiple (LCM) of 2, 5, and 3?

A: The least common multiple (LCM) of 2, 5, and 3 is 30.

Q: How do I rewrite fractions with a common denominator?

A: To rewrite fractions with a common denominator, you need to multiply the numerator and denominator of each fraction by the necessary multiples to obtain the common denominator. For example, to rewrite $\frac{-1}{2}$ with a denominator of 30, you would multiply the numerator and denominator by 15.

Q: Can I simplify the fraction $\frac{-47}{30}$ further?

A: Yes, you can simplify the fraction $\frac{-47}{30}$ further by dividing the numerator and denominator by their greatest common divisor (GCD). However, in this case, the GCD is 1, so the fraction cannot be simplified further.

Q: How do I express the fraction $\frac{-47}{30}$ as a mixed number?

A: To express the fraction $\frac{-47}{30}$ as a mixed number, you need to divide the numerator by the denominator and write the remainder as the new numerator. In this case, you would divide -47 by 30 and write the remainder as the new numerator.

Q: What is the final answer to the expression $\left(\frac{-1}{2}\right) - \frac{2}{5} - \frac{2}{3}$?

A: The final answer to the expression $\left(\frac{-1}{2}\right) - \frac{2}{5} - \frac{2}{3}$ is $\boxed{-1\frac{17}{30}}$.

Additional Tips

• When evaluating expressions involving fractions, it's essential to follow the order of operations, which includes simplifying the expression by finding a common denominator and then performing the arithmetic operations.
• To add or subtract fractions, you need to have a common denominator. The least common multiple (LCM) of the denominators is the common denominator.
• You can simplify fractions by dividing the numerator and denominator by their greatest common divisor (GCD).
• You can express fractions as mixed numbers by dividing the numerator by the denominator and writing the remainder as the new numerator.

Conclusion

In this article, we answered some frequently asked questions related to the evaluation of the expression $\left(\frac{-1}{2}\right) - \frac{2}{5} - \frac{2}{3}$. We provided additional tips and resources to help you evaluate expressions involving fractions. If you have any further questions or need additional help, please don't hesitate to ask.

Final Answer

The final answer is $\boxed{-1\frac{17}{30}}$.