Choose All The Options That Are Equivalent To -\left(\frac{3}{5}\right ].A. − 3 5 \frac{-3}{5} 5 − 3 B. − 3 − 5 \frac{-3}{-5} − 5 − 3 C. 3 − 5 \frac{3}{-5} − 5 3 D. 3 5 \frac{3}{5} 5 3 E. − 3 5 -\frac{3}{5} − 5 3

Mar 12, 2025 by ADMIN 223 views

Understanding Negative Numbers and Fractions

When dealing with negative numbers and fractions, it's essential to understand the rules of operations to simplify expressions and solve problems. In this article, we will explore the concept of equivalent fractions and how to choose the correct option that is equivalent to a given expression.

What are Equivalent Fractions?

Equivalent fractions are fractions that have the same value, but may appear different. For example, $\frac{1}{2}$ and $\frac{2}{4}$ are equivalent fractions because they both represent the same value. To determine if two fractions are equivalent, we can multiply or divide both the numerator and denominator by the same number.

Understanding Negative Numbers

Negative numbers are numbers that are less than zero. When we multiply a negative number by a positive number, the result is always negative. When we multiply two negative numbers, the result is always positive. For example, $-3 \times 2 = -6$ and $-3 \times -2 = 6$ .

Simplifying the Given Expression

The given expression is $-\left(\frac{3}{5}\right)$ . To simplify this expression, we need to follow the order of operations (PEMDAS):

Evaluate the expression inside the parentheses: $\frac{3}{5}$
Multiply the result by -1: $-\frac{3}{5}$

Choosing the Correct Option

Now that we have simplified the given expression, we can choose the correct option that is equivalent to $-\left(\frac{3}{5}\right)$ . Let's examine each option:

A. $\frac{-3}{5}$ : This option is incorrect because it has a negative numerator, but the denominator is positive.

B. $\frac{-3}{-5}$ : This option is incorrect because it has two negative signs, which would result in a positive number.

C. $\frac{3}{-5}$ : This option is incorrect because it has a positive numerator and a negative denominator, which would result in a negative number.

D. $\frac{3}{5}$ : This option is incorrect because it has a positive numerator and a positive denominator, which would result in a positive number.

E. $-\frac{3}{5}$ : This option is correct because it has a negative sign in front of the fraction, which results in a negative number.

Conclusion

In conclusion, the correct option that is equivalent to $-\left(\frac{3}{5}\right)$ is E. $-\frac{3}{5}$ . This option has a negative sign in front of the fraction, which results in a negative number. Understanding negative numbers and fractions is essential to simplify expressions and solve problems in mathematics.

Additional Examples

Here are some additional examples to help you understand equivalent fractions and negative numbers:

$-\left(\frac{2}{3}\right) = -\frac{2}{3}$
$-\left(\frac{-4}{5}\right) = \frac{4}{5}$
$-\left(\frac{1}{2}\right) = -\frac{1}{2}$

Tips and Tricks

Here are some tips and tricks to help you understand equivalent fractions and negative numbers:

When dealing with negative numbers, remember that a negative sign in front of a fraction results in a negative number.
When dealing with equivalent fractions, remember that you can multiply or divide both the numerator and denominator by the same number to simplify the fraction.
Practice, practice, practice! The more you practice, the more comfortable you will become with equivalent fractions and negative numbers.

Common Mistakes

Here are some common mistakes to avoid when dealing with equivalent fractions and negative numbers:

Not following the order of operations (PEMDAS)
Not simplifying fractions correctly
Not understanding the concept of negative numbers

Conclusion

In conclusion, understanding equivalent fractions and negative numbers is essential to simplify expressions and solve problems in mathematics. By following the order of operations (PEMDAS) and simplifying fractions correctly, you can choose the correct option that is equivalent to a given expression. Remember to practice, practice, practice to become more comfortable with equivalent fractions and negative numbers.
Frequently Asked Questions: Equivalent Fractions and Negative Numbers

In this article, we will answer some frequently asked questions about equivalent fractions and negative numbers.

Q: What is the difference between a positive and negative fraction?

A: A positive fraction is a fraction with a positive numerator and a positive denominator, while a negative fraction is a fraction with a negative numerator or a negative denominator.

Q: How do I simplify a fraction with a negative numerator?

A: To simplify a fraction with a negative numerator, you can multiply the numerator and denominator by -1. For example, $-\frac{3}{5}$ can be simplified to $\frac{3}{-5}$ .

Q: How do I simplify a fraction with a negative denominator?

A: To simplify a fraction with a negative denominator, you can multiply the numerator and denominator by -1. For example, $\frac{3}{-5}$ can be simplified to $-\frac{3}{5}$ .

Q: What is the rule for multiplying negative numbers?

A: When multiplying two negative numbers, the result is always positive. When multiplying a negative number and a positive number, the result is always negative.

Q: How do I determine if two fractions are equivalent?

A: To determine if two fractions are equivalent, you can multiply or divide both the numerator and denominator by the same number. For example, $\frac{1}{2}$ and $\frac{2}{4}$ are equivalent fractions because you can multiply both the numerator and denominator of $\frac{1}{2}$ by 2 to get $\frac{2}{4}$ .

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells you which operations to perform first when simplifying an expression. The acronym PEMDAS stands for:

Parentheses: Evaluate expressions inside parentheses first.
Exponents: Evaluate any exponential expressions next.
Multiplication and Division: Evaluate any multiplication and division operations from left to right.
Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

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

A: To simplify an expression with multiple operations, you can follow the order of operations (PEMDAS). For example, to simplify the expression $3 \times 2 + 5 - 1$ , you would first multiply 3 and 2 to get 6, then add 5 to get 11, and finally subtract 1 to get 10.

Q: What are some common mistakes to avoid when working with equivalent fractions and negative numbers?

A: Some common mistakes to avoid when working with equivalent fractions and negative numbers include:

Not following the order of operations (PEMDAS)
Not simplifying fractions correctly
Not understanding the concept of negative numbers
Not being careful with signs when multiplying or dividing fractions

Q: How can I practice working with equivalent fractions and negative numbers?

A: You can practice working with equivalent fractions and negative numbers by:

Simplifying fractions with negative numerators or denominators
Multiplying or dividing fractions with negative numbers
Solving problems that involve equivalent fractions and negative numbers
Using online resources or worksheets to practice

Conclusion