Which expression has the same value as minus, 2, start fraction, 3, divided by, 5, end fraction, minus, 4, one third−2 
5
3
​
 −4 
3
1
​
 ?
Answer
Multiple Choice Answers
minus, 2, start fraction, 3, divided by, 5, end fraction, plus, left parenthesis, minus, 4, one third, right parenthesis−2 
5
3
​
 +(−4 
3
1
​
 )
4, one third, minus, left parenthesis, minus, 2, start fraction, 3, divided by, 5, end fraction, right parenthesis4 
3
1
​
 −(−2 
5
3
​
 )
2, start fraction, 3, divided by, 5, end fraction, plus, left parenthesis, minus, 4, one third, right parenthesis2 
5
3
​
 +(−4 
3
1
​
 )
minus, 4, one third, minus, left parenthesis, minus, 2, start fraction, 3, divided by, 5, end fraction, right parenthesis−4 
3
1
​
 −(−2 
5
3
​
 )

Let's break down the given expression and analyze the multiple choice answers.

The expression provided is:

\[
- \frac{2}{\frac{3}{5}} - \frac{4}{\frac{1}{3}}
\]

Now let's look at each of the multiple choice answers:

1. **\(-\frac{2}{\frac{3}{5}} + (-\frac{4}{\frac{1}{3}})\)**

   This option modifies the original subtraction into addition by introducing a negative sign in front of the second fraction. It's a simplified transformation of the original expression because subtraction of a fraction can be seen as adding its negative. This is algebraically valid.

2. **\(\frac{4}{\frac{1}{3}} - (-\frac{2}{\frac{3}{5}})\)**

   This reverses the order of the terms and changes the signs, which also makes sense mathematically.

3. **\(\frac{2}{\frac{3}{5}} + (-\frac{4}{\frac{1}{3}})\)**

   This changes the original negative sign in front of \(\frac{2}{\frac{3}{5}}\) to positive, which is incorrect because the original expression has a negative sign in front of this term.

4. **\(-\frac{4}{\frac{1}{3}} - (-\frac{2}{\frac{3}{5}})\)**

   This reverses the terms and introduces a negative in front of both, which makes the expression mathematically equivalent to the original.

### Conclusion:
Both answer choices 2 and 4 represent mathematically equivalent forms of the original expression.

If I were to choose the best match, **option 4** is correct because it closely matches the structure of the original while accounting for the negative signs properly.

---

Would you like more details or further explanation?

### 5 Related Questions:
1. What is the process of simplifying complex fractions?
2. How do you apply the negative sign when dealing with fractions?
3. Can you explain how to add and subtract algebraic fractions?
4. How do you convert a fraction division problem into multiplication?
5. What are some real-world applications of rational expressions?

### Tip:
Always remember to check for sign changes when rewriting expressions, especially when dealing with subtraction or adding negatives!

Which expression has the same value as minus 2/3 divided by 5, minus 4 1/3?

Learn how to simplify expressions involving fraction subtraction with negative numbers, such as 'minus 2/3 divided by 5 minus 4 1/3.' This example covers key algebraic techniques, including fraction manipulation and properties of negative numbers. Suitable for students in Grades 6-8.

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