Question

Choose the equivalent expression.
−6
9
5
​
+
6
5
​
−5
9
1
​


−6
9
5
​
+
6
5
​
+5
9
1
​


−6
9
5
​
+
6
5
​
+(−5
9
1
​
)

−6
9
5
​
−
6
5
​
+(−5
9
1
​
)

Answer 1

To determine the equivalent expression among the given options, let's start with the original expression and analyze the proposed options based on the rules of addition and subtraction.

The original expression is:

\[
-\frac{6}{9} + \frac{6}{5} - \frac{5}{9}
\]

Now we can analyze each proposed option:

1. **Option 1:**
\[
-\frac{6}{9} + \frac{6}{5} + \frac{5}{9}
\]
- This changes the subtraction of \(-\frac{5}{9}\) to addition of \(\frac{5}{9}\), which alters the expression's value.

2. **Option 2:**
\[
-\frac{6}{9} + \frac{6}{5} + (-\frac{5}{9})
\]
- This changes the \(-\frac{5}{9}\) to \((-\frac{5}{9})\), which maintains the original subtraction operation; this is equivalent to the original expression.

3. **Option 3:**
\[
-\frac{6}{9} - \frac{6}{5} + (-\frac{5}{9})
\]
- This changes the addition of \(\frac{6}{5}\) to subtraction, which alters the expression's value.

From these analyses, we see that **Option 2** correctly represents the original expression since it correctly maintains the original operations:

\[
-\frac{6}{9} + \frac{6}{5} + (-\frac{5}{9})
\]

Thus, the equivalent expression is option 2.