Question

Choose the equivalent expression.
3
9
2
​
− 3
8
1
​


3
9
2
​
+(−3
8
1
​
)

3
9
2
​
+3
8
1
​


−3
9
2
​
+(−3
8
1
​
)

Answer 1

To find the equivalent expression to \( 3 \frac{9}{2} - 3 \frac{8}{1} \), we first need to convert the mixed numbers into improper fractions and then perform the calculations.

1. Convert the mixed numbers to improper fractions:
- \( 3 \frac{9}{2} = 3 + \frac{9}{2} = \frac{3 \times 2 + 9}{2} = \frac{6 + 9}{2} = \frac{15}{2} \)
- \( 3 \frac{8}{1} = 3 + 8 = 11 \) (this is simply 11, which can also be written as \( \frac{11}{1} \))

2. Now the expression becomes:
\( \frac{15}{2} - 11 \)

3. We can express 11 as a fraction over 2:
\( 11 = \frac{22}{2} \)

4. Now, the expression is:
\( \frac{15}{2} - \frac{22}{2} = \frac{15 - 22}{2} = \frac{-7}{2} \)

Now, let's look at the options presented and find the one that is equivalent:

- \( 3 \frac{9}{2} - 3 \frac{8}{1} \)
- \( 3 \frac{9}{2} + (-3 \frac{8}{1}) \) = \( \frac{15}{2} - \frac{22}{2} = \frac{-7}{2} \) (equivalent)
- \( 3 \frac{9}{2} + 3 \frac{8}{1} \) = \( \frac{15}{2} + 11 = \frac{15 + 22}{2} = \frac{37}{2} \) (not equivalent)
- \( -3 \frac{9}{2} + (-3 \frac{8}{1}) \) = \( -\frac{15}{2} - 11 = -\frac{15 + 22}{2} = -\frac{37}{2} \) (not equivalent)

So the equivalent expression is:
**\( 3 \frac{9}{2} + (-3 \frac{8}{1}) \)**