Explanation:
1. Convert 3 2/5 and -4 1/2 into improper fractions. To do that:
1a. Multiply the whole number by the denominator.
3 2/5 = 17/5
-4 1/2 = -9/2
2. We also need to find the LCD (Least Common Denominator)
2a. The LCD of 17/5 and -9/2 is 10.
3. Change the original denominator to the LCD.
3a. Remember, what you did to the bottom, you do to the top.
3b. I got 10 by multiplying 2 by 5. So, you multiply 17 by 5.
17 x 5 = 34
3c. The first fraction is 34/10
4. Now, we do the same thing, but for the other fraction, which is -9/2.
4a. I got 10 by multiplying 5 by 2. So, you multiply -9 by 5.
-9 x 5 = (-45)
4b. The second fraction is -45/10
5. Now we can subtract!
Therefore, your answer is 79/10, but, something's wrong with it, it's improper!
Now, we must convert 79/10 into a mixed number.
To do that, we divide the numerator by the denominator.
79 / 10 = 7.9.
Note: The denominator NEVER changes.
The 7 will be your mixed number and the 9 will be the numerator. You know the 10 will be the denominator.
Therefore, your final answer is: 7 9/10