Subtracting mixed numbers is quite easy.
We know that mixed number consists of integer part and fractional part.
Example 1. Find 153−294.
Convert each mixed number into improper fraction: 153=58 and 294=922.
Now subtract fractions: 58−922=5⋅98⋅9−9⋅522⋅5=4572−45110=−4538.
Convert fraction to mixed number: can't convert because fraction is proper.
Answer: −4538.
Next example.
Example 2. Find −261−321.
Convert each mixed number into improper fraction: −261=−613 and 321=27.
Now subtract fractions: −613−27=−613−2⋅37⋅3=−613−621=−634.
Reduce fraction: −634=−317.
Convert fraction to mixed number: −317=−532.
Answer: −317=−532.
Next example.
Example 3. Find −2−5118.
Since first number has no fractional part, we can easier subtract numbers.
Subtract integer parts: −2−5=−7 and fractional part leave the same.
Warning. This works only when we subtract either negative and positive numbers (this case) or positive and negative numbers (like 2−(−5118)=7118).
Answer: −7118=−1185.
Now, take pen and paper and do following exercises.
Exercise 1. Find 561−387.
Answer: 2431=1247.
Next exercise.
Exercise 2. Find 794−(−265).
Answer: 18185=10185.
Next exercise.
Exercise 3. Find −561−(−387).
Answer: −2431=−1247.
Next exercise.
Exercise 4. Find 365−75.
365−75=623−75=42161−4230=42131=3425.
Answer: 42131=3425.
Next exercise.
Exercise 5. Find 561−7.
Here we just can't add fractional parts to obtain −261. This is not correct, because both numbers are positive.
We do it as always.
561−7=631−642=−611=−165.
Answer: −611=−165.
If you are not sure whether it is possible to subtract integer parts, use the three-step method. It guarantees correct answer.