-8 1/2 - (-3 1/4)

-8 1/2 - (-3 1/4)

$\begin{array}{lcr} -8 \frac12 - (-3 \frac14 )\\ &=& -8 \frac12 + 3 \frac14 \\ &=& -8 -\frac12 +3 + \frac14 \\ &=& -8 +3 - \frac12 + \frac14 \\ &=& -5 - \frac12 + \frac14 \\ &=& -5 - \frac24 + \frac14 \\ &=& -5 - \frac14 \\ &=& -5 \frac14 \\ -8 \frac12 - (-3 \frac14 )&=& -5 \frac14 \\ \end{array}$

-8 1/2 - (-3 1/4)

Simplify the following:
-(8+1/2)-(-(3+1/4))

(-1)^2 = 1:
-(8+1/2)+3+1/4

Put 8+1/2 over the common denominator 2. 8+1/2  =  (2×8)/2+1/2:
-(2×8)/2+1/2+3+1/4

2×8  =  16:
-(16/2+1/2)+3+1/4

16/2+1/2  =  (16+1)/2:
-(16+1)/2+3+1/4

16+1 = 17:
-17/2+3+1/4

Put -17/2+3+1/4 over the common denominator 4. -17/2+3+1/4  =  (2 (-17))/4+(4×3)/4+1/4:
(2 (-17))/4+(4×3)/4+1/4

2 (-17)  =  -34:
-34/4+(4×3)/4+1/4

4×3  =  12:
(-34)/4+12/4+1/4

(-34)/4+12/4+1/4  =  (-34+12+1)/4:
(-34+12+1)/4

12+1 = 13:
13-34/4

13-34  =  -(34-13):
-(34-13)/4

| 3 | 4
- | 1 | 3
| 2 | 1:
Answer: | 
| (-21)/4