Answer: 26 1/8
whole part = 26, fractional part = 1/8
Work Shown
1/4 = 0.25
3/4 = 0.75
1/8 = 0.125
3/8 = 0.375
13 & 1/4 = 13 + (1/4) = 13 + 0.25 = 13.25
39 & 3/4 = 39 + (3/4) = 39 + 0.75 = 39.75
The entire board is 39.75 inches long. The portion we want is 13.25 inches long. Then there's 0.375 inches of wasted wood (i.e. scrap wood) which is the width of the saw.
This would mean 13.25+0.375 = 13.625 inches of wood is taken up, and the leftover amount is 39.75 - 13.625 = 26.125 inches
Because 1/8 = 0.125, the decimal 26.125 converts to the mixed number 26 & 1/8, which is the final answer. There's 26 full inches, and then another 1/8 of an extra inch, of this board left over.
We can express 26 & 1/8 as 26 1/8; both mean the same thing. The first format is probably more descriptive in my opinion. But I've seen many teachers accept the second format as well.