2)
so the board is 2 feet and 10 3/4 inches
well, 2 feet is 24 inches, plus 10 3/4 is 34 and 3/4 inches then. Then he sawed off 7/16 inches from it.
what's leftover is their difference.
let's first convert the mixed fraction to "improper" and then subtract them.
[tex]\bf 34\frac{3}{4}\implies \cfrac{34\cdot 4+3}{4}\implies \cfrac{139}{4}\\\\
-------------------------------\\\\
\cfrac{139}{4}-\cfrac{7}{16}\impliedby \textit{we'll use an LCD of 16}\implies \cfrac{(2\cdot 139)-7}{16}
\\\\\\
\cfrac{278-7}{16}\implies \cfrac{271}{16}\implies \stackrel{inches}{16\frac{15}{16}}\implies \stackrel{foot}{1}+\stackrel{inches}{4\frac{15}{16}}[/tex]
3)
so... from the plywood sheet, we'll be ripping 1 1/4 inch strips, however, in the process, there's a sawdust waste of 1/8 inch, how much is sawn from the sheet anyway, including the strips and the waste?
first off, again, let's make the mixed fraction to "improper", and add the waste to the strip, to see how much really each strip is using up from the sheet, and then we'll add the sums.
[tex]\bf 1\frac{1}{4}\implies \cfrac{1\cdot 4+1}{4}\implies \cfrac{5}{4}\\\\
-------------------------------\\\\
\cfrac{5}{4}+\cfrac{1}{8}\impliedby \textit{we'll use an LCD of 8}\implies \cfrac{(2\cdot 5)+1}{8}\implies \cfrac{11}{8}
\\\\\\
\textit{now, there are 15 strips, each using up }\frac{11}{8}\quad thus\implies 15\cdot \cfrac{11}{8}
\\\\\\
\cfrac{165}{8}\implies \stackrel{inches}{20\frac{5}{8}}\implies \stackrel{foot}{1}+\stackrel{inches}{8\frac{5}{8}}[/tex]
