Sara has 434 yards of red fleece and 223 yards of blue fleece fabric. How...

We can add the amounts:
${\displaystyle 4\frac{3}{4}+2\frac{2}{3}}$
${\displaystyle 4+\frac{3}{4}+2+\frac{2}{3}}$
${\displaystyle 6+\frac{3}{4}+\frac{2}{3}}$
At this point, I need to find a common denominator (which is 12):
${\displaystyle 6+\frac{3}{4}\left(1\right)+\frac{2}{3}\left(1\right)}$
${\displaystyle 6+\frac{3}{4}\left(\frac{3}{3}\right)+\frac{2}{3}\left(\frac{4}{4}\right)}$
${\displaystyle 6+\frac{9}{12}+\frac{8}{12}}$
${\displaystyle 6+\frac{17}{12}}$
${\displaystyle 6+\frac{12}{12}+\frac{5}{12}}$
${\displaystyle 6+1+\frac{5}{12}}$
${\displaystyle 7\frac{5}{12}}$ yrds

${\displaystyle 4\frac{3}{4}+2\frac{2}{3}}$
Multiply 4 and 4 to get 16.
${\displaystyle \frac{16+3}{4}+\frac{2\times 3+2}{3}}$
Add 16 and 3 to get 19.
${\displaystyle \frac{19}{4}+\frac{2\times 3+2}{3}}$
Multiply 2 and 3 to get 6.
${\displaystyle \frac{19}{4}+\frac{6+2}{3}}$
Add 6 and 2 to get 8.
${\displaystyle \frac{19}{4}+\frac{8}{3}}$
Least common multiple of 4 and 3 is 12. Convert ${\displaystyle \frac{19}{4}\text{and}\frac{8}{4}}$ to fractions with denominator 12.
${\displaystyle \frac{57}{12}+\frac{32}{12}}$
Since ${\displaystyle \frac{57}{12}\text{and}\frac{32}{12}}$ have the same denominator, add them by adding their numerators.
${\displaystyle \frac{57+32}{12}}$
Add 57 and 32 to get 89.
${\displaystyle \frac{89}{12}}$

$4\frac{3}{4}+2\frac{2}{3}$ $=\frac{19}{4}+2\frac{2}{3}$ $=\frac{19}{4}+\frac{8}{3}$ $=\frac{89}{12}$ $=7\frac{5}{12}$