2022-01-21

Sara has $4\frac{3}{4}$ yards of red fleece and $2\frac{2}{3}$ yards of blue fleece fabric. How many yards of red and blue fleece fabric does she have altogether?

sjkuzy5

Expert

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

fumanchuecf

Expert

$4\frac{3}{4}+2\frac{2}{3}$
Multiply 4 and 4 to get 16.
$\frac{16+3}{4}+\frac{2×3+2}{3}$
Add 16 and 3 to get 19.
$\frac{19}{4}+\frac{2×3+2}{3}$
Multiply 2 and 3 to get 6.
$\frac{19}{4}+\frac{6+2}{3}$
Add 6 and 2 to get 8.
$\frac{19}{4}+\frac{8}{3}$
Least common multiple of 4 and 3 is 12. Convert to fractions with denominator 12.
$\frac{57}{12}+\frac{32}{12}$
$\frac{57+32}{12}$
Add 57 and 32 to get 89.
$\frac{89}{12}$

RizerMix

Expert

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