4 frac{1}{2} + 3 frac{1}{6} + x + 2 frac{1}{3 | vedclass

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Question

(NONE) Convert the mixed fractions into improper fractions:
$4 \frac{1}{2} = \frac{9}{2}$,$3 \frac{1}{6} = \frac{19}{6}$,$2 \frac{1}{3} = \frac{7}{3}

Vedclass · Accepted Answer

$3 \frac{2}{3}$

Vedclass · Answer

(NONE) Convert the mixed fractions into improper fractions:
$4 \frac{1}{2} = \frac{9}{2}$,$3 \frac{1}{6} = \frac{19}{6}$,$2 \frac{1}{3} = \frac{7}{3}$,and $13 \frac{2}{3} = \frac{41}{3}$.
The equation becomes: $\frac{9}{2} + \frac{19}{6} + x + \frac{7}{3} = \frac{41}{3}$.
Find a common denominator for the fractions on the left side,which is $6$:
$\frac{27}{6} + \frac{19}{6} + \frac{14}{6} + x = \frac{41}{3}$.
Sum the fractions: $\frac{27 + 19 + 14}{6} + x = \frac{41}{3}$.
$\frac{60}{6} + x = \frac{41}{3}$.
$10 + x = \frac{41}{3}$.
$x = \frac{41}{3} - 10$.
$x = \frac{41 - 30}{3} = \frac{11}{3} = 3 \frac{2}{3}$.

$4 \frac{1}{2} + 3 \frac{1}{6} + x + 2 \frac{1}{3} = 13 \frac{2}{3}$

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