Solve 272/3-1585/6+2084/9=?

$$27 \frac { 2 } { 3 } - 158 \frac { 5 } { 6 } + 208 \frac { 4 } { 9 } = ?$$

Evaluate

$$\frac{1391}{18}\approx 77.277777778$$

Solution Steps

Multiply 27 and 3 to get 81.

$$\frac{81+2}{3}-\frac{158\times 6+5}{6}+\frac{208\times 9+4}{9}$$

Add 81 and 2 to get 83.

$$\frac{83}{3}-\frac{158\times 6+5}{6}+\frac{208\times 9+4}{9}$$

Multiply 158 and 6 to get 948.

$$\frac{83}{3}-\frac{948+5}{6}+\frac{208\times 9+4}{9}$$

Add 948 and 5 to get 953.

$$\frac{83}{3}-\frac{953}{6}+\frac{208\times 9+4}{9}$$

Least common multiple of 3 and 6 is 6. Convert \frac{83}{3} and \frac{953}{6} to fractions with denominator 6.

$$\frac{166}{6}-\frac{953}{6}+\frac{208\times 9+4}{9}$$

Since \frac{166}{6} and \frac{953}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{166-953}{6}+\frac{208\times 9+4}{9}$$

Subtract 953 from 166 to get -787.

$$-\frac{787}{6}+\frac{208\times 9+4}{9}$$

Multiply 208 and 9 to get 1872.

$$-\frac{787}{6}+\frac{1872+4}{9}$$

Add 1872 and 4 to get 1876.

$$-\frac{787}{6}+\frac{1876}{9}$$

Least common multiple of 6 and 9 is 18. Convert -\frac{787}{6} and \frac{1876}{9} to fractions with denominator 18.

$$-\frac{2361}{18}+\frac{3752}{18}$$

Since -\frac{2361}{18} and \frac{3752}{18} have the same denominator, add them by adding their numerators.

$$\frac{-2361+3752}{18}$$

Add -2361 and 3752 to get 1391.

$$\frac{1391}{18}$$

Factor

$$\frac{13 \cdot 107}{2 \cdot 3 ^ {2}} = 77\frac{5}{18} = 77.27777777777777$$