Solve 7/8-3/4+5/6quad25/9-frac{2}{3}+frac{4}{9}

$$\frac { 7 } { 8 } - \frac { 3 } { 4 } + \frac { 5 } { 6 } \quad 2 \frac { 5 } { 9 } - \frac { 2 } { 3 } + \frac { 4 } { 9 }$$

Evaluate

$$\frac{439}{216}\approx 2.032407407$$

Solution Steps

Least common multiple of 8 and 4 is 8. Convert \frac{7}{8} and \frac{3}{4} to fractions with denominator 8.

$$\frac{7}{8}-\frac{6}{8}+\frac{5}{6}\times \frac{2\times 9+5}{9}-\frac{2}{3}+\frac{4}{9}$$

Since \frac{7}{8} and \frac{6}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7-6}{8}+\frac{5}{6}\times \frac{2\times 9+5}{9}-\frac{2}{3}+\frac{4}{9}$$

Subtract 6 from 7 to get 1.

$$\frac{1}{8}+\frac{5}{6}\times \frac{2\times 9+5}{9}-\frac{2}{3}+\frac{4}{9}$$

Multiply 2 and 9 to get 18.

$$\frac{1}{8}+\frac{5}{6}\times \frac{18+5}{9}-\frac{2}{3}+\frac{4}{9}$$

Add 18 and 5 to get 23.

$$\frac{1}{8}+\frac{5}{6}\times \frac{23}{9}-\frac{2}{3}+\frac{4}{9}$$

Multiply \frac{5}{6} times \frac{23}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{8}+\frac{5\times 23}{6\times 9}-\frac{2}{3}+\frac{4}{9}$$

Do the multiplications in the fraction \frac{5\times 23}{6\times 9}.

$$\frac{1}{8}+\frac{115}{54}-\frac{2}{3}+\frac{4}{9}$$

Least common multiple of 8 and 54 is 216. Convert \frac{1}{8} and \frac{115}{54} to fractions with denominator 216.

$$\frac{27}{216}+\frac{460}{216}-\frac{2}{3}+\frac{4}{9}$$

Since \frac{27}{216} and \frac{460}{216} have the same denominator, add them by adding their numerators.

$$\frac{27+460}{216}-\frac{2}{3}+\frac{4}{9}$$

Add 27 and 460 to get 487.

$$\frac{487}{216}-\frac{2}{3}+\frac{4}{9}$$

Least common multiple of 216 and 3 is 216. Convert \frac{487}{216} and \frac{2}{3} to fractions with denominator 216.

$$\frac{487}{216}-\frac{144}{216}+\frac{4}{9}$$

Since \frac{487}{216} and \frac{144}{216} have the same denominator, subtract them by subtracting their numerators.

$$\frac{487-144}{216}+\frac{4}{9}$$

Subtract 144 from 487 to get 343.

$$\frac{343}{216}+\frac{4}{9}$$

Least common multiple of 216 and 9 is 216. Convert \frac{343}{216} and \frac{4}{9} to fractions with denominator 216.

$$\frac{343}{216}+\frac{96}{216}$$

Since \frac{343}{216} and \frac{96}{216} have the same denominator, add them by adding their numerators.

$$\frac{343+96}{216}$$

Add 343 and 96 to get 439.

$$\frac{439}{216}$$

Factor

$$\frac{439}{2 ^ {3} \cdot 3 ^ {3}} = 2\frac{7}{216} = 2.0324074074074074$$