Solve 63/4+31/3-75/6+125/9

$$6 \frac { 3 } { 4 } + 3 \frac { 1 } { 3 } - 7 \frac { 5 } { 6 } + 12 \frac { 5 } { 9 }$$

Evaluate

$$\frac{533}{36}\approx 14.805555556$$

Solution Steps

Multiply 6 and 4 to get 24.

$$\frac{24+3}{4}+\frac{3\times 3+1}{3}-\frac{7\times 6+5}{6}+\frac{12\times 9+5}{9}$$

Add 24 and 3 to get 27.

$$\frac{27}{4}+\frac{3\times 3+1}{3}-\frac{7\times 6+5}{6}+\frac{12\times 9+5}{9}$$

Multiply 3 and 3 to get 9.

$$\frac{27}{4}+\frac{9+1}{3}-\frac{7\times 6+5}{6}+\frac{12\times 9+5}{9}$$

Add 9 and 1 to get 10.

$$\frac{27}{4}+\frac{10}{3}-\frac{7\times 6+5}{6}+\frac{12\times 9+5}{9}$$

Least common multiple of 4 and 3 is 12. Convert \frac{27}{4} and \frac{10}{3} to fractions with denominator 12.

$$\frac{81}{12}+\frac{40}{12}-\frac{7\times 6+5}{6}+\frac{12\times 9+5}{9}$$

Since \frac{81}{12} and \frac{40}{12} have the same denominator, add them by adding their numerators.

$$\frac{81+40}{12}-\frac{7\times 6+5}{6}+\frac{12\times 9+5}{9}$$

Add 81 and 40 to get 121.

$$\frac{121}{12}-\frac{7\times 6+5}{6}+\frac{12\times 9+5}{9}$$

Multiply 7 and 6 to get 42.

$$\frac{121}{12}-\frac{42+5}{6}+\frac{12\times 9+5}{9}$$

Add 42 and 5 to get 47.

$$\frac{121}{12}-\frac{47}{6}+\frac{12\times 9+5}{9}$$

Least common multiple of 12 and 6 is 12. Convert \frac{121}{12} and \frac{47}{6} to fractions with denominator 12.

$$\frac{121}{12}-\frac{94}{12}+\frac{12\times 9+5}{9}$$

Since \frac{121}{12} and \frac{94}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{121-94}{12}+\frac{12\times 9+5}{9}$$

Subtract 94 from 121 to get 27.

$$\frac{27}{12}+\frac{12\times 9+5}{9}$$

Reduce the fraction \frac{27}{12} to lowest terms by extracting and canceling out 3.

$$\frac{9}{4}+\frac{12\times 9+5}{9}$$

Multiply 12 and 9 to get 108.

$$\frac{9}{4}+\frac{108+5}{9}$$

Add 108 and 5 to get 113.

$$\frac{9}{4}+\frac{113}{9}$$

Least common multiple of 4 and 9 is 36. Convert \frac{9}{4} and \frac{113}{9} to fractions with denominator 36.

$$\frac{81}{36}+\frac{452}{36}$$

Since \frac{81}{36} and \frac{452}{36} have the same denominator, add them by adding their numerators.

$$\frac{81+452}{36}$$

Add 81 and 452 to get 533.

$$\frac{533}{36}$$

Factor

$$\frac{13 \cdot 41}{2 ^ {2} \cdot 3 ^ {2}} = 14\frac{29}{36} = 14.805555555555555$$