Solve 51/2+3+41/3+31/6div4

$$5 \frac { 1 } { 2 } + 3 + 4 \frac { 1 } { 3 } + 3 \frac { 1 } { 6 } \div 4$$

Evaluate

$$\frac{109}{8}=13.625$$

Solution Steps

Multiply 5 and 2 to get 10.

$$\frac{10+1}{2}+3+\frac{4\times 3+1}{3}+\frac{\frac{3\times 6+1}{6}}{4}$$

Add 10 and 1 to get 11.

$$\frac{11}{2}+3+\frac{4\times 3+1}{3}+\frac{\frac{3\times 6+1}{6}}{4}$$

Convert 3 to fraction \frac{6}{2}.

$$\frac{11}{2}+\frac{6}{2}+\frac{4\times 3+1}{3}+\frac{\frac{3\times 6+1}{6}}{4}$$

Since \frac{11}{2} and \frac{6}{2} have the same denominator, add them by adding their numerators.

$$\frac{11+6}{2}+\frac{4\times 3+1}{3}+\frac{\frac{3\times 6+1}{6}}{4}$$

Add 11 and 6 to get 17.

$$\frac{17}{2}+\frac{4\times 3+1}{3}+\frac{\frac{3\times 6+1}{6}}{4}$$

Multiply 4 and 3 to get 12.

$$\frac{17}{2}+\frac{12+1}{3}+\frac{\frac{3\times 6+1}{6}}{4}$$

Add 12 and 1 to get 13.

$$\frac{17}{2}+\frac{13}{3}+\frac{\frac{3\times 6+1}{6}}{4}$$

Least common multiple of 2 and 3 is 6. Convert \frac{17}{2} and \frac{13}{3} to fractions with denominator 6.

$$\frac{51}{6}+\frac{26}{6}+\frac{\frac{3\times 6+1}{6}}{4}$$

Since \frac{51}{6} and \frac{26}{6} have the same denominator, add them by adding their numerators.

$$\frac{51+26}{6}+\frac{\frac{3\times 6+1}{6}}{4}$$

Add 51 and 26 to get 77.

$$\frac{77}{6}+\frac{\frac{3\times 6+1}{6}}{4}$$

Express \frac{\frac{3\times 6+1}{6}}{4} as a single fraction.

$$\frac{77}{6}+\frac{3\times 6+1}{6\times 4}$$

Multiply 3 and 6 to get 18.

$$\frac{77}{6}+\frac{18+1}{6\times 4}$$

Add 18 and 1 to get 19.

$$\frac{77}{6}+\frac{19}{6\times 4}$$

Multiply 6 and 4 to get 24.

$$\frac{77}{6}+\frac{19}{24}$$

Least common multiple of 6 and 24 is 24. Convert \frac{77}{6} and \frac{19}{24} to fractions with denominator 24.

$$\frac{308}{24}+\frac{19}{24}$$

Since \frac{308}{24} and \frac{19}{24} have the same denominator, add them by adding their numerators.

$$\frac{308+19}{24}$$

Add 308 and 19 to get 327.

$$\frac{327}{24}$$

Reduce the fraction \frac{327}{24} to lowest terms by extracting and canceling out 3.

$$\frac{109}{8}$$

Factor

$$\frac{109}{2 ^ {3}} = 13\frac{5}{8} = 13.625$$