Solve 11/4+11/2+11/3+21/8

$$1 \frac { 1 } { 4 } + 1 \frac { 1 } { 2 } + 1 \frac { 1 } { 3 } + 2 \frac { 1 } { 8 }$$

Evaluate

$$\frac{149}{24}\approx 6.208333333$$

Solution Steps

Multiply 1 and 4 to get 4.

$$\frac{4+1}{4}+\frac{1\times 2+1}{2}+\frac{1\times 3+1}{3}+\frac{2\times 8+1}{8}$$

Add 4 and 1 to get 5.

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

Multiply 1 and 2 to get 2.

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

Add 2 and 1 to get 3.

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

Least common multiple of 4 and 2 is 4. Convert \frac{5}{4} and \frac{3}{2} to fractions with denominator 4.

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

Since \frac{5}{4} and \frac{6}{4} have the same denominator, add them by adding their numerators.

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

Add 5 and 6 to get 11.

$$\frac{11}{4}+\frac{1\times 3+1}{3}+\frac{2\times 8+1}{8}$$

Multiply 1 and 3 to get 3.

$$\frac{11}{4}+\frac{3+1}{3}+\frac{2\times 8+1}{8}$$

Add 3 and 1 to get 4.

$$\frac{11}{4}+\frac{4}{3}+\frac{2\times 8+1}{8}$$

Least common multiple of 4 and 3 is 12. Convert \frac{11}{4} and \frac{4}{3} to fractions with denominator 12.

$$\frac{33}{12}+\frac{16}{12}+\frac{2\times 8+1}{8}$$

Since \frac{33}{12} and \frac{16}{12} have the same denominator, add them by adding their numerators.

$$\frac{33+16}{12}+\frac{2\times 8+1}{8}$$

Add 33 and 16 to get 49.

$$\frac{49}{12}+\frac{2\times 8+1}{8}$$

Multiply 2 and 8 to get 16.

$$\frac{49}{12}+\frac{16+1}{8}$$

Add 16 and 1 to get 17.

$$\frac{49}{12}+\frac{17}{8}$$

Least common multiple of 12 and 8 is 24. Convert \frac{49}{12} and \frac{17}{8} to fractions with denominator 24.

$$\frac{98}{24}+\frac{51}{24}$$

Since \frac{98}{24} and \frac{51}{24} have the same denominator, add them by adding their numerators.

$$\frac{98+51}{24}$$

Add 98 and 51 to get 149.

$$\frac{149}{24}$$

Factor

$$\frac{149}{2 ^ {3} \cdot 3} = 6\frac{5}{24} = 6.208333333333333$$