Solve 43/8-21/6+35/12

$$4 \frac { 3 } { 8 } - 2 \frac { 1 } { 6 } + 3 \frac { 5 } { 12 }$$

Evaluate

$$\frac{45}{8}=5.625$$

Solution Steps

Multiply 4 and 8 to get 32.

$$\frac{32+3}{8}-\frac{2\times 6+1}{6}+\frac{3\times 12+5}{12}$$

Add 32 and 3 to get 35.

$$\frac{35}{8}-\frac{2\times 6+1}{6}+\frac{3\times 12+5}{12}$$

Multiply 2 and 6 to get 12.

$$\frac{35}{8}-\frac{12+1}{6}+\frac{3\times 12+5}{12}$$

Add 12 and 1 to get 13.

$$\frac{35}{8}-\frac{13}{6}+\frac{3\times 12+5}{12}$$

Least common multiple of 8 and 6 is 24. Convert \frac{35}{8} and \frac{13}{6} to fractions with denominator 24.

$$\frac{105}{24}-\frac{52}{24}+\frac{3\times 12+5}{12}$$

Since \frac{105}{24} and \frac{52}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{105-52}{24}+\frac{3\times 12+5}{12}$$

Subtract 52 from 105 to get 53.

$$\frac{53}{24}+\frac{3\times 12+5}{12}$$

Multiply 3 and 12 to get 36.

$$\frac{53}{24}+\frac{36+5}{12}$$

Add 36 and 5 to get 41.

$$\frac{53}{24}+\frac{41}{12}$$

Least common multiple of 24 and 12 is 24. Convert \frac{53}{24} and \frac{41}{12} to fractions with denominator 24.

$$\frac{53}{24}+\frac{82}{24}$$

Since \frac{53}{24} and \frac{82}{24} have the same denominator, add them by adding their numerators.

$$\frac{53+82}{24}$$

Add 53 and 82 to get 135.

$$\frac{135}{24}$$

Reduce the fraction \frac{135}{24} to lowest terms by extracting and canceling out 3.

$$\frac{45}{8}$$

Factor

$$\frac{3 ^ {2} \cdot 5}{2 ^ {3}} = 5\frac{5}{8} = 5.625$$