Solve 31/2+41/3-11/5=

$$3 \frac { 1 } { 2 } + 4 \frac { 1 } { 3 } - 1 \frac { 1 } { 5 } =$$

Evaluate

$$\frac{199}{30}\approx 6.633333333$$

Solution Steps

Multiply 3 and 2 to get 6.

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

Add 6 and 1 to get 7.

$$\frac{7}{2}+\frac{4\times 3+1}{3}-\frac{1\times 5+1}{5}$$

Multiply 4 and 3 to get 12.

$$\frac{7}{2}+\frac{12+1}{3}-\frac{1\times 5+1}{5}$$

Add 12 and 1 to get 13.

$$\frac{7}{2}+\frac{13}{3}-\frac{1\times 5+1}{5}$$

Least common multiple of 2 and 3 is 6. Convert \frac{7}{2} and \frac{13}{3} to fractions with denominator 6.

$$\frac{21}{6}+\frac{26}{6}-\frac{1\times 5+1}{5}$$

Since \frac{21}{6} and \frac{26}{6} have the same denominator, add them by adding their numerators.

$$\frac{21+26}{6}-\frac{1\times 5+1}{5}$$

Add 21 and 26 to get 47.

$$\frac{47}{6}-\frac{1\times 5+1}{5}$$

Multiply 1 and 5 to get 5.

$$\frac{47}{6}-\frac{5+1}{5}$$

Add 5 and 1 to get 6.

$$\frac{47}{6}-\frac{6}{5}$$

Least common multiple of 6 and 5 is 30. Convert \frac{47}{6} and \frac{6}{5} to fractions with denominator 30.

$$\frac{235}{30}-\frac{36}{30}$$

Since \frac{235}{30} and \frac{36}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{235-36}{30}$$

Subtract 36 from 235 to get 199.

$$\frac{199}{30}$$

Factor

$$\frac{199}{2 \cdot 3 \cdot 5} = 6\frac{19}{30} = 6.633333333333334$$