Solve 41/5-6/7+21/3=

$$4 \frac { 1 } { 5 } - \frac { 6 } { 7 } + 2 \frac { 1 } { 3 } =$$

Evaluate

$$\frac{596}{105}\approx 5.676190476$$

Solution Steps

Multiply 4 and 5 to get 20.

$$\frac{20+1}{5}-\frac{6}{7}+\frac{2\times 3+1}{3}$$

Add 20 and 1 to get 21.

$$\frac{21}{5}-\frac{6}{7}+\frac{2\times 3+1}{3}$$

Least common multiple of 5 and 7 is 35. Convert \frac{21}{5} and \frac{6}{7} to fractions with denominator 35.

$$\frac{147}{35}-\frac{30}{35}+\frac{2\times 3+1}{3}$$

Since \frac{147}{35} and \frac{30}{35} have the same denominator, subtract them by subtracting their numerators.

$$\frac{147-30}{35}+\frac{2\times 3+1}{3}$$

Subtract 30 from 147 to get 117.

$$\frac{117}{35}+\frac{2\times 3+1}{3}$$

Multiply 2 and 3 to get 6.

$$\frac{117}{35}+\frac{6+1}{3}$$

Add 6 and 1 to get 7.

$$\frac{117}{35}+\frac{7}{3}$$

Least common multiple of 35 and 3 is 105. Convert \frac{117}{35} and \frac{7}{3} to fractions with denominator 105.

$$\frac{351}{105}+\frac{245}{105}$$

Since \frac{351}{105} and \frac{245}{105} have the same denominator, add them by adding their numerators.

$$\frac{351+245}{105}$$

Add 351 and 245 to get 596.

$$\frac{596}{105}$$

Factor

$$\frac{2 ^ {2} \cdot 149}{3 \cdot 5 \cdot 7} = 5\frac{71}{105} = 5.6761904761904765$$