Solve 21/5+14/7-41/2-3/5+2frac{2}{35}

$$2 \frac { 1 } { 5 } + 1 \frac { 4 } { 7 } - 4 \frac { 1 } { 2 } - \frac { 3 } { 5 } + 2 \frac { 2 } { 35 }$$

Evaluate

$$\frac{51}{70}\approx 0.728571429$$

Solution Steps

Multiply 2 and 5 to get 10.

$$\frac{10+1}{5}+\frac{1\times 7+4}{7}-\frac{4\times 2+1}{2}-\frac{3}{5}+\frac{2\times 35+2}{35}$$

Add 10 and 1 to get 11.

$$\frac{11}{5}+\frac{1\times 7+4}{7}-\frac{4\times 2+1}{2}-\frac{3}{5}+\frac{2\times 35+2}{35}$$

Multiply 1 and 7 to get 7.

$$\frac{11}{5}+\frac{7+4}{7}-\frac{4\times 2+1}{2}-\frac{3}{5}+\frac{2\times 35+2}{35}$$

Add 7 and 4 to get 11.

$$\frac{11}{5}+\frac{11}{7}-\frac{4\times 2+1}{2}-\frac{3}{5}+\frac{2\times 35+2}{35}$$

Least common multiple of 5 and 7 is 35. Convert \frac{11}{5} and \frac{11}{7} to fractions with denominator 35.

$$\frac{77}{35}+\frac{55}{35}-\frac{4\times 2+1}{2}-\frac{3}{5}+\frac{2\times 35+2}{35}$$

Since \frac{77}{35} and \frac{55}{35} have the same denominator, add them by adding their numerators.

$$\frac{77+55}{35}-\frac{4\times 2+1}{2}-\frac{3}{5}+\frac{2\times 35+2}{35}$$

Add 77 and 55 to get 132.

$$\frac{132}{35}-\frac{4\times 2+1}{2}-\frac{3}{5}+\frac{2\times 35+2}{35}$$

Multiply 4 and 2 to get 8.

$$\frac{132}{35}-\frac{8+1}{2}-\frac{3}{5}+\frac{2\times 35+2}{35}$$

Add 8 and 1 to get 9.

$$\frac{132}{35}-\frac{9}{2}-\frac{3}{5}+\frac{2\times 35+2}{35}$$

Least common multiple of 35 and 2 is 70. Convert \frac{132}{35} and \frac{9}{2} to fractions with denominator 70.

$$\frac{264}{70}-\frac{315}{70}-\frac{3}{5}+\frac{2\times 35+2}{35}$$

Since \frac{264}{70} and \frac{315}{70} have the same denominator, subtract them by subtracting their numerators.

$$\frac{264-315}{70}-\frac{3}{5}+\frac{2\times 35+2}{35}$$

Subtract 315 from 264 to get -51.

$$-\frac{51}{70}-\frac{3}{5}+\frac{2\times 35+2}{35}$$

Least common multiple of 70 and 5 is 70. Convert -\frac{51}{70} and \frac{3}{5} to fractions with denominator 70.

$$-\frac{51}{70}-\frac{42}{70}+\frac{2\times 35+2}{35}$$

Since -\frac{51}{70} and \frac{42}{70} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-51-42}{70}+\frac{2\times 35+2}{35}$$

Subtract 42 from -51 to get -93.

$$-\frac{93}{70}+\frac{2\times 35+2}{35}$$

Multiply 2 and 35 to get 70.

$$-\frac{93}{70}+\frac{70+2}{35}$$

Add 70 and 2 to get 72.

$$-\frac{93}{70}+\frac{72}{35}$$

Least common multiple of 70 and 35 is 70. Convert -\frac{93}{70} and \frac{72}{35} to fractions with denominator 70.

$$-\frac{93}{70}+\frac{144}{70}$$

Since -\frac{93}{70} and \frac{144}{70} have the same denominator, add them by adding their numerators.

$$\frac{-93+144}{70}$$

Add -93 and 144 to get 51.

$$\frac{51}{70}$$

Factor

$$\frac{3 \cdot 17}{2 \cdot 5 \cdot 7} = 0.7285714285714285$$