Solve (21/2+32/3)div(72/5)

$$(2 \frac{ 1 }{ 2 } +3 \frac{ 2 }{ 3 } ) \div (7 \frac{ 2 }{ 5 } )$$

Evaluate

$$\frac{5}{6}\approx 0.833333333$$

Solution Steps

Multiply 2 and 2 to get 4.

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

Add 4 and 1 to get 5.

$$\frac{\frac{5}{2}+\frac{3\times 3+2}{3}}{\frac{7\times 5+2}{5}}$$

Multiply 3 and 3 to get 9.

$$\frac{\frac{5}{2}+\frac{9+2}{3}}{\frac{7\times 5+2}{5}}$$

Add 9 and 2 to get 11.

$$\frac{\frac{5}{2}+\frac{11}{3}}{\frac{7\times 5+2}{5}}$$

Least common multiple of 2 and 3 is 6. Convert \frac{5}{2} and \frac{11}{3} to fractions with denominator 6.

$$\frac{\frac{15}{6}+\frac{22}{6}}{\frac{7\times 5+2}{5}}$$

Since \frac{15}{6} and \frac{22}{6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{15+22}{6}}{\frac{7\times 5+2}{5}}$$

Add 15 and 22 to get 37.

$$\frac{\frac{37}{6}}{\frac{7\times 5+2}{5}}$$

Multiply 7 and 5 to get 35.

$$\frac{\frac{37}{6}}{\frac{35+2}{5}}$$

Add 35 and 2 to get 37.

$$\frac{\frac{37}{6}}{\frac{37}{5}}$$

Divide \frac{37}{6} by \frac{37}{5} by multiplying \frac{37}{6} by the reciprocal of \frac{37}{5}.

$$\frac{37}{6}\times \frac{5}{37}$$

Multiply \frac{37}{6} times \frac{5}{37} by multiplying numerator times numerator and denominator times denominator.

$$\frac{37\times 5}{6\times 37}$$

Cancel out 37 in both numerator and denominator.

$$\frac{5}{6}$$

Factor

$$\frac{5}{2 \cdot 3} = 0.8333333333333334$$