Solve 2+2/3+3/4div3/7

$$2 + \frac { 2 } { 3 } + \frac { 3 } { 4 } \div \frac { 3 } { 7 }$$

Evaluate

$$\frac{53}{12}\approx 4.416666667$$

Solution Steps

Convert 2 to fraction \frac{6}{3}.

$$\frac{6}{3}+\frac{2}{3}+\frac{\frac{3}{4}}{\frac{3}{7}}$$

Since \frac{6}{3} and \frac{2}{3} have the same denominator, add them by adding their numerators.

$$\frac{6+2}{3}+\frac{\frac{3}{4}}{\frac{3}{7}}$$

Add 6 and 2 to get 8.

$$\frac{8}{3}+\frac{\frac{3}{4}}{\frac{3}{7}}$$

Divide \frac{3}{4} by \frac{3}{7} by multiplying \frac{3}{4} by the reciprocal of \frac{3}{7}.

$$\frac{8}{3}+\frac{3}{4}\times \frac{7}{3}$$

Multiply \frac{3}{4} times \frac{7}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8}{3}+\frac{3\times 7}{4\times 3}$$

Cancel out 3 in both numerator and denominator.

$$\frac{8}{3}+\frac{7}{4}$$

Least common multiple of 3 and 4 is 12. Convert \frac{8}{3} and \frac{7}{4} to fractions with denominator 12.

$$\frac{32}{12}+\frac{21}{12}$$

Since \frac{32}{12} and \frac{21}{12} have the same denominator, add them by adding their numerators.

$$\frac{32+21}{12}$$

Add 32 and 21 to get 53.

$$\frac{53}{12}$$

Factor

$$\frac{53}{2 ^ {2} \cdot 3} = 4\frac{5}{12} = 4.416666666666667$$