Solve 11/2+21/3div31/4

$$1 \frac{ 1 }{ 2 } +2 \frac{ 1 }{ 3 } \div 3 \frac{ 1 }{ 4 }$$

Evaluate

$$\frac{173}{78}\approx 2.217948718$$

Solution Steps

Multiply 1 and 2 to get 2.

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

Add 2 and 1 to get 3.

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

Divide \frac{2\times 3+1}{3} by \frac{3\times 4+1}{4} by multiplying \frac{2\times 3+1}{3} by the reciprocal of \frac{3\times 4+1}{4}.

$$\frac{3}{2}+\frac{\left(2\times 3+1\right)\times 4}{3\left(3\times 4+1\right)}$$

Multiply 2 and 3 to get 6.

$$\frac{3}{2}+\frac{\left(6+1\right)\times 4}{3\left(3\times 4+1\right)}$$

Add 6 and 1 to get 7.

$$\frac{3}{2}+\frac{7\times 4}{3\left(3\times 4+1\right)}$$

Multiply 7 and 4 to get 28.

$$\frac{3}{2}+\frac{28}{3\left(3\times 4+1\right)}$$

Multiply 3 and 4 to get 12.

$$\frac{3}{2}+\frac{28}{3\left(12+1\right)}$$

Add 12 and 1 to get 13.

$$\frac{3}{2}+\frac{28}{3\times 13}$$

Multiply 3 and 13 to get 39.

$$\frac{3}{2}+\frac{28}{39}$$

Least common multiple of 2 and 39 is 78. Convert \frac{3}{2} and \frac{28}{39} to fractions with denominator 78.

$$\frac{117}{78}+\frac{56}{78}$$

Since \frac{117}{78} and \frac{56}{78} have the same denominator, add them by adding their numerators.

$$\frac{117+56}{78}$$

Add 117 and 56 to get 173.

$$\frac{173}{78}$$

Factor

$$\frac{173}{2 \cdot 3 \cdot 13} = 2\frac{17}{78} = 2.217948717948718$$