Solve 41/4+62/3div21/2

$$4 \frac { 1 } { 4 } + 6 \frac { 2 } { 3 } \div 2 \frac { 1 } { 2 }$$

Evaluate

$$\frac{83}{12}\approx 6.916666667$$

Solution Steps

Multiply 4 and 4 to get 16.

$$\frac{16+1}{4}+\frac{\frac{6\times 3+2}{3}}{\frac{2\times 2+1}{2}}$$

Add 16 and 1 to get 17.

$$\frac{17}{4}+\frac{\frac{6\times 3+2}{3}}{\frac{2\times 2+1}{2}}$$

Divide \frac{6\times 3+2}{3} by \frac{2\times 2+1}{2} by multiplying \frac{6\times 3+2}{3} by the reciprocal of \frac{2\times 2+1}{2}.

$$\frac{17}{4}+\frac{\left(6\times 3+2\right)\times 2}{3\left(2\times 2+1\right)}$$

Multiply 6 and 3 to get 18.

$$\frac{17}{4}+\frac{\left(18+2\right)\times 2}{3\left(2\times 2+1\right)}$$

Add 18 and 2 to get 20.

$$\frac{17}{4}+\frac{20\times 2}{3\left(2\times 2+1\right)}$$

Multiply 20 and 2 to get 40.

$$\frac{17}{4}+\frac{40}{3\left(2\times 2+1\right)}$$

Multiply 2 and 2 to get 4.

$$\frac{17}{4}+\frac{40}{3\left(4+1\right)}$$

Add 4 and 1 to get 5.

$$\frac{17}{4}+\frac{40}{3\times 5}$$

Multiply 3 and 5 to get 15.

$$\frac{17}{4}+\frac{40}{15}$$

Reduce the fraction \frac{40}{15} to lowest terms by extracting and canceling out 5.

$$\frac{17}{4}+\frac{8}{3}$$

Least common multiple of 4 and 3 is 12. Convert \frac{17}{4} and \frac{8}{3} to fractions with denominator 12.

$$\frac{51}{12}+\frac{32}{12}$$

Since \frac{51}{12} and \frac{32}{12} have the same denominator, add them by adding their numerators.

$$\frac{51+32}{12}$$

Add 51 and 32 to get 83.

$$\frac{83}{12}$$

Factor

$$\frac{83}{2 ^ {2} \cdot 3} = 6\frac{11}{12} = 6.916666666666667$$