Solve 11/2+21/3*71/7=

$$1 \frac { 1 } { 2 } + 2 \frac { 1 } { 3 } \cdot 7 \frac { 1 } { 7 } =$$

Evaluate

$$\frac{109}{6}\approx 18.166666667$$

Solution Steps

Multiply 1 and 2 to get 2.

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

Add 2 and 1 to get 3.

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

Multiply 2 and 3 to get 6.

$$\frac{3}{2}+\frac{6+1}{3}\times \frac{7\times 7+1}{7}$$

Add 6 and 1 to get 7.

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

Multiply 7 and 7 to get 49.

$$\frac{3}{2}+\frac{7}{3}\times \frac{49+1}{7}$$

Add 49 and 1 to get 50.

$$\frac{3}{2}+\frac{7}{3}\times \frac{50}{7}$$

Multiply \frac{7}{3} times \frac{50}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{2}+\frac{7\times 50}{3\times 7}$$

Cancel out 7 in both numerator and denominator.

$$\frac{3}{2}+\frac{50}{3}$$

Least common multiple of 2 and 3 is 6. Convert \frac{3}{2} and \frac{50}{3} to fractions with denominator 6.

$$\frac{9}{6}+\frac{100}{6}$$

Since \frac{9}{6} and \frac{100}{6} have the same denominator, add them by adding their numerators.

$$\frac{9+100}{6}$$

Add 9 and 100 to get 109.

$$\frac{109}{6}$$

Factor

$$\frac{109}{2 \cdot 3} = 18\frac{1}{6} = 18.166666666666668$$