Solve 11/4+11/2/5frac{1{8}-33/4}

$$\frac { 1 \frac { 1 } { 4 } + 1 \frac { 1 } { 2 } } { 5 \frac { 1 } { 8 } - 3 \frac { 3 } { 4 } }$$

Evaluate

$$2$$

Solution Steps

Multiply 1 and 4 to get 4.

$$\frac{\frac{4+1}{4}+\frac{1\times 2+1}{2}}{\frac{5\times 8+1}{8}-\frac{3\times 4+3}{4}}$$

Add 4 and 1 to get 5.

$$\frac{\frac{5}{4}+\frac{1\times 2+1}{2}}{\frac{5\times 8+1}{8}-\frac{3\times 4+3}{4}}$$

Multiply 1 and 2 to get 2.

$$\frac{\frac{5}{4}+\frac{2+1}{2}}{\frac{5\times 8+1}{8}-\frac{3\times 4+3}{4}}$$

Add 2 and 1 to get 3.

$$\frac{\frac{5}{4}+\frac{3}{2}}{\frac{5\times 8+1}{8}-\frac{3\times 4+3}{4}}$$

Least common multiple of 4 and 2 is 4. Convert \frac{5}{4} and \frac{3}{2} to fractions with denominator 4.

$$\frac{\frac{5}{4}+\frac{6}{4}}{\frac{5\times 8+1}{8}-\frac{3\times 4+3}{4}}$$

Since \frac{5}{4} and \frac{6}{4} have the same denominator, add them by adding their numerators.

$$\frac{\frac{5+6}{4}}{\frac{5\times 8+1}{8}-\frac{3\times 4+3}{4}}$$

Add 5 and 6 to get 11.

$$\frac{\frac{11}{4}}{\frac{5\times 8+1}{8}-\frac{3\times 4+3}{4}}$$

Multiply 5 and 8 to get 40.

$$\frac{\frac{11}{4}}{\frac{40+1}{8}-\frac{3\times 4+3}{4}}$$

Add 40 and 1 to get 41.

$$\frac{\frac{11}{4}}{\frac{41}{8}-\frac{3\times 4+3}{4}}$$

Multiply 3 and 4 to get 12.

$$\frac{\frac{11}{4}}{\frac{41}{8}-\frac{12+3}{4}}$$

Add 12 and 3 to get 15.

$$\frac{\frac{11}{4}}{\frac{41}{8}-\frac{15}{4}}$$

Least common multiple of 8 and 4 is 8. Convert \frac{41}{8} and \frac{15}{4} to fractions with denominator 8.

$$\frac{\frac{11}{4}}{\frac{41}{8}-\frac{30}{8}}$$

Since \frac{41}{8} and \frac{30}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{11}{4}}{\frac{41-30}{8}}$$

Subtract 30 from 41 to get 11.

$$\frac{\frac{11}{4}}{\frac{11}{8}}$$

Divide \frac{11}{4} by \frac{11}{8} by multiplying \frac{11}{4} by the reciprocal of \frac{11}{8}.

$$\frac{11}{4}\times \frac{8}{11}$$

Multiply \frac{11}{4} times \frac{8}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{11\times 8}{4\times 11}$$

Cancel out 11 in both numerator and denominator.

$$\frac{8}{4}$$

Divide 8 by 4 to get 2.

$$2$$

Factor

$$2$$