Solve 11/4+1/3div13/4-11/12=

$$1 \frac { 1 } { 4 } + \frac { 1 } { 3 } \div 1 \frac { 3 } { 4 } - 1 \frac { 1 } { 12 } =$$

Evaluate

$$\frac{5}{14}\approx 0.357142857$$

Solution Steps

Multiply 1 and 4 to get 4.

$$\frac{4+1}{4}+\frac{\frac{1}{3}}{\frac{1\times 4+3}{4}}-\frac{1\times 12+1}{12}$$

Add 4 and 1 to get 5.

$$\frac{5}{4}+\frac{\frac{1}{3}}{\frac{1\times 4+3}{4}}-\frac{1\times 12+1}{12}$$

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

$$\frac{5}{4}+\frac{4}{3\left(1\times 4+3\right)}-\frac{1\times 12+1}{12}$$

Multiply 1 and 4 to get 4.

$$\frac{5}{4}+\frac{4}{3\left(4+3\right)}-\frac{1\times 12+1}{12}$$

Add 4 and 3 to get 7.

$$\frac{5}{4}+\frac{4}{3\times 7}-\frac{1\times 12+1}{12}$$

Multiply 3 and 7 to get 21.

$$\frac{5}{4}+\frac{4}{21}-\frac{1\times 12+1}{12}$$

Least common multiple of 4 and 21 is 84. Convert \frac{5}{4} and \frac{4}{21} to fractions with denominator 84.

$$\frac{105}{84}+\frac{16}{84}-\frac{1\times 12+1}{12}$$

Since \frac{105}{84} and \frac{16}{84} have the same denominator, add them by adding their numerators.

$$\frac{105+16}{84}-\frac{1\times 12+1}{12}$$

Add 105 and 16 to get 121.

$$\frac{121}{84}-\frac{1\times 12+1}{12}$$

Multiply 1 and 12 to get 12.

$$\frac{121}{84}-\frac{12+1}{12}$$

Add 12 and 1 to get 13.

$$\frac{121}{84}-\frac{13}{12}$$

Least common multiple of 84 and 12 is 84. Convert \frac{121}{84} and \frac{13}{12} to fractions with denominator 84.

$$\frac{121}{84}-\frac{91}{84}$$

Since \frac{121}{84} and \frac{91}{84} have the same denominator, subtract them by subtracting their numerators.

$$\frac{121-91}{84}$$

Subtract 91 from 121 to get 30.

$$\frac{30}{84}$$

Reduce the fraction \frac{30}{84} to lowest terms by extracting and canceling out 6.

$$\frac{5}{14}$$

Factor

$$\frac{5}{2 \cdot 7} = 0.35714285714285715$$