Solve 71/2+1/19div1/3+1/2-3

$$7 \frac{ 1 }{ 2 } + \frac{ 1 }{ 19 } \div \frac{ 1 }{ 3 } + \frac{ 1 }{ 2 } -3$$

Evaluate

$$\frac{98}{19}\approx 5.157894737$$

Solution Steps

Multiply 7 and 2 to get 14.

$$\frac{14+1}{2}+\frac{\frac{1}{19}}{\frac{1}{3}}+\frac{1}{2}-3$$

Add 14 and 1 to get 15.

$$\frac{15}{2}+\frac{\frac{1}{19}}{\frac{1}{3}}+\frac{1}{2}-3$$

Divide \frac{1}{19} by \frac{1}{3} by multiplying \frac{1}{19} by the reciprocal of \frac{1}{3}.

$$\frac{15}{2}+\frac{1}{19}\times 3+\frac{1}{2}-3$$

Multiply \frac{1}{19} and 3 to get \frac{3}{19}.

$$\frac{15}{2}+\frac{3}{19}+\frac{1}{2}-3$$

Least common multiple of 2 and 19 is 38. Convert \frac{15}{2} and \frac{3}{19} to fractions with denominator 38.

$$\frac{285}{38}+\frac{6}{38}+\frac{1}{2}-3$$

Since \frac{285}{38} and \frac{6}{38} have the same denominator, add them by adding their numerators.

$$\frac{285+6}{38}+\frac{1}{2}-3$$

Add 285 and 6 to get 291.

$$\frac{291}{38}+\frac{1}{2}-3$$

Least common multiple of 38 and 2 is 38. Convert \frac{291}{38} and \frac{1}{2} to fractions with denominator 38.

$$\frac{291}{38}+\frac{19}{38}-3$$

Since \frac{291}{38} and \frac{19}{38} have the same denominator, add them by adding their numerators.

$$\frac{291+19}{38}-3$$

Add 291 and 19 to get 310.

$$\frac{310}{38}-3$$

Reduce the fraction \frac{310}{38} to lowest terms by extracting and canceling out 2.

$$\frac{155}{19}-3$$

Convert 3 to fraction \frac{57}{19}.

$$\frac{155}{19}-\frac{57}{19}$$

Since \frac{155}{19} and \frac{57}{19} have the same denominator, subtract them by subtracting their numerators.

$$\frac{155-57}{19}$$

Subtract 57 from 155 to get 98.

$$\frac{98}{19}$$

Factor

$$\frac{2 \cdot 7 ^ {2}}{19} = 5\frac{3}{19} = 5.157894736842105$$