Solve 46/35*1frac{1{3}-51/2div32/3+37}=

$$\frac { 46 } { 35 \times 1 \frac { 1 } { 3 } - 5 \frac { 1 } { 2 } \div 3 \frac { 2 } { 3 } + 37 } =$$

Evaluate

$$\frac{276}{493}\approx 0.559837728$$

Solution Steps

Multiply 1 and 3 to get 3.

$$\frac{46}{35\times \frac{3+1}{3}-\frac{\frac{5\times 2+1}{2}}{\frac{3\times 3+2}{3}}+37}$$

Add 3 and 1 to get 4.

$$\frac{46}{35\times \frac{4}{3}-\frac{\frac{5\times 2+1}{2}}{\frac{3\times 3+2}{3}}+37}$$

Express 35\times \frac{4}{3} as a single fraction.

$$\frac{46}{\frac{35\times 4}{3}-\frac{\frac{5\times 2+1}{2}}{\frac{3\times 3+2}{3}}+37}$$

Multiply 35 and 4 to get 140.

$$\frac{46}{\frac{140}{3}-\frac{\frac{5\times 2+1}{2}}{\frac{3\times 3+2}{3}}+37}$$

Divide \frac{5\times 2+1}{2} by \frac{3\times 3+2}{3} by multiplying \frac{5\times 2+1}{2} by the reciprocal of \frac{3\times 3+2}{3}.

$$\frac{46}{\frac{140}{3}-\frac{\left(5\times 2+1\right)\times 3}{2\left(3\times 3+2\right)}+37}$$

Multiply 5 and 2 to get 10.

$$\frac{46}{\frac{140}{3}-\frac{\left(10+1\right)\times 3}{2\left(3\times 3+2\right)}+37}$$

Add 10 and 1 to get 11.

$$\frac{46}{\frac{140}{3}-\frac{11\times 3}{2\left(3\times 3+2\right)}+37}$$

Multiply 11 and 3 to get 33.

$$\frac{46}{\frac{140}{3}-\frac{33}{2\left(3\times 3+2\right)}+37}$$

Multiply 3 and 3 to get 9.

$$\frac{46}{\frac{140}{3}-\frac{33}{2\left(9+2\right)}+37}$$

Add 9 and 2 to get 11.

$$\frac{46}{\frac{140}{3}-\frac{33}{2\times 11}+37}$$

Multiply 2 and 11 to get 22.

$$\frac{46}{\frac{140}{3}-\frac{33}{22}+37}$$

Reduce the fraction \frac{33}{22} to lowest terms by extracting and canceling out 11.

$$\frac{46}{\frac{140}{3}-\frac{3}{2}+37}$$

Least common multiple of 3 and 2 is 6. Convert \frac{140}{3} and \frac{3}{2} to fractions with denominator 6.

$$\frac{46}{\frac{280}{6}-\frac{9}{6}+37}$$

Since \frac{280}{6} and \frac{9}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{46}{\frac{280-9}{6}+37}$$

Subtract 9 from 280 to get 271.

$$\frac{46}{\frac{271}{6}+37}$$

Convert 37 to fraction \frac{222}{6}.

$$\frac{46}{\frac{271}{6}+\frac{222}{6}}$$

Since \frac{271}{6} and \frac{222}{6} have the same denominator, add them by adding their numerators.

$$\frac{46}{\frac{271+222}{6}}$$

Add 271 and 222 to get 493.

$$\frac{46}{\frac{493}{6}}$$

Divide 46 by \frac{493}{6} by multiplying 46 by the reciprocal of \frac{493}{6}.

$$46\times \frac{6}{493}$$

Express 46\times \frac{6}{493} as a single fraction.

$$\frac{46\times 6}{493}$$

Multiply 46 and 6 to get 276.

$$\frac{276}{493}$$

Factor

$$\frac{2 ^ {2} \cdot 3 \cdot 23}{17 \cdot 29} = 0.5598377281947262$$