Solve 46/.35*1frac{1{3}-51/2div32/3+3.7}=

$$\frac { 46 } { .35 \times 1 \frac { 1 } { 3 } - 5 \frac { 1 } { 2 } \div 3 \frac { 2 } { 3 } + 3.7 } =$$

Evaluate

$$17.25$$

Solution Steps

Multiply 1 and 3 to get 3.

$$\frac{46}{0.35\times \frac{3+1}{3}-\frac{\frac{5\times 2+1}{2}}{\frac{3\times 3+2}{3}}+3.7}$$

Add 3 and 1 to get 4.

$$\frac{46}{0.35\times \frac{4}{3}-\frac{\frac{5\times 2+1}{2}}{\frac{3\times 3+2}{3}}+3.7}$$

Convert decimal number 0.35 to fraction \frac{35}{100}. Reduce the fraction \frac{35}{100} to lowest terms by extracting and canceling out 5.

$$\frac{46}{\frac{7}{20}\times \frac{4}{3}-\frac{\frac{5\times 2+1}{2}}{\frac{3\times 3+2}{3}}+3.7}$$

Multiply \frac{7}{20} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{46}{\frac{7\times 4}{20\times 3}-\frac{\frac{5\times 2+1}{2}}{\frac{3\times 3+2}{3}}+3.7}$$

Do the multiplications in the fraction \frac{7\times 4}{20\times 3}.

$$\frac{46}{\frac{28}{60}-\frac{\frac{5\times 2+1}{2}}{\frac{3\times 3+2}{3}}+3.7}$$

Reduce the fraction \frac{28}{60} to lowest terms by extracting and canceling out 4.

$$\frac{46}{\frac{7}{15}-\frac{\frac{5\times 2+1}{2}}{\frac{3\times 3+2}{3}}+3.7}$$

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}.

$$\frac{46}{\frac{7}{15}-\frac{\left(5\times 2+1\right)\times 3}{2\left(3\times 3+2\right)}+3.7}$$

Multiply 5 and 2 to get 10.

$$\frac{46}{\frac{7}{15}-\frac{\left(10+1\right)\times 3}{2\left(3\times 3+2\right)}+3.7}$$

Add 10 and 1 to get 11.

$$\frac{46}{\frac{7}{15}-\frac{11\times 3}{2\left(3\times 3+2\right)}+3.7}$$

Multiply 11 and 3 to get 33.

$$\frac{46}{\frac{7}{15}-\frac{33}{2\left(3\times 3+2\right)}+3.7}$$

Multiply 3 and 3 to get 9.

$$\frac{46}{\frac{7}{15}-\frac{33}{2\left(9+2\right)}+3.7}$$

Add 9 and 2 to get 11.

$$\frac{46}{\frac{7}{15}-\frac{33}{2\times 11}+3.7}$$

Multiply 2 and 11 to get 22.

$$\frac{46}{\frac{7}{15}-\frac{33}{22}+3.7}$$

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

$$\frac{46}{\frac{7}{15}-\frac{3}{2}+3.7}$$

Least common multiple of 15 and 2 is 30. Convert \frac{7}{15} and \frac{3}{2} to fractions with denominator 30.

$$\frac{46}{\frac{14}{30}-\frac{45}{30}+3.7}$$

Since \frac{14}{30} and \frac{45}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{46}{\frac{14-45}{30}+3.7}$$

Subtract 45 from 14 to get -31.

$$\frac{46}{-\frac{31}{30}+3.7}$$

Convert decimal number 3.7 to fraction \frac{37}{10}.

$$\frac{46}{-\frac{31}{30}+\frac{37}{10}}$$

Least common multiple of 30 and 10 is 30. Convert -\frac{31}{30} and \frac{37}{10} to fractions with denominator 30.

$$\frac{46}{-\frac{31}{30}+\frac{111}{30}}$$

Since -\frac{31}{30} and \frac{111}{30} have the same denominator, add them by adding their numerators.

$$\frac{46}{\frac{-31+111}{30}}$$

Add -31 and 111 to get 80.

$$\frac{46}{\frac{80}{30}}$$

Reduce the fraction \frac{80}{30} to lowest terms by extracting and canceling out 10.

$$\frac{46}{\frac{8}{3}}$$

Divide 46 by \frac{8}{3} by multiplying 46 by the reciprocal of \frac{8}{3}.

$$46\times \frac{3}{8}$$

Express 46\times \frac{3}{8} as a single fraction.

$$\frac{46\times 3}{8}$$

Multiply 46 and 3 to get 138.

$$\frac{138}{8}$$

Reduce the fraction \frac{138}{8} to lowest terms by extracting and canceling out 2.

$$\frac{69}{4}$$

Factor

$$\frac{3 \cdot 23}{2 ^ {2}} = 17\frac{1}{4} = 17.25$$