Solve 44/2*(315/32+43/4-(-3/8)div6frac{3}{16}

$$4 \frac { 4 } { 2 } \times ( 3 \frac { 15 } { 32 } + 4 \frac { 3 } { 4 } - ( - \frac { 3 } { 8 } ) \div 6 \frac { 3 } { 16 }$$

Evaluate

$$\frac{8743}{176}\approx 49.676136364$$

Solution Steps

Multiply 4 and 2 to get 8.

$$\frac{8+4}{2}\left(\frac{3\times 32+15}{32}+\frac{4\times 4+3}{4}-\frac{-\frac{3}{8}}{\frac{6\times 16+3}{16}}\right)$$

Add 8 and 4 to get 12.

$$\frac{12}{2}\left(\frac{3\times 32+15}{32}+\frac{4\times 4+3}{4}-\frac{-\frac{3}{8}}{\frac{6\times 16+3}{16}}\right)$$

Divide 12 by 2 to get 6.

$$6\left(\frac{3\times 32+15}{32}+\frac{4\times 4+3}{4}-\frac{-\frac{3}{8}}{\frac{6\times 16+3}{16}}\right)$$

Multiply 3 and 32 to get 96.

$$6\left(\frac{96+15}{32}+\frac{4\times 4+3}{4}-\frac{-\frac{3}{8}}{\frac{6\times 16+3}{16}}\right)$$

Add 96 and 15 to get 111.

$$6\left(\frac{111}{32}+\frac{4\times 4+3}{4}-\frac{-\frac{3}{8}}{\frac{6\times 16+3}{16}}\right)$$

Multiply 4 and 4 to get 16.

$$6\left(\frac{111}{32}+\frac{16+3}{4}-\frac{-\frac{3}{8}}{\frac{6\times 16+3}{16}}\right)$$

Add 16 and 3 to get 19.

$$6\left(\frac{111}{32}+\frac{19}{4}-\frac{-\frac{3}{8}}{\frac{6\times 16+3}{16}}\right)$$

Least common multiple of 32 and 4 is 32. Convert \frac{111}{32} and \frac{19}{4} to fractions with denominator 32.

$$6\left(\frac{111}{32}+\frac{152}{32}-\frac{-\frac{3}{8}}{\frac{6\times 16+3}{16}}\right)$$

Since \frac{111}{32} and \frac{152}{32} have the same denominator, add them by adding their numerators.

$$6\left(\frac{111+152}{32}-\frac{-\frac{3}{8}}{\frac{6\times 16+3}{16}}\right)$$

Add 111 and 152 to get 263.

$$6\left(\frac{263}{32}-\frac{-\frac{3}{8}}{\frac{6\times 16+3}{16}}\right)$$

Divide -\frac{3}{8} by \frac{6\times 16+3}{16} by multiplying -\frac{3}{8} by the reciprocal of \frac{6\times 16+3}{16}.

$$6\left(\frac{263}{32}-\frac{-3\times 16}{8\left(6\times 16+3\right)}\right)$$

Cancel out 8 in both numerator and denominator.

$$6\left(\frac{263}{32}-\frac{-3\times 2}{3+6\times 16}\right)$$

Multiply -3 and 2 to get -6.

$$6\left(\frac{263}{32}-\frac{-6}{3+6\times 16}\right)$$

Multiply 6 and 16 to get 96.

$$6\left(\frac{263}{32}-\frac{-6}{3+96}\right)$$

Add 3 and 96 to get 99.

$$6\left(\frac{263}{32}-\frac{-6}{99}\right)$$

Reduce the fraction \frac{-6}{99} to lowest terms by extracting and canceling out 3.

$$6\left(\frac{263}{32}-\left(-\frac{2}{33}\right)\right)$$

The opposite of -\frac{2}{33} is \frac{2}{33}.

$$6\left(\frac{263}{32}+\frac{2}{33}\right)$$

Least common multiple of 32 and 33 is 1056. Convert \frac{263}{32} and \frac{2}{33} to fractions with denominator 1056.

$$6\left(\frac{8679}{1056}+\frac{64}{1056}\right)$$

Since \frac{8679}{1056} and \frac{64}{1056} have the same denominator, add them by adding their numerators.

$$6\times \frac{8679+64}{1056}$$

Add 8679 and 64 to get 8743.

$$6\times \frac{8743}{1056}$$

Express 6\times \frac{8743}{1056} as a single fraction.

$$\frac{6\times 8743}{1056}$$

Multiply 6 and 8743 to get 52458.

$$\frac{52458}{1056}$$

Reduce the fraction \frac{52458}{1056} to lowest terms by extracting and canceling out 6.

$$\frac{8743}{176}$$

Factor

$$\frac{7 \cdot 1249}{2 ^ {4} \cdot 11} = 49\frac{119}{176} = 49.67613636363637$$