Solve 727/40-(61/4+517/40)+43/8=

$$7 \frac{ 27 }{ 40 } -(6 \frac{ 1 }{ 4 } +5 \frac{ 17 }{ 40 } )+4 \frac{ 3 }{ 8 } =$$

Evaluate

$$\frac{3}{8}=0.375$$

Solution Steps

Multiply 7 and 40 to get 280.

$$\frac{280+27}{40}-\left(\frac{6\times 4+1}{4}+\frac{5\times 40+17}{40}\right)+\frac{4\times 8+3}{8}$$

Add 280 and 27 to get 307.

$$\frac{307}{40}-\left(\frac{6\times 4+1}{4}+\frac{5\times 40+17}{40}\right)+\frac{4\times 8+3}{8}$$

Multiply 6 and 4 to get 24.

$$\frac{307}{40}-\left(\frac{24+1}{4}+\frac{5\times 40+17}{40}\right)+\frac{4\times 8+3}{8}$$

Add 24 and 1 to get 25.

$$\frac{307}{40}-\left(\frac{25}{4}+\frac{5\times 40+17}{40}\right)+\frac{4\times 8+3}{8}$$

Multiply 5 and 40 to get 200.

$$\frac{307}{40}-\left(\frac{25}{4}+\frac{200+17}{40}\right)+\frac{4\times 8+3}{8}$$

Add 200 and 17 to get 217.

$$\frac{307}{40}-\left(\frac{25}{4}+\frac{217}{40}\right)+\frac{4\times 8+3}{8}$$

Least common multiple of 4 and 40 is 40. Convert \frac{25}{4} and \frac{217}{40} to fractions with denominator 40.

$$\frac{307}{40}-\left(\frac{250}{40}+\frac{217}{40}\right)+\frac{4\times 8+3}{8}$$

Since \frac{250}{40} and \frac{217}{40} have the same denominator, add them by adding their numerators.

$$\frac{307}{40}-\frac{250+217}{40}+\frac{4\times 8+3}{8}$$

Add 250 and 217 to get 467.

$$\frac{307}{40}-\frac{467}{40}+\frac{4\times 8+3}{8}$$

Since \frac{307}{40} and \frac{467}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{307-467}{40}+\frac{4\times 8+3}{8}$$

Subtract 467 from 307 to get -160.

$$\frac{-160}{40}+\frac{4\times 8+3}{8}$$

Divide -160 by 40 to get -4.

$$-4+\frac{4\times 8+3}{8}$$

Multiply 4 and 8 to get 32.

$$-4+\frac{32+3}{8}$$

Add 32 and 3 to get 35.

$$-4+\frac{35}{8}$$

Convert -4 to fraction -\frac{32}{8}.

$$-\frac{32}{8}+\frac{35}{8}$$

Since -\frac{32}{8} and \frac{35}{8} have the same denominator, add them by adding their numerators.

$$\frac{-32+35}{8}$$

Add -32 and 35 to get 3.

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

Factor

$$\frac{3}{2 ^ {3}} = 0.375$$