Solve 71/8*(67/8-43/16)=

$$7 \frac { 1 } { 8 } \times ( 6 \frac { 7 } { 8 } - 4 \frac { 3 } { 16 } ) =$$

Evaluate

$$\frac{2451}{128}=19.1484375$$

Solution Steps

Multiply 7 and 8 to get 56.

$$\frac{56+1}{8}\left(\frac{6\times 8+7}{8}-\frac{4\times 16+3}{16}\right)$$

Add 56 and 1 to get 57.

$$\frac{57}{8}\left(\frac{6\times 8+7}{8}-\frac{4\times 16+3}{16}\right)$$

Multiply 6 and 8 to get 48.

$$\frac{57}{8}\left(\frac{48+7}{8}-\frac{4\times 16+3}{16}\right)$$

Add 48 and 7 to get 55.

$$\frac{57}{8}\left(\frac{55}{8}-\frac{4\times 16+3}{16}\right)$$

Multiply 4 and 16 to get 64.

$$\frac{57}{8}\left(\frac{55}{8}-\frac{64+3}{16}\right)$$

Add 64 and 3 to get 67.

$$\frac{57}{8}\left(\frac{55}{8}-\frac{67}{16}\right)$$

Least common multiple of 8 and 16 is 16. Convert \frac{55}{8} and \frac{67}{16} to fractions with denominator 16.

$$\frac{57}{8}\left(\frac{110}{16}-\frac{67}{16}\right)$$

Since \frac{110}{16} and \frac{67}{16} have the same denominator, subtract them by subtracting their numerators.

$$\frac{57}{8}\times \frac{110-67}{16}$$

Subtract 67 from 110 to get 43.

$$\frac{57}{8}\times \frac{43}{16}$$

Multiply \frac{57}{8} times \frac{43}{16} by multiplying numerator times numerator and denominator times denominator.

$$\frac{57\times 43}{8\times 16}$$

Do the multiplications in the fraction \frac{57\times 43}{8\times 16}.

$$\frac{2451}{128}$$

Factor

$$\frac{3 \cdot 19 \cdot 43}{2 ^ {7}} = 19\frac{19}{128} = 19.1484375$$