Solve 47/7-5/5text{of}1/3div8-201/4*3frac{1}{9}text{of}frac{1}{28}divfrac{3}{16}text{of}2

$$4 \frac { 7 } { 7 } - \frac { 5 } { 5 } \text { of } \frac { 1 } { 3 } \div 8 - 20 \frac { 1 } { 4 } \times 3 \frac { 1 } { 9 } \text { of } \frac { 1 } { 28 } \div \frac { 3 } { 16 } \text { of } 2$$

Evaluate

$$-\frac{457}{24}\approx -19.041666667$$

Solution Steps

Divide 5 by 5 to get 1.

$$\frac{4\times 7+7}{7}-\frac{1\times \frac{1}{3}}{8}-\frac{\frac{20\times 4+1}{4}\times \frac{3\times 9+1}{9}\times \frac{1}{28}}{\frac{3}{16}}\times 2$$

Multiply 4 and 7 to get 28.

$$\frac{28+7}{7}-\frac{1\times \frac{1}{3}}{8}-\frac{\frac{20\times 4+1}{4}\times \frac{3\times 9+1}{9}\times \frac{1}{28}}{\frac{3}{16}}\times 2$$

Add 28 and 7 to get 35.

$$\frac{35}{7}-\frac{1\times \frac{1}{3}}{8}-\frac{\frac{20\times 4+1}{4}\times \frac{3\times 9+1}{9}\times \frac{1}{28}}{\frac{3}{16}}\times 2$$

Divide 35 by 7 to get 5.

$$5-\frac{1\times \frac{1}{3}}{8}-\frac{\frac{20\times 4+1}{4}\times \frac{3\times 9+1}{9}\times \frac{1}{28}}{\frac{3}{16}}\times 2$$

Multiply 1 and \frac{1}{3} to get \frac{1}{3}.

$$5-\frac{\frac{1}{3}}{8}-\frac{\frac{20\times 4+1}{4}\times \frac{3\times 9+1}{9}\times \frac{1}{28}}{\frac{3}{16}}\times 2$$

Express \frac{\frac{1}{3}}{8} as a single fraction.

$$5-\frac{1}{3\times 8}-\frac{\frac{20\times 4+1}{4}\times \frac{3\times 9+1}{9}\times \frac{1}{28}}{\frac{3}{16}}\times 2$$

Multiply 3 and 8 to get 24.

$$5-\frac{1}{24}-\frac{\frac{20\times 4+1}{4}\times \frac{3\times 9+1}{9}\times \frac{1}{28}}{\frac{3}{16}}\times 2$$

Convert 5 to fraction \frac{120}{24}.

$$\frac{120}{24}-\frac{1}{24}-\frac{\frac{20\times 4+1}{4}\times \frac{3\times 9+1}{9}\times \frac{1}{28}}{\frac{3}{16}}\times 2$$

Since \frac{120}{24} and \frac{1}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{120-1}{24}-\frac{\frac{20\times 4+1}{4}\times \frac{3\times 9+1}{9}\times \frac{1}{28}}{\frac{3}{16}}\times 2$$

Subtract 1 from 120 to get 119.

$$\frac{119}{24}-\frac{\frac{20\times 4+1}{4}\times \frac{3\times 9+1}{9}\times \frac{1}{28}}{\frac{3}{16}}\times 2$$

Multiply 20 and 4 to get 80.

$$\frac{119}{24}-\frac{\frac{80+1}{4}\times \frac{3\times 9+1}{9}\times \frac{1}{28}}{\frac{3}{16}}\times 2$$

Add 80 and 1 to get 81.

$$\frac{119}{24}-\frac{\frac{81}{4}\times \frac{3\times 9+1}{9}\times \frac{1}{28}}{\frac{3}{16}}\times 2$$

Multiply 3 and 9 to get 27.

$$\frac{119}{24}-\frac{\frac{81}{4}\times \frac{27+1}{9}\times \frac{1}{28}}{\frac{3}{16}}\times 2$$

Add 27 and 1 to get 28.

$$\frac{119}{24}-\frac{\frac{81}{4}\times \frac{28}{9}\times \frac{1}{28}}{\frac{3}{16}}\times 2$$

Multiply \frac{81}{4} times \frac{28}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{119}{24}-\frac{\frac{81\times 28}{4\times 9}\times \frac{1}{28}}{\frac{3}{16}}\times 2$$

Do the multiplications in the fraction \frac{81\times 28}{4\times 9}.

$$\frac{119}{24}-\frac{\frac{2268}{36}\times \frac{1}{28}}{\frac{3}{16}}\times 2$$

Divide 2268 by 36 to get 63.

$$\frac{119}{24}-\frac{63\times \frac{1}{28}}{\frac{3}{16}}\times 2$$

Multiply 63 and \frac{1}{28} to get \frac{63}{28}.

$$\frac{119}{24}-\frac{\frac{63}{28}}{\frac{3}{16}}\times 2$$

Reduce the fraction \frac{63}{28} to lowest terms by extracting and canceling out 7.

$$\frac{119}{24}-\frac{\frac{9}{4}}{\frac{3}{16}}\times 2$$

Divide \frac{9}{4} by \frac{3}{16} by multiplying \frac{9}{4} by the reciprocal of \frac{3}{16}.

$$\frac{119}{24}-\frac{9}{4}\times \frac{16}{3}\times 2$$

Multiply \frac{9}{4} times \frac{16}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{119}{24}-\frac{9\times 16}{4\times 3}\times 2$$

Do the multiplications in the fraction \frac{9\times 16}{4\times 3}.

$$\frac{119}{24}-\frac{144}{12}\times 2$$

Divide 144 by 12 to get 12.

$$\frac{119}{24}-12\times 2$$

Multiply 12 and 2 to get 24.

$$\frac{119}{24}-24$$

Convert 24 to fraction \frac{576}{24}.

$$\frac{119}{24}-\frac{576}{24}$$

Since \frac{119}{24} and \frac{576}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{119-576}{24}$$

Subtract 576 from 119 to get -457.

$$-\frac{457}{24}$$

Factor

$$-\frac{457}{24} = -19\frac{1}{24} = -19.041666666666668$$