Solve 5.32:(152/100-18/100):(0.626+1.6*7/8)

$$5.32 : ( 1 \frac { 52 } { 100 } - \frac { 18 } { 100 } ) : ( 0.626 + 1.6 \cdot \frac { 7 } { 8 } )$$

Evaluate

$$\frac{133000}{67871}\approx 1.959599829$$

Solution Steps

Multiply 1 and 100 to get 100.

$$\frac{\frac{5.32}{\frac{100+52}{100}-\frac{18}{100}}}{0.626+1.6\times \frac{7}{8}}$$

Add 100 and 52 to get 152.

$$\frac{\frac{5.32}{\frac{152}{100}-\frac{18}{100}}}{0.626+1.6\times \frac{7}{8}}$$

Reduce the fraction \frac{152}{100} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{5.32}{\frac{38}{25}-\frac{18}{100}}}{0.626+1.6\times \frac{7}{8}}$$

Reduce the fraction \frac{18}{100} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{5.32}{\frac{38}{25}-\frac{9}{50}}}{0.626+1.6\times \frac{7}{8}}$$

Least common multiple of 25 and 50 is 50. Convert \frac{38}{25} and \frac{9}{50} to fractions with denominator 50.

$$\frac{\frac{5.32}{\frac{76}{50}-\frac{9}{50}}}{0.626+1.6\times \frac{7}{8}}$$

Since \frac{76}{50} and \frac{9}{50} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5.32}{\frac{76-9}{50}}}{0.626+1.6\times \frac{7}{8}}$$

Subtract 9 from 76 to get 67.

$$\frac{\frac{5.32}{\frac{67}{50}}}{0.626+1.6\times \frac{7}{8}}$$

Divide 5.32 by \frac{67}{50} by multiplying 5.32 by the reciprocal of \frac{67}{50}.

$$\frac{5.32\times \frac{50}{67}}{0.626+1.6\times \frac{7}{8}}$$

Convert decimal number 5.32 to fraction \frac{532}{100}. Reduce the fraction \frac{532}{100} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{133}{25}\times \frac{50}{67}}{0.626+1.6\times \frac{7}{8}}$$

Multiply \frac{133}{25} times \frac{50}{67} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{133\times 50}{25\times 67}}{0.626+1.6\times \frac{7}{8}}$$

Do the multiplications in the fraction \frac{133\times 50}{25\times 67}.

$$\frac{\frac{6650}{1675}}{0.626+1.6\times \frac{7}{8}}$$

Reduce the fraction \frac{6650}{1675} to lowest terms by extracting and canceling out 25.

$$\frac{\frac{266}{67}}{0.626+1.6\times \frac{7}{8}}$$

Convert decimal number 1.6 to fraction \frac{16}{10}. Reduce the fraction \frac{16}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{266}{67}}{0.626+\frac{8}{5}\times \frac{7}{8}}$$

Multiply \frac{8}{5} times \frac{7}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{266}{67}}{0.626+\frac{8\times 7}{5\times 8}}$$

Cancel out 8 in both numerator and denominator.

$$\frac{\frac{266}{67}}{0.626+\frac{7}{5}}$$

Convert decimal number 0.626 to fraction \frac{626}{1000}. Reduce the fraction \frac{626}{1000} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{266}{67}}{\frac{313}{500}+\frac{7}{5}}$$

Least common multiple of 500 and 5 is 500. Convert \frac{313}{500} and \frac{7}{5} to fractions with denominator 500.

$$\frac{\frac{266}{67}}{\frac{313}{500}+\frac{700}{500}}$$

Since \frac{313}{500} and \frac{700}{500} have the same denominator, add them by adding their numerators.

$$\frac{\frac{266}{67}}{\frac{313+700}{500}}$$

Add 313 and 700 to get 1013.

$$\frac{\frac{266}{67}}{\frac{1013}{500}}$$

Divide \frac{266}{67} by \frac{1013}{500} by multiplying \frac{266}{67} by the reciprocal of \frac{1013}{500}.

$$\frac{266}{67}\times \frac{500}{1013}$$

Multiply \frac{266}{67} times \frac{500}{1013} by multiplying numerator times numerator and denominator times denominator.

$$\frac{266\times 500}{67\times 1013}$$

Do the multiplications in the fraction \frac{266\times 500}{67\times 1013}.

$$\frac{133000}{67871}$$

Factor

$$\frac{7 \cdot 19 \cdot 2 ^ {3} \cdot 5 ^ {3}}{67 \cdot 1013} = 1\frac{65129}{67871} = 1.9595998290875336$$