Solve 40(15/40)(1-0.004|0-75|)(0.7+7.5/150)(1-5/12)

$$40 ( \frac { 15 } { 40 } ) ( 1 - 0.004 | 0 - 75 | ) ( 0.7 + \frac { 7.5 } { 150 } ) ( 1 - \frac { 5 } { 12 } )$$

Evaluate

$$4.59375$$

Solution Steps

Reduce the fraction \frac{15}{40} to lowest terms by extracting and canceling out 5.

$$40\times \frac{3}{8}\left(1-0.004|0-75|\right)\left(0.7+\frac{7.5}{150}\right)\left(1-\frac{5}{12}\right)$$

Express 40\times \frac{3}{8} as a single fraction.

$$\frac{40\times 3}{8}\left(1-0.004|0-75|\right)\left(0.7+\frac{7.5}{150}\right)\left(1-\frac{5}{12}\right)$$

Multiply 40 and 3 to get 120.

$$\frac{120}{8}\left(1-0.004|0-75|\right)\left(0.7+\frac{7.5}{150}\right)\left(1-\frac{5}{12}\right)$$

Divide 120 by 8 to get 15.

$$15\left(1-0.004|0-75|\right)\left(0.7+\frac{7.5}{150}\right)\left(1-\frac{5}{12}\right)$$

Subtract 75 from 0 to get -75.

$$15\left(1-0.004|-75|\right)\left(0.7+\frac{7.5}{150}\right)\left(1-\frac{5}{12}\right)$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -75 is 75.

$$15\left(1-0.004\times 75\right)\left(0.7+\frac{7.5}{150}\right)\left(1-\frac{5}{12}\right)$$

Multiply 0.004 and 75 to get 0.3.

$$15\left(1-0.3\right)\left(0.7+\frac{7.5}{150}\right)\left(1-\frac{5}{12}\right)$$

Subtract 0.3 from 1 to get 0.7.

$$15\times 0.7\left(0.7+\frac{7.5}{150}\right)\left(1-\frac{5}{12}\right)$$

Multiply 15 and 0.7 to get 10.5.

$$10.5\left(0.7+\frac{7.5}{150}\right)\left(1-\frac{5}{12}\right)$$

Expand \frac{7.5}{150} by multiplying both numerator and the denominator by 10.

$$10.5\left(0.7+\frac{75}{1500}\right)\left(1-\frac{5}{12}\right)$$

Reduce the fraction \frac{75}{1500} to lowest terms by extracting and canceling out 75.

$$10.5\left(0.7+\frac{1}{20}\right)\left(1-\frac{5}{12}\right)$$

Convert decimal number 0.7 to fraction \frac{7}{10}.

$$10.5\left(\frac{7}{10}+\frac{1}{20}\right)\left(1-\frac{5}{12}\right)$$

Least common multiple of 10 and 20 is 20. Convert \frac{7}{10} and \frac{1}{20} to fractions with denominator 20.

$$10.5\left(\frac{14}{20}+\frac{1}{20}\right)\left(1-\frac{5}{12}\right)$$

Since \frac{14}{20} and \frac{1}{20} have the same denominator, add them by adding their numerators.

$$10.5\times \frac{14+1}{20}\left(1-\frac{5}{12}\right)$$

Add 14 and 1 to get 15.

$$10.5\times \frac{15}{20}\left(1-\frac{5}{12}\right)$$

Reduce the fraction \frac{15}{20} to lowest terms by extracting and canceling out 5.

$$10.5\times \frac{3}{4}\left(1-\frac{5}{12}\right)$$

Convert decimal number 10.5 to fraction \frac{105}{10}. Reduce the fraction \frac{105}{10} to lowest terms by extracting and canceling out 5.

$$\frac{21}{2}\times \frac{3}{4}\left(1-\frac{5}{12}\right)$$

Multiply \frac{21}{2} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{21\times 3}{2\times 4}\left(1-\frac{5}{12}\right)$$

Do the multiplications in the fraction \frac{21\times 3}{2\times 4}.

$$\frac{63}{8}\left(1-\frac{5}{12}\right)$$

Convert 1 to fraction \frac{12}{12}.

$$\frac{63}{8}\left(\frac{12}{12}-\frac{5}{12}\right)$$

Since \frac{12}{12} and \frac{5}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{63}{8}\times \frac{12-5}{12}$$

Subtract 5 from 12 to get 7.

$$\frac{63}{8}\times \frac{7}{12}$$

Multiply \frac{63}{8} times \frac{7}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{63\times 7}{8\times 12}$$

Do the multiplications in the fraction \frac{63\times 7}{8\times 12}.

$$\frac{441}{96}$$

Reduce the fraction \frac{441}{96} to lowest terms by extracting and canceling out 3.

$$\frac{147}{32}$$

Factor

$$\frac{3 \cdot 7 ^ {2}}{2 ^ {5}} = 4\frac{19}{32} = 4.59375$$