Solve 0.144div1.2/0.016div0.02+2/5-21/8

$$\frac { 0.144 \div 1.2 } { 0.016 \div 0.02 } + \frac { 2 } { 5 } - \frac { 21 } { 8 }$$

Evaluate

$$-2.075$$

Solution Steps

Divide \frac{0.144}{1.2} by \frac{0.016}{0.02} by multiplying \frac{0.144}{1.2} by the reciprocal of \frac{0.016}{0.02}.

$$\frac{0.144\times 0.02}{1.2\times 0.016}+\frac{2}{5}-\frac{21}{8}$$

Multiply 0.144 and 0.02 to get 0.00288.

$$\frac{0.00288}{1.2\times 0.016}+\frac{2}{5}-\frac{21}{8}$$

Multiply 1.2 and 0.016 to get 0.0192.

$$\frac{0.00288}{0.0192}+\frac{2}{5}-\frac{21}{8}$$

Expand \frac{0.00288}{0.0192} by multiplying both numerator and the denominator by 100000.

$$\frac{288}{1920}+\frac{2}{5}-\frac{21}{8}$$

Reduce the fraction \frac{288}{1920} to lowest terms by extracting and canceling out 96.

$$\frac{3}{20}+\frac{2}{5}-\frac{21}{8}$$

Least common multiple of 20 and 5 is 20. Convert \frac{3}{20} and \frac{2}{5} to fractions with denominator 20.

$$\frac{3}{20}+\frac{8}{20}-\frac{21}{8}$$

Since \frac{3}{20} and \frac{8}{20} have the same denominator, add them by adding their numerators.

$$\frac{3+8}{20}-\frac{21}{8}$$

Add 3 and 8 to get 11.

$$\frac{11}{20}-\frac{21}{8}$$

Least common multiple of 20 and 8 is 40. Convert \frac{11}{20} and \frac{21}{8} to fractions with denominator 40.

$$\frac{22}{40}-\frac{105}{40}$$

Since \frac{22}{40} and \frac{105}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{22-105}{40}$$

Subtract 105 from 22 to get -83.

$$-\frac{83}{40}$$

Factor

$$-2.075$$