Solve (1/10-1/12)*(51/4+0.75)

$$( \frac { 1 } { 10 } - \frac { 1 } { 12 } ) \times ( 5 \frac { 1 } { 4 } + 0.75 )$$

Evaluate

$$0.1$$

Solution Steps

Least common multiple of 10 and 12 is 60. Convert \frac{1}{10} and \frac{1}{12} to fractions with denominator 60.

$$\left(\frac{6}{60}-\frac{5}{60}\right)\left(\frac{5\times 4+1}{4}+0.75\right)$$

Since \frac{6}{60} and \frac{5}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6-5}{60}\left(\frac{5\times 4+1}{4}+0.75\right)$$

Subtract 5 from 6 to get 1.

$$\frac{1}{60}\left(\frac{5\times 4+1}{4}+0.75\right)$$

Multiply 5 and 4 to get 20.

$$\frac{1}{60}\left(\frac{20+1}{4}+0.75\right)$$

Add 20 and 1 to get 21.

$$\frac{1}{60}\left(\frac{21}{4}+0.75\right)$$

Convert decimal number 0.75 to fraction \frac{75}{100}. Reduce the fraction \frac{75}{100} to lowest terms by extracting and canceling out 25.

$$\frac{1}{60}\left(\frac{21}{4}+\frac{3}{4}\right)$$

Since \frac{21}{4} and \frac{3}{4} have the same denominator, add them by adding their numerators.

$$\frac{1}{60}\times \frac{21+3}{4}$$

Add 21 and 3 to get 24.

$$\frac{1}{60}\times \frac{24}{4}$$

Divide 24 by 4 to get 6.

$$\frac{1}{60}\times 6$$

Multiply \frac{1}{60} and 6 to get \frac{6}{60}.

$$\frac{6}{60}$$

Reduce the fraction \frac{6}{60} to lowest terms by extracting and canceling out 6.

$$\frac{1}{10}$$

Factor

$$\frac{1}{2 \cdot 5} = 0.1$$