Solve 63/12*2/3-65/12*1/6

$$6 \frac { 3 } { 12 } \times \frac { 2 } { 3 } - 6 \frac { 5 } { 12 } \times \frac { 1 } { 6 }$$

Evaluate

$$\frac{223}{72}\approx 3.097222222$$

Solution Steps

Multiply 6 and 12 to get 72.

$$\frac{72+3}{12}\times \frac{2}{3}-\frac{6\times 12+5}{12}\times \frac{1}{6}$$

Add 72 and 3 to get 75.

$$\frac{75}{12}\times \frac{2}{3}-\frac{6\times 12+5}{12}\times \frac{1}{6}$$

Reduce the fraction \frac{75}{12} to lowest terms by extracting and canceling out 3.

$$\frac{25}{4}\times \frac{2}{3}-\frac{6\times 12+5}{12}\times \frac{1}{6}$$

Multiply \frac{25}{4} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{25\times 2}{4\times 3}-\frac{6\times 12+5}{12}\times \frac{1}{6}$$

Do the multiplications in the fraction \frac{25\times 2}{4\times 3}.

$$\frac{50}{12}-\frac{6\times 12+5}{12}\times \frac{1}{6}$$

Reduce the fraction \frac{50}{12} to lowest terms by extracting and canceling out 2.

$$\frac{25}{6}-\frac{6\times 12+5}{12}\times \frac{1}{6}$$

Multiply 6 and 12 to get 72.

$$\frac{25}{6}-\frac{72+5}{12}\times \frac{1}{6}$$

Add 72 and 5 to get 77.

$$\frac{25}{6}-\frac{77}{12}\times \frac{1}{6}$$

Multiply \frac{77}{12} times \frac{1}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{25}{6}-\frac{77\times 1}{12\times 6}$$

Do the multiplications in the fraction \frac{77\times 1}{12\times 6}.

$$\frac{25}{6}-\frac{77}{72}$$

Least common multiple of 6 and 72 is 72. Convert \frac{25}{6} and \frac{77}{72} to fractions with denominator 72.

$$\frac{300}{72}-\frac{77}{72}$$

Since \frac{300}{72} and \frac{77}{72} have the same denominator, subtract them by subtracting their numerators.

$$\frac{300-77}{72}$$

Subtract 77 from 300 to get 223.

$$\frac{223}{72}$$

Factor

$$\frac{223}{2 ^ {3} \cdot 3 ^ {2}} = 3\frac{7}{72} = 3.0972222222222223$$