Solve 122/18-43/18-312/19

$$12 \frac { 2 } { 18 } - 4 \frac { 3 } { 18 } - 3 \frac { 12 } { 19 }$$

Evaluate

$$\frac{1475}{342}\approx 4.312865497$$

Solution Steps

Multiply 12 and 18 to get 216.

$$\frac{216+2}{18}-\frac{4\times 18+3}{18}-\frac{3\times 19+12}{19}$$

Add 216 and 2 to get 218.

$$\frac{218}{18}-\frac{4\times 18+3}{18}-\frac{3\times 19+12}{19}$$

Reduce the fraction \frac{218}{18} to lowest terms by extracting and canceling out 2.

$$\frac{109}{9}-\frac{4\times 18+3}{18}-\frac{3\times 19+12}{19}$$

Multiply 4 and 18 to get 72.

$$\frac{109}{9}-\frac{72+3}{18}-\frac{3\times 19+12}{19}$$

Add 72 and 3 to get 75.

$$\frac{109}{9}-\frac{75}{18}-\frac{3\times 19+12}{19}$$

Reduce the fraction \frac{75}{18} to lowest terms by extracting and canceling out 3.

$$\frac{109}{9}-\frac{25}{6}-\frac{3\times 19+12}{19}$$

Least common multiple of 9 and 6 is 18. Convert \frac{109}{9} and \frac{25}{6} to fractions with denominator 18.

$$\frac{218}{18}-\frac{75}{18}-\frac{3\times 19+12}{19}$$

Since \frac{218}{18} and \frac{75}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{218-75}{18}-\frac{3\times 19+12}{19}$$

Subtract 75 from 218 to get 143.

$$\frac{143}{18}-\frac{3\times 19+12}{19}$$

Multiply 3 and 19 to get 57.

$$\frac{143}{18}-\frac{57+12}{19}$$

Add 57 and 12 to get 69.

$$\frac{143}{18}-\frac{69}{19}$$

Least common multiple of 18 and 19 is 342. Convert \frac{143}{18} and \frac{69}{19} to fractions with denominator 342.

$$\frac{2717}{342}-\frac{1242}{342}$$

Since \frac{2717}{342} and \frac{1242}{342} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2717-1242}{342}$$

Subtract 1242 from 2717 to get 1475.

$$\frac{1475}{342}$$

Factor

$$\frac{5 ^ {2} \cdot 59}{2 \cdot 3 ^ {2} \cdot 19} = 4\frac{107}{342} = 4.312865497076023$$