Solve 5/33-7/12+7/4

$$\frac{ 5 }{ 33 } - \frac{ 7 }{ 12 } + \frac{ 7 }{ 4 }$$

Evaluate

$$\frac{29}{22}\approx 1.318181818$$

Solution Steps

Least common multiple of 33 and 12 is 132. Convert \frac{5}{33} and \frac{7}{12} to fractions with denominator 132.

$$\frac{20}{132}-\frac{77}{132}+\frac{7}{4}$$

Since \frac{20}{132} and \frac{77}{132} have the same denominator, subtract them by subtracting their numerators.

$$\frac{20-77}{132}+\frac{7}{4}$$

Subtract 77 from 20 to get -57.

$$\frac{-57}{132}+\frac{7}{4}$$

Reduce the fraction \frac{-57}{132} to lowest terms by extracting and canceling out 3.

$$-\frac{19}{44}+\frac{7}{4}$$

Least common multiple of 44 and 4 is 44. Convert -\frac{19}{44} and \frac{7}{4} to fractions with denominator 44.

$$-\frac{19}{44}+\frac{77}{44}$$

Since -\frac{19}{44} and \frac{77}{44} have the same denominator, add them by adding their numerators.

$$\frac{-19+77}{44}$$

Add -19 and 77 to get 58.

$$\frac{58}{44}$$

Reduce the fraction \frac{58}{44} to lowest terms by extracting and canceling out 2.

$$\frac{29}{22}$$

Factor

$$\frac{29}{2 \cdot 11} = 1\frac{7}{22} = 1.3181818181818181$$