Solve left(1/2+2/3right)*15/4-1/6

$$\left( \frac{ 1 }{ 2 } + \frac{ 2 }{ 3 } \right) \times 1 \frac{ 5 }{ 4 } - \frac{ 1 }{ 6 }$$

Evaluate

$$\frac{59}{24}\approx 2.458333333$$

Solution Steps

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{2}{3} to fractions with denominator 6.

$$\left(\frac{3}{6}+\frac{4}{6}\right)\times \frac{1\times 4+5}{4}-\frac{1}{6}$$

Since \frac{3}{6} and \frac{4}{6} have the same denominator, add them by adding their numerators.

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

Add 3 and 4 to get 7.

$$\frac{7}{6}\times \frac{1\times 4+5}{4}-\frac{1}{6}$$

Multiply 1 and 4 to get 4.

$$\frac{7}{6}\times \frac{4+5}{4}-\frac{1}{6}$$

Add 4 and 5 to get 9.

$$\frac{7}{6}\times \frac{9}{4}-\frac{1}{6}$$

Multiply \frac{7}{6} times \frac{9}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 9}{6\times 4}-\frac{1}{6}$$

Do the multiplications in the fraction \frac{7\times 9}{6\times 4}.

$$\frac{63}{24}-\frac{1}{6}$$

Reduce the fraction \frac{63}{24} to lowest terms by extracting and canceling out 3.

$$\frac{21}{8}-\frac{1}{6}$$

Least common multiple of 8 and 6 is 24. Convert \frac{21}{8} and \frac{1}{6} to fractions with denominator 24.

$$\frac{63}{24}-\frac{4}{24}$$

Since \frac{63}{24} and \frac{4}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{63-4}{24}$$

Subtract 4 from 63 to get 59.

$$\frac{59}{24}$$

Factor

$$\frac{59}{2 ^ {3} \cdot 3} = 2\frac{11}{24} = 2.4583333333333335$$