Solve (1/2+2/3)*15/4-1/61

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

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.

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

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

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

Add 3 and 4 to get 7.

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

Multiply 1 and 4 to get 4.

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

Add 4 and 5 to get 9.

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

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

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

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

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

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

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

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

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

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

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