Solve (1/6-1/8+5/12)*varphi_{8}

$$( \frac { 1 } { 6 } - \frac { 1 } { 8 } + \frac { 5 } { 12 } ) \times \varphi _ { 8 }$$

Evaluate

$$\frac{11\phi _{8}}{24}$$

Solution Steps

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

$$\left(\frac{4}{24}-\frac{3}{24}+\frac{5}{12}\right)\phi _{8}$$

Since \frac{4}{24} and \frac{3}{24} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{4-3}{24}+\frac{5}{12}\right)\phi _{8}$$

Subtract 3 from 4 to get 1.

$$\left(\frac{1}{24}+\frac{5}{12}\right)\phi _{8}$$

Least common multiple of 24 and 12 is 24. Convert \frac{1}{24} and \frac{5}{12} to fractions with denominator 24.

$$\left(\frac{1}{24}+\frac{10}{24}\right)\phi _{8}$$

Since \frac{1}{24} and \frac{10}{24} have the same denominator, add them by adding their numerators.

$$\frac{1+10}{24}\phi _{8}$$

Add 1 and 10 to get 11.

$$\frac{11}{24}\phi _{8}$$

Expand

$$\frac{11\phi _{8}}{24}$$

Solution Steps

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

$$\left(\frac{4}{24}-\frac{3}{24}+\frac{5}{12}\right)\phi _{8}$$

Since \frac{4}{24} and \frac{3}{24} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{4-3}{24}+\frac{5}{12}\right)\phi _{8}$$

Subtract 3 from 4 to get 1.

$$\left(\frac{1}{24}+\frac{5}{12}\right)\phi _{8}$$

Least common multiple of 24 and 12 is 24. Convert \frac{1}{24} and \frac{5}{12} to fractions with denominator 24.

$$\left(\frac{1}{24}+\frac{10}{24}\right)\phi _{8}$$

Since \frac{1}{24} and \frac{10}{24} have the same denominator, add them by adding their numerators.

$$\frac{1+10}{24}\phi _{8}$$

Add 1 and 10 to get 11.

$$\frac{11}{24}\phi _{8}$$