Solve 1/6-5/12*9/10+13/8

$$\frac { 1 } { 6 } - \frac { 5 } { 12 } \times \frac { 9 } { 10 } + \frac { 13 } { 8 }$$

Evaluate

$$\frac{17}{12}\approx 1.416666667$$

Solution Steps

Multiply \frac{5}{12} times \frac{9}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{6}-\frac{5\times 9}{12\times 10}+\frac{13}{8}$$

Do the multiplications in the fraction \frac{5\times 9}{12\times 10}.

$$\frac{1}{6}-\frac{45}{120}+\frac{13}{8}$$

Reduce the fraction \frac{45}{120} to lowest terms by extracting and canceling out 15.

$$\frac{1}{6}-\frac{3}{8}+\frac{13}{8}$$

Least common multiple of 6 and 8 is 24. Convert \frac{1}{6} and \frac{3}{8} to fractions with denominator 24.

$$\frac{4}{24}-\frac{9}{24}+\frac{13}{8}$$

Since \frac{4}{24} and \frac{9}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4-9}{24}+\frac{13}{8}$$

Subtract 9 from 4 to get -5.

$$-\frac{5}{24}+\frac{13}{8}$$

Least common multiple of 24 and 8 is 24. Convert -\frac{5}{24} and \frac{13}{8} to fractions with denominator 24.

$$-\frac{5}{24}+\frac{39}{24}$$

Since -\frac{5}{24} and \frac{39}{24} have the same denominator, add them by adding their numerators.

$$\frac{-5+39}{24}$$

Add -5 and 39 to get 34.

$$\frac{34}{24}$$

Reduce the fraction \frac{34}{24} to lowest terms by extracting and canceling out 2.

$$\frac{17}{12}$$

Factor

$$\frac{17}{2 ^ {2} \cdot 3} = 1\frac{5}{12} = 1.4166666666666667$$