Solve (1/3+2/5+1/10)div23/30

$$( \frac{ 1 }{ 3 } + \frac{ 2 }{ 5 } + \frac{ 1 }{ 10 } ) \div \frac{ 23 }{ 30 }$$

Evaluate

$$\frac{25}{23}\approx 1.086956522$$

Solution Steps

Least common multiple of 3 and 5 is 15. Convert \frac{1}{3} and \frac{2}{5} to fractions with denominator 15.

$$\frac{\frac{5}{15}+\frac{6}{15}+\frac{1}{10}}{\frac{23}{30}}$$

Since \frac{5}{15} and \frac{6}{15} have the same denominator, add them by adding their numerators.

$$\frac{\frac{5+6}{15}+\frac{1}{10}}{\frac{23}{30}}$$

Add 5 and 6 to get 11.

$$\frac{\frac{11}{15}+\frac{1}{10}}{\frac{23}{30}}$$

Least common multiple of 15 and 10 is 30. Convert \frac{11}{15} and \frac{1}{10} to fractions with denominator 30.

$$\frac{\frac{22}{30}+\frac{3}{30}}{\frac{23}{30}}$$

Since \frac{22}{30} and \frac{3}{30} have the same denominator, add them by adding their numerators.

$$\frac{\frac{22+3}{30}}{\frac{23}{30}}$$

Add 22 and 3 to get 25.

$$\frac{\frac{25}{30}}{\frac{23}{30}}$$

Reduce the fraction \frac{25}{30} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{5}{6}}{\frac{23}{30}}$$

Divide \frac{5}{6} by \frac{23}{30} by multiplying \frac{5}{6} by the reciprocal of \frac{23}{30}.

$$\frac{5}{6}\times \frac{30}{23}$$

Multiply \frac{5}{6} times \frac{30}{23} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 30}{6\times 23}$$

Do the multiplications in the fraction \frac{5\times 30}{6\times 23}.

$$\frac{150}{138}$$

Reduce the fraction \frac{150}{138} to lowest terms by extracting and canceling out 6.

$$\frac{25}{23}$$

Factor

$$\frac{5 ^ {2}}{23} = 1\frac{2}{23} = 1.0869565217391304$$