Solve 20div[(1/8+5/6)*6/23]

$$20 \div [ ( \frac { 1 } { 8 } + \frac { 5 } { 6 } ) \times \frac { 6 } { 23 } ]$$

Evaluate

$$80$$

Solution Steps

Least common multiple of 8 and 6 is 24. Convert \frac{1}{8} and \frac{5}{6} to fractions with denominator 24.

$$\frac{20}{\left(\frac{3}{24}+\frac{20}{24}\right)\times \frac{6}{23}}$$

Since \frac{3}{24} and \frac{20}{24} have the same denominator, add them by adding their numerators.

$$\frac{20}{\frac{3+20}{24}\times \frac{6}{23}}$$

Add 3 and 20 to get 23.

$$\frac{20}{\frac{23}{24}\times \frac{6}{23}}$$

Multiply \frac{23}{24} times \frac{6}{23} by multiplying numerator times numerator and denominator times denominator.

$$\frac{20}{\frac{23\times 6}{24\times 23}}$$

Cancel out 23 in both numerator and denominator.

$$\frac{20}{\frac{6}{24}}$$

Reduce the fraction \frac{6}{24} to lowest terms by extracting and canceling out 6.

$$\frac{20}{\frac{1}{4}}$$

Divide 20 by \frac{1}{4} by multiplying 20 by the reciprocal of \frac{1}{4}.

$$20\times 4$$

Multiply 20 and 4 to get 80.

$$80$$

Factor

$$2^{4}\times 5$$