Solve 1/30div((2/3+1/5)*1/26)

$$\frac { 1 } { 30 } \div ( ( \frac { 2 } { 3 } + \frac { 1 } { 5 } ) \times \frac { 1 } { 26 } )$$

Evaluate

$$1$$

Solution Steps

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

$$\frac{\frac{1}{30}}{\left(\frac{10}{15}+\frac{3}{15}\right)\times \frac{1}{26}}$$

Since \frac{10}{15} and \frac{3}{15} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1}{30}}{\frac{10+3}{15}\times \frac{1}{26}}$$

Add 10 and 3 to get 13.

$$\frac{\frac{1}{30}}{\frac{13}{15}\times \frac{1}{26}}$$

Multiply \frac{13}{15} times \frac{1}{26} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1}{30}}{\frac{13\times 1}{15\times 26}}$$

Do the multiplications in the fraction \frac{13\times 1}{15\times 26}.

$$\frac{\frac{1}{30}}{\frac{13}{390}}$$

Reduce the fraction \frac{13}{390} to lowest terms by extracting and canceling out 13.

$$\frac{\frac{1}{30}}{\frac{1}{30}}$$

Divide \frac{1}{30} by \frac{1}{30} to get 1.

$$1$$

Factor

$$1$$