Solve 30div[(1/4+2/7)*7/20]

$$30 \div [ ( \frac { 1 } { 4 } + \frac { 2 } { 7 } ) \times \frac { 7 } { 20 } ]$$

Evaluate

$$160$$

Solution Steps

Least common multiple of 4 and 7 is 28. Convert \frac{1}{4} and \frac{2}{7} to fractions with denominator 28.

$$\frac{30}{\left(\frac{7}{28}+\frac{8}{28}\right)\times \frac{7}{20}}$$

Since \frac{7}{28} and \frac{8}{28} have the same denominator, add them by adding their numerators.

$$\frac{30}{\frac{7+8}{28}\times \frac{7}{20}}$$

Add 7 and 8 to get 15.

$$\frac{30}{\frac{15}{28}\times \frac{7}{20}}$$

Multiply \frac{15}{28} times \frac{7}{20} by multiplying numerator times numerator and denominator times denominator.

$$\frac{30}{\frac{15\times 7}{28\times 20}}$$

Do the multiplications in the fraction \frac{15\times 7}{28\times 20}.

$$\frac{30}{\frac{105}{560}}$$

Reduce the fraction \frac{105}{560} to lowest terms by extracting and canceling out 35.

$$\frac{30}{\frac{3}{16}}$$

Divide 30 by \frac{3}{16} by multiplying 30 by the reciprocal of \frac{3}{16}.

$$30\times \frac{16}{3}$$

Express 30\times \frac{16}{3} as a single fraction.

$$\frac{30\times 16}{3}$$

Multiply 30 and 16 to get 480.

$$\frac{480}{3}$$

Divide 480 by 3 to get 160.

$$160$$

Factor

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