Solve 21/2div(61/4-21/5)=

$$2 \frac { 1 } { 2 } \div ( 6 \frac { 1 } { 4 } - 2 \frac { 1 } { 5 } ) =$$

Evaluate

$$\frac{50}{81}\approx 0.617283951$$

Solution Steps

Multiply 2 and 2 to get 4.

$$\frac{\frac{4+1}{2}}{\frac{6\times 4+1}{4}-\frac{2\times 5+1}{5}}$$

Add 4 and 1 to get 5.

$$\frac{\frac{5}{2}}{\frac{6\times 4+1}{4}-\frac{2\times 5+1}{5}}$$

Multiply 6 and 4 to get 24.

$$\frac{\frac{5}{2}}{\frac{24+1}{4}-\frac{2\times 5+1}{5}}$$

Add 24 and 1 to get 25.

$$\frac{\frac{5}{2}}{\frac{25}{4}-\frac{2\times 5+1}{5}}$$

Multiply 2 and 5 to get 10.

$$\frac{\frac{5}{2}}{\frac{25}{4}-\frac{10+1}{5}}$$

Add 10 and 1 to get 11.

$$\frac{\frac{5}{2}}{\frac{25}{4}-\frac{11}{5}}$$

Least common multiple of 4 and 5 is 20. Convert \frac{25}{4} and \frac{11}{5} to fractions with denominator 20.

$$\frac{\frac{5}{2}}{\frac{125}{20}-\frac{44}{20}}$$

Since \frac{125}{20} and \frac{44}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5}{2}}{\frac{125-44}{20}}$$

Subtract 44 from 125 to get 81.

$$\frac{\frac{5}{2}}{\frac{81}{20}}$$

Divide \frac{5}{2} by \frac{81}{20} by multiplying \frac{5}{2} by the reciprocal of \frac{81}{20}.

$$\frac{5}{2}\times \frac{20}{81}$$

Multiply \frac{5}{2} times \frac{20}{81} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 20}{2\times 81}$$

Do the multiplications in the fraction \frac{5\times 20}{2\times 81}.

$$\frac{100}{162}$$

Reduce the fraction \frac{100}{162} to lowest terms by extracting and canceling out 2.

$$\frac{50}{81}$$

Factor

$$\frac{2 \cdot 5 ^ {2}}{3 ^ {4}} = 0.6172839506172839$$