Solve (1/2)^2div(1/5*2/3+1/4)

$$( \frac { 1 } { 2 } ) ^ { 2 } \div ( \frac { 1 } { 5 } \times \frac { 2 } { 3 } + \frac { 1 } { 4 } )$$

Evaluate

$$\frac{15}{23}\approx 0.652173913$$

Solution Steps

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$\frac{\frac{1}{4}}{\frac{1}{5}\times \frac{2}{3}+\frac{1}{4}}$$

Multiply \frac{1}{5} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1}{4}}{\frac{1\times 2}{5\times 3}+\frac{1}{4}}$$

Do the multiplications in the fraction \frac{1\times 2}{5\times 3}.

$$\frac{\frac{1}{4}}{\frac{2}{15}+\frac{1}{4}}$$

Least common multiple of 15 and 4 is 60. Convert \frac{2}{15} and \frac{1}{4} to fractions with denominator 60.

$$\frac{\frac{1}{4}}{\frac{8}{60}+\frac{15}{60}}$$

Since \frac{8}{60} and \frac{15}{60} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1}{4}}{\frac{8+15}{60}}$$

Add 8 and 15 to get 23.

$$\frac{\frac{1}{4}}{\frac{23}{60}}$$

Divide \frac{1}{4} by \frac{23}{60} by multiplying \frac{1}{4} by the reciprocal of \frac{23}{60}.

$$\frac{1}{4}\times \frac{60}{23}$$

Multiply \frac{1}{4} times \frac{60}{23} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 60}{4\times 23}$$

Do the multiplications in the fraction \frac{1\times 60}{4\times 23}.

$$\frac{60}{92}$$

Reduce the fraction \frac{60}{92} to lowest terms by extracting and canceling out 4.

$$\frac{15}{23}$$

Factor

$$\frac{3 \cdot 5}{23} = 0.6521739130434783$$