Solve 1/3*1/frac{1{3}+1/3*0.75+1/3*0.5}

$$\frac { \frac { 1 } { 3 } \times 1 } { \frac { 1 } { 3 } + \frac { 1 } { 3 } \times 0.75 + \frac { 1 } { 3 } \times 0.5 }$$

Evaluate

$$\frac{4}{9}\approx 0.444444444$$

Solution Steps

Multiply \frac{1}{3} and 1 to get \frac{1}{3}.

$$\frac{\frac{1}{3}}{\frac{1}{3}+\frac{1}{3}\times 0.75+\frac{1}{3}\times 0.5}$$

Convert decimal number 0.75 to fraction \frac{75}{100}. Reduce the fraction \frac{75}{100} to lowest terms by extracting and canceling out 25.

$$\frac{\frac{1}{3}}{\frac{1}{3}+\frac{1}{3}\times \frac{3}{4}+\frac{1}{3}\times 0.5}$$

Multiply \frac{1}{3} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1}{3}}{\frac{1}{3}+\frac{1\times 3}{3\times 4}+\frac{1}{3}\times 0.5}$$

Cancel out 3 in both numerator and denominator.

$$\frac{\frac{1}{3}}{\frac{1}{3}+\frac{1}{4}+\frac{1}{3}\times 0.5}$$

Least common multiple of 3 and 4 is 12. Convert \frac{1}{3} and \frac{1}{4} to fractions with denominator 12.

$$\frac{\frac{1}{3}}{\frac{4}{12}+\frac{3}{12}+\frac{1}{3}\times 0.5}$$

Since \frac{4}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1}{3}}{\frac{4+3}{12}+\frac{1}{3}\times 0.5}$$

Add 4 and 3 to get 7.

$$\frac{\frac{1}{3}}{\frac{7}{12}+\frac{1}{3}\times 0.5}$$

Convert decimal number 0.5 to fraction \frac{5}{10}. Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{1}{3}}{\frac{7}{12}+\frac{1}{3}\times \frac{1}{2}}$$

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

$$\frac{\frac{1}{3}}{\frac{7}{12}+\frac{1\times 1}{3\times 2}}$$

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

$$\frac{\frac{1}{3}}{\frac{7}{12}+\frac{1}{6}}$$

Least common multiple of 12 and 6 is 12. Convert \frac{7}{12} and \frac{1}{6} to fractions with denominator 12.

$$\frac{\frac{1}{3}}{\frac{7}{12}+\frac{2}{12}}$$

Since \frac{7}{12} and \frac{2}{12} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1}{3}}{\frac{7+2}{12}}$$

Add 7 and 2 to get 9.

$$\frac{\frac{1}{3}}{\frac{9}{12}}$$

Reduce the fraction \frac{9}{12} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{1}{3}}{\frac{3}{4}}$$

Divide \frac{1}{3} by \frac{3}{4} by multiplying \frac{1}{3} by the reciprocal of \frac{3}{4}.

$$\frac{1}{3}\times \frac{4}{3}$$

Multiply \frac{1}{3} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 4}{3\times 3}$$

Do the multiplications in the fraction \frac{1\times 4}{3\times 3}.

$$\frac{4}{9}$$

Factor

$$\frac{2 ^ {2}}{3 ^ {2}} = 0.4444444444444444$$