Solve 1/3*7/14+1/3*5/14+frac{1}{3}*frac{5}{14}=

$$\frac { 1 } { 3 } \cdot \frac { 7 } { 14 } + \frac { 1 } { 3 } \cdot \frac { 5 } { 14 } + \frac { 1 } { 3 } \cdot \frac { 5 } { 14 } =$$

Evaluate

$$\frac{17}{42}\approx 0.404761905$$

Solution Steps

Reduce the fraction \frac{7}{14} to lowest terms by extracting and canceling out 7.

$$\frac{1}{3}\times \frac{1}{2}+\frac{1}{3}\times \frac{5}{14}+\frac{1}{3}\times \frac{5}{14}$$

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

$$\frac{1\times 1}{3\times 2}+\frac{1}{3}\times \frac{5}{14}+\frac{1}{3}\times \frac{5}{14}$$

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

$$\frac{1}{6}+\frac{1}{3}\times \frac{5}{14}+\frac{1}{3}\times \frac{5}{14}$$

Multiply \frac{1}{3} times \frac{5}{14} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{6}+\frac{1\times 5}{3\times 14}+\frac{1}{3}\times \frac{5}{14}$$

Do the multiplications in the fraction \frac{1\times 5}{3\times 14}.

$$\frac{1}{6}+\frac{5}{42}+\frac{1}{3}\times \frac{5}{14}$$

Least common multiple of 6 and 42 is 42. Convert \frac{1}{6} and \frac{5}{42} to fractions with denominator 42.

$$\frac{7}{42}+\frac{5}{42}+\frac{1}{3}\times \frac{5}{14}$$

Since \frac{7}{42} and \frac{5}{42} have the same denominator, add them by adding their numerators.

$$\frac{7+5}{42}+\frac{1}{3}\times \frac{5}{14}$$

Add 7 and 5 to get 12.

$$\frac{12}{42}+\frac{1}{3}\times \frac{5}{14}$$

Reduce the fraction \frac{12}{42} to lowest terms by extracting and canceling out 6.

$$\frac{2}{7}+\frac{1}{3}\times \frac{5}{14}$$

Multiply \frac{1}{3} times \frac{5}{14} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{7}+\frac{1\times 5}{3\times 14}$$

Do the multiplications in the fraction \frac{1\times 5}{3\times 14}.

$$\frac{2}{7}+\frac{5}{42}$$

Least common multiple of 7 and 42 is 42. Convert \frac{2}{7} and \frac{5}{42} to fractions with denominator 42.

$$\frac{12}{42}+\frac{5}{42}$$

Since \frac{12}{42} and \frac{5}{42} have the same denominator, add them by adding their numerators.

$$\frac{12+5}{42}$$

Add 12 and 5 to get 17.

$$\frac{17}{42}$$

Factor

$$\frac{17}{2 \cdot 3 \cdot 7} = 0.40476190476190477$$