Solve =(5/12*5/12)+(4/12*4/12)+(frac{2}{12}*frac{2}{12})+(frac{1}{12}*frac{1}{12})

$$= ( \frac { 5 } { 12 } \cdot \frac { 5 } { 12 } ) + ( \frac { 4 } { 12 } \cdot \frac { 4 } { 12 } ) + ( \frac { 2 } { 12 } \cdot \frac { 2 } { 12 } ) + ( \frac { 1 } { 12 } \cdot \frac { 1 } { 12 } )$$

Evaluate

$$\frac{23}{72}\approx 0.319444444$$

Solution Steps

Multiply \frac{4}{12} and \frac{4}{12} to get \left(\frac{4}{12}\right)^{2}.

$$\frac{5}{12}\times \frac{5}{12}+\left(\frac{4}{12}\right)^{2}+\frac{2}{12}\times \frac{2}{12}+\frac{1}{12}\times \frac{1}{12}$$

Multiply \frac{2}{12} and \frac{2}{12} to get \left(\frac{2}{12}\right)^{2}.

$$\frac{5}{12}\times \frac{5}{12}+\left(\frac{4}{12}\right)^{2}+\left(\frac{2}{12}\right)^{2}+\frac{1}{12}\times \frac{1}{12}$$

Multiply \frac{5}{12} times \frac{5}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 5}{12\times 12}+\left(\frac{4}{12}\right)^{2}+\left(\frac{2}{12}\right)^{2}+\frac{1}{12}\times \frac{1}{12}$$

Do the multiplications in the fraction \frac{5\times 5}{12\times 12}.

$$\frac{25}{144}+\left(\frac{4}{12}\right)^{2}+\left(\frac{2}{12}\right)^{2}+\frac{1}{12}\times \frac{1}{12}$$

Reduce the fraction \frac{4}{12} to lowest terms by extracting and canceling out 4.

$$\frac{25}{144}+\left(\frac{1}{3}\right)^{2}+\left(\frac{2}{12}\right)^{2}+\frac{1}{12}\times \frac{1}{12}$$

Calculate \frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$\frac{25}{144}+\frac{1}{9}+\left(\frac{2}{12}\right)^{2}+\frac{1}{12}\times \frac{1}{12}$$

Least common multiple of 144 and 9 is 144. Convert \frac{25}{144} and \frac{1}{9} to fractions with denominator 144.

$$\frac{25}{144}+\frac{16}{144}+\left(\frac{2}{12}\right)^{2}+\frac{1}{12}\times \frac{1}{12}$$

Since \frac{25}{144} and \frac{16}{144} have the same denominator, add them by adding their numerators.

$$\frac{25+16}{144}+\left(\frac{2}{12}\right)^{2}+\frac{1}{12}\times \frac{1}{12}$$

Add 25 and 16 to get 41.

$$\frac{41}{144}+\left(\frac{2}{12}\right)^{2}+\frac{1}{12}\times \frac{1}{12}$$

Reduce the fraction \frac{2}{12} to lowest terms by extracting and canceling out 2.

$$\frac{41}{144}+\left(\frac{1}{6}\right)^{2}+\frac{1}{12}\times \frac{1}{12}$$

Calculate \frac{1}{6} to the power of 2 and get \frac{1}{36}.

$$\frac{41}{144}+\frac{1}{36}+\frac{1}{12}\times \frac{1}{12}$$

Least common multiple of 144 and 36 is 144. Convert \frac{41}{144} and \frac{1}{36} to fractions with denominator 144.

$$\frac{41}{144}+\frac{4}{144}+\frac{1}{12}\times \frac{1}{12}$$

Since \frac{41}{144} and \frac{4}{144} have the same denominator, add them by adding their numerators.

$$\frac{41+4}{144}+\frac{1}{12}\times \frac{1}{12}$$

Add 41 and 4 to get 45.

$$\frac{45}{144}+\frac{1}{12}\times \frac{1}{12}$$

Reduce the fraction \frac{45}{144} to lowest terms by extracting and canceling out 9.

$$\frac{5}{16}+\frac{1}{12}\times \frac{1}{12}$$

Multiply \frac{1}{12} times \frac{1}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5}{16}+\frac{1\times 1}{12\times 12}$$

Do the multiplications in the fraction \frac{1\times 1}{12\times 12}.

$$\frac{5}{16}+\frac{1}{144}$$

Least common multiple of 16 and 144 is 144. Convert \frac{5}{16} and \frac{1}{144} to fractions with denominator 144.

$$\frac{45}{144}+\frac{1}{144}$$

Since \frac{45}{144} and \frac{1}{144} have the same denominator, add them by adding their numerators.

$$\frac{45+1}{144}$$

Add 45 and 1 to get 46.

$$\frac{46}{144}$$

Reduce the fraction \frac{46}{144} to lowest terms by extracting and canceling out 2.

$$\frac{23}{72}$$

Factor

$$\frac{23}{2 ^ {3} \cdot 3 ^ {2}} = 0.3194444444444444$$