Solve 6/11*5/21+2/11*3/21+frac{6}{11}+frac{11}{21}

$$\frac { 6 } { 11 } \cdot \frac { 5 } { 21 } + \frac { 2 } { 11 } \cdot \frac { 3 } { 21 } + \frac { 6 } { 11 } + \frac { 11 } { 21 }$$

Evaluate

$$\frac{283}{231}\approx 1.225108225$$

Solution Steps

Multiply \frac{6}{11} times \frac{5}{21} by multiplying numerator times numerator and denominator times denominator.

$$\frac{6\times 5}{11\times 21}+\frac{2}{11}\times \frac{3}{21}+\frac{6}{11}+\frac{11}{21}$$

Do the multiplications in the fraction \frac{6\times 5}{11\times 21}.

$$\frac{30}{231}+\frac{2}{11}\times \frac{3}{21}+\frac{6}{11}+\frac{11}{21}$$

Reduce the fraction \frac{30}{231} to lowest terms by extracting and canceling out 3.

$$\frac{10}{77}+\frac{2}{11}\times \frac{3}{21}+\frac{6}{11}+\frac{11}{21}$$

Reduce the fraction \frac{3}{21} to lowest terms by extracting and canceling out 3.

$$\frac{10}{77}+\frac{2}{11}\times \frac{1}{7}+\frac{6}{11}+\frac{11}{21}$$

Multiply \frac{2}{11} times \frac{1}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{10}{77}+\frac{2\times 1}{11\times 7}+\frac{6}{11}+\frac{11}{21}$$

Do the multiplications in the fraction \frac{2\times 1}{11\times 7}.

$$\frac{10}{77}+\frac{2}{77}+\frac{6}{11}+\frac{11}{21}$$

Since \frac{10}{77} and \frac{2}{77} have the same denominator, add them by adding their numerators.

$$\frac{10+2}{77}+\frac{6}{11}+\frac{11}{21}$$

Add 10 and 2 to get 12.

$$\frac{12}{77}+\frac{6}{11}+\frac{11}{21}$$

Least common multiple of 77 and 11 is 77. Convert \frac{12}{77} and \frac{6}{11} to fractions with denominator 77.

$$\frac{12}{77}+\frac{42}{77}+\frac{11}{21}$$

Since \frac{12}{77} and \frac{42}{77} have the same denominator, add them by adding their numerators.

$$\frac{12+42}{77}+\frac{11}{21}$$

Add 12 and 42 to get 54.

$$\frac{54}{77}+\frac{11}{21}$$

Least common multiple of 77 and 21 is 231. Convert \frac{54}{77} and \frac{11}{21} to fractions with denominator 231.

$$\frac{162}{231}+\frac{121}{231}$$

Since \frac{162}{231} and \frac{121}{231} have the same denominator, add them by adding their numerators.

$$\frac{162+121}{231}$$

Add 162 and 121 to get 283.

$$\frac{283}{231}$$

Factor

$$\frac{283}{3 \cdot 7 \cdot 11} = 1\frac{52}{231} = 1.225108225108225$$