Solve M=11/6+21/6+31/6+41/6+5frac{1}{6}+6frac{1}{6}

$$M = 1 \frac{ 1 }{ 6 } +2 \frac{ 1 }{ 6 } +3 \frac{ 1 }{ 6 } +4 \frac{ 1 }{ 6 } +5 \frac{ 1 }{ 6 } +6 \frac{ 1 }{ 6 }$$

Solve for M

$$M=22$$

Steps for Solving Linear Equation

Multiply 1 and 6 to get 6.

$$M=\frac{6+1}{6}+\frac{2\times 6+1}{6}+\frac{3\times 6+1}{6}+\frac{4\times 6+1}{6}+\frac{5\times 6+1}{6}+\frac{6\times 6+1}{6}$$

Add 6 and 1 to get 7.

$$M=\frac{7}{6}+\frac{2\times 6+1}{6}+\frac{3\times 6+1}{6}+\frac{4\times 6+1}{6}+\frac{5\times 6+1}{6}+\frac{6\times 6+1}{6}$$

Multiply 2 and 6 to get 12.

$$M=\frac{7}{6}+\frac{12+1}{6}+\frac{3\times 6+1}{6}+\frac{4\times 6+1}{6}+\frac{5\times 6+1}{6}+\frac{6\times 6+1}{6}$$

Add 12 and 1 to get 13.

$$M=\frac{7}{6}+\frac{13}{6}+\frac{3\times 6+1}{6}+\frac{4\times 6+1}{6}+\frac{5\times 6+1}{6}+\frac{6\times 6+1}{6}$$

Since \frac{7}{6} and \frac{13}{6} have the same denominator, add them by adding their numerators.

$$M=\frac{7+13}{6}+\frac{3\times 6+1}{6}+\frac{4\times 6+1}{6}+\frac{5\times 6+1}{6}+\frac{6\times 6+1}{6}$$

Add 7 and 13 to get 20.

$$M=\frac{20}{6}+\frac{3\times 6+1}{6}+\frac{4\times 6+1}{6}+\frac{5\times 6+1}{6}+\frac{6\times 6+1}{6}$$

Reduce the fraction \frac{20}{6} to lowest terms by extracting and canceling out 2.

$$M=\frac{10}{3}+\frac{3\times 6+1}{6}+\frac{4\times 6+1}{6}+\frac{5\times 6+1}{6}+\frac{6\times 6+1}{6}$$

Multiply 3 and 6 to get 18.

$$M=\frac{10}{3}+\frac{18+1}{6}+\frac{4\times 6+1}{6}+\frac{5\times 6+1}{6}+\frac{6\times 6+1}{6}$$

Add 18 and 1 to get 19.

$$M=\frac{10}{3}+\frac{19}{6}+\frac{4\times 6+1}{6}+\frac{5\times 6+1}{6}+\frac{6\times 6+1}{6}$$

Least common multiple of 3 and 6 is 6. Convert \frac{10}{3} and \frac{19}{6} to fractions with denominator 6.

$$M=\frac{20}{6}+\frac{19}{6}+\frac{4\times 6+1}{6}+\frac{5\times 6+1}{6}+\frac{6\times 6+1}{6}$$

Since \frac{20}{6} and \frac{19}{6} have the same denominator, add them by adding their numerators.

$$M=\frac{20+19}{6}+\frac{4\times 6+1}{6}+\frac{5\times 6+1}{6}+\frac{6\times 6+1}{6}$$

Add 20 and 19 to get 39.

$$M=\frac{39}{6}+\frac{4\times 6+1}{6}+\frac{5\times 6+1}{6}+\frac{6\times 6+1}{6}$$

Reduce the fraction \frac{39}{6} to lowest terms by extracting and canceling out 3.

$$M=\frac{13}{2}+\frac{4\times 6+1}{6}+\frac{5\times 6+1}{6}+\frac{6\times 6+1}{6}$$

Multiply 4 and 6 to get 24.

$$M=\frac{13}{2}+\frac{24+1}{6}+\frac{5\times 6+1}{6}+\frac{6\times 6+1}{6}$$

Add 24 and 1 to get 25.

$$M=\frac{13}{2}+\frac{25}{6}+\frac{5\times 6+1}{6}+\frac{6\times 6+1}{6}$$

Least common multiple of 2 and 6 is 6. Convert \frac{13}{2} and \frac{25}{6} to fractions with denominator 6.

$$M=\frac{39}{6}+\frac{25}{6}+\frac{5\times 6+1}{6}+\frac{6\times 6+1}{6}$$

Since \frac{39}{6} and \frac{25}{6} have the same denominator, add them by adding their numerators.

$$M=\frac{39+25}{6}+\frac{5\times 6+1}{6}+\frac{6\times 6+1}{6}$$

Add 39 and 25 to get 64.

$$M=\frac{64}{6}+\frac{5\times 6+1}{6}+\frac{6\times 6+1}{6}$$

Reduce the fraction \frac{64}{6} to lowest terms by extracting and canceling out 2.

$$M=\frac{32}{3}+\frac{5\times 6+1}{6}+\frac{6\times 6+1}{6}$$

Multiply 5 and 6 to get 30.

$$M=\frac{32}{3}+\frac{30+1}{6}+\frac{6\times 6+1}{6}$$

Add 30 and 1 to get 31.

$$M=\frac{32}{3}+\frac{31}{6}+\frac{6\times 6+1}{6}$$

Least common multiple of 3 and 6 is 6. Convert \frac{32}{3} and \frac{31}{6} to fractions with denominator 6.

$$M=\frac{64}{6}+\frac{31}{6}+\frac{6\times 6+1}{6}$$

Since \frac{64}{6} and \frac{31}{6} have the same denominator, add them by adding their numerators.

$$M=\frac{64+31}{6}+\frac{6\times 6+1}{6}$$

Add 64 and 31 to get 95.

$$M=\frac{95}{6}+\frac{6\times 6+1}{6}$$

Multiply 6 and 6 to get 36.

$$M=\frac{95}{6}+\frac{36+1}{6}$$

Add 36 and 1 to get 37.

$$M=\frac{95}{6}+\frac{37}{6}$$

Since \frac{95}{6} and \frac{37}{6} have the same denominator, add them by adding their numerators.

$$M=\frac{95+37}{6}$$

Add 95 and 37 to get 132.

$$M=\frac{132}{6}$$

Divide 132 by 6 to get 22.

$$M=22$$

Assign M

$$M≔22$$