Solve (31/4+25/6)+13/4

$$( 3 \frac { 1 } { 4 } + 2 \frac { 5 } { 6 } ) + 1 \frac { 3 } { 4 }$$

Evaluate

$$\frac{47}{6}\approx 7.833333333$$

Solution Steps

Multiply 3 and 4 to get 12.

$$\frac{12+1}{4}+\frac{2\times 6+5}{6}+\frac{1\times 4+3}{4}$$

Add 12 and 1 to get 13.

$$\frac{13}{4}+\frac{2\times 6+5}{6}+\frac{1\times 4+3}{4}$$

Multiply 2 and 6 to get 12.

$$\frac{13}{4}+\frac{12+5}{6}+\frac{1\times 4+3}{4}$$

Add 12 and 5 to get 17.

$$\frac{13}{4}+\frac{17}{6}+\frac{1\times 4+3}{4}$$

Least common multiple of 4 and 6 is 12. Convert \frac{13}{4} and \frac{17}{6} to fractions with denominator 12.

$$\frac{39}{12}+\frac{34}{12}+\frac{1\times 4+3}{4}$$

Since \frac{39}{12} and \frac{34}{12} have the same denominator, add them by adding their numerators.

$$\frac{39+34}{12}+\frac{1\times 4+3}{4}$$

Add 39 and 34 to get 73.

$$\frac{73}{12}+\frac{1\times 4+3}{4}$$

Multiply 1 and 4 to get 4.

$$\frac{73}{12}+\frac{4+3}{4}$$

Add 4 and 3 to get 7.

$$\frac{73}{12}+\frac{7}{4}$$

Least common multiple of 12 and 4 is 12. Convert \frac{73}{12} and \frac{7}{4} to fractions with denominator 12.

$$\frac{73}{12}+\frac{21}{12}$$

Since \frac{73}{12} and \frac{21}{12} have the same denominator, add them by adding their numerators.

$$\frac{73+21}{12}$$

Add 73 and 21 to get 94.

$$\frac{94}{12}$$

Reduce the fraction \frac{94}{12} to lowest terms by extracting and canceling out 2.

$$\frac{47}{6}$$

Factor

$$\frac{47}{2 \cdot 3} = 7\frac{5}{6} = 7.833333333333333$$