Solve (51/3-25/6)+31/4

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

Evaluate

$$\frac{23}{4}=5.75$$

Solution Steps

Multiply 5 and 3 to get 15.

$$\frac{15+1}{3}-\frac{2\times 6+5}{6}+\frac{3\times 4+1}{4}$$

Add 15 and 1 to get 16.

$$\frac{16}{3}-\frac{2\times 6+5}{6}+\frac{3\times 4+1}{4}$$

Multiply 2 and 6 to get 12.

$$\frac{16}{3}-\frac{12+5}{6}+\frac{3\times 4+1}{4}$$

Add 12 and 5 to get 17.

$$\frac{16}{3}-\frac{17}{6}+\frac{3\times 4+1}{4}$$

Least common multiple of 3 and 6 is 6. Convert \frac{16}{3} and \frac{17}{6} to fractions with denominator 6.

$$\frac{32}{6}-\frac{17}{6}+\frac{3\times 4+1}{4}$$

Since \frac{32}{6} and \frac{17}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{32-17}{6}+\frac{3\times 4+1}{4}$$

Subtract 17 from 32 to get 15.

$$\frac{15}{6}+\frac{3\times 4+1}{4}$$

Reduce the fraction \frac{15}{6} to lowest terms by extracting and canceling out 3.

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

Multiply 3 and 4 to get 12.

$$\frac{5}{2}+\frac{12+1}{4}$$

Add 12 and 1 to get 13.

$$\frac{5}{2}+\frac{13}{4}$$

Least common multiple of 2 and 4 is 4. Convert \frac{5}{2} and \frac{13}{4} to fractions with denominator 4.

$$\frac{10}{4}+\frac{13}{4}$$

Since \frac{10}{4} and \frac{13}{4} have the same denominator, add them by adding their numerators.

$$\frac{10+13}{4}$$

Add 10 and 13 to get 23.

$$\frac{23}{4}$$

Factor

$$\frac{23}{2 ^ {2}} = 5\frac{3}{4} = 5.75$$