Solve (41/4+13/4)*(51/2-11/4)

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

Evaluate

$$\frac{51}{2}=25.5$$

Solution Steps

Multiply 4 and 4 to get 16.

$$\left(\frac{16+1}{4}+\frac{1\times 4+3}{4}\right)\left(\frac{5\times 2+1}{2}-\frac{1\times 4+1}{4}\right)$$

Add 16 and 1 to get 17.

$$\left(\frac{17}{4}+\frac{1\times 4+3}{4}\right)\left(\frac{5\times 2+1}{2}-\frac{1\times 4+1}{4}\right)$$

Multiply 1 and 4 to get 4.

$$\left(\frac{17}{4}+\frac{4+3}{4}\right)\left(\frac{5\times 2+1}{2}-\frac{1\times 4+1}{4}\right)$$

Add 4 and 3 to get 7.

$$\left(\frac{17}{4}+\frac{7}{4}\right)\left(\frac{5\times 2+1}{2}-\frac{1\times 4+1}{4}\right)$$

Since \frac{17}{4} and \frac{7}{4} have the same denominator, add them by adding their numerators.

$$\frac{17+7}{4}\left(\frac{5\times 2+1}{2}-\frac{1\times 4+1}{4}\right)$$

Add 17 and 7 to get 24.

$$\frac{24}{4}\left(\frac{5\times 2+1}{2}-\frac{1\times 4+1}{4}\right)$$

Divide 24 by 4 to get 6.

$$6\left(\frac{5\times 2+1}{2}-\frac{1\times 4+1}{4}\right)$$

Multiply 5 and 2 to get 10.

$$6\left(\frac{10+1}{2}-\frac{1\times 4+1}{4}\right)$$

Add 10 and 1 to get 11.

$$6\left(\frac{11}{2}-\frac{1\times 4+1}{4}\right)$$

Multiply 1 and 4 to get 4.

$$6\left(\frac{11}{2}-\frac{4+1}{4}\right)$$

Add 4 and 1 to get 5.

$$6\left(\frac{11}{2}-\frac{5}{4}\right)$$

Least common multiple of 2 and 4 is 4. Convert \frac{11}{2} and \frac{5}{4} to fractions with denominator 4.

$$6\left(\frac{22}{4}-\frac{5}{4}\right)$$

Since \frac{22}{4} and \frac{5}{4} have the same denominator, subtract them by subtracting their numerators.

$$6\times \frac{22-5}{4}$$

Subtract 5 from 22 to get 17.

$$6\times \frac{17}{4}$$

Express 6\times \frac{17}{4} as a single fraction.

$$\frac{6\times 17}{4}$$

Multiply 6 and 17 to get 102.

$$\frac{102}{4}$$

Reduce the fraction \frac{102}{4} to lowest terms by extracting and canceling out 2.

$$\frac{51}{2}$$

Factor

$$\frac{3 \cdot 17}{2} = 25\frac{1}{2} = 25.5$$