Solve (53/4-21/4)-11/16

$$( 5 \frac { 3 } { 4 } - 2 \frac { 1 } { 4 } )- 1 \frac { 1 } { 16 }$$

Evaluate

$$\frac{39}{16}=2.4375$$

Solution Steps

Multiply 5 and 4 to get 20.

$$\frac{20+3}{4}-\frac{2\times 4+1}{4}-\frac{1\times 16+1}{16}$$

Add 20 and 3 to get 23.

$$\frac{23}{4}-\frac{2\times 4+1}{4}-\frac{1\times 16+1}{16}$$

Multiply 2 and 4 to get 8.

$$\frac{23}{4}-\frac{8+1}{4}-\frac{1\times 16+1}{16}$$

Add 8 and 1 to get 9.

$$\frac{23}{4}-\frac{9}{4}-\frac{1\times 16+1}{16}$$

Since \frac{23}{4} and \frac{9}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{23-9}{4}-\frac{1\times 16+1}{16}$$

Subtract 9 from 23 to get 14.

$$\frac{14}{4}-\frac{1\times 16+1}{16}$$

Reduce the fraction \frac{14}{4} to lowest terms by extracting and canceling out 2.

$$\frac{7}{2}-\frac{1\times 16+1}{16}$$

Multiply 1 and 16 to get 16.

$$\frac{7}{2}-\frac{16+1}{16}$$

Add 16 and 1 to get 17.

$$\frac{7}{2}-\frac{17}{16}$$

Least common multiple of 2 and 16 is 16. Convert \frac{7}{2} and \frac{17}{16} to fractions with denominator 16.

$$\frac{56}{16}-\frac{17}{16}$$

Since \frac{56}{16} and \frac{17}{16} have the same denominator, subtract them by subtracting their numerators.

$$\frac{56-17}{16}$$

Subtract 17 from 56 to get 39.

$$\frac{39}{16}$$

Factor

$$\frac{3 \cdot 13}{2 ^ {4}} = 2\frac{7}{16} = 2.4375$$