Solve (21/2+7/8)(21/2-7/8)

$$( 2 \frac { 1 } { 2 } + \frac { 7 } { 8 } ) ( 2 \frac { 1 } { 2 } - \frac { 7 } { 8 } )$$

Evaluate

$$\frac{351}{64}=5.484375$$

Solution Steps

Multiply 2 and 2 to get 4.

$$\left(\frac{4+1}{2}+\frac{7}{8}\right)\left(\frac{2\times 2+1}{2}-\frac{7}{8}\right)$$

Add 4 and 1 to get 5.

$$\left(\frac{5}{2}+\frac{7}{8}\right)\left(\frac{2\times 2+1}{2}-\frac{7}{8}\right)$$

Least common multiple of 2 and 8 is 8. Convert \frac{5}{2} and \frac{7}{8} to fractions with denominator 8.

$$\left(\frac{20}{8}+\frac{7}{8}\right)\left(\frac{2\times 2+1}{2}-\frac{7}{8}\right)$$

Since \frac{20}{8} and \frac{7}{8} have the same denominator, add them by adding their numerators.

$$\frac{20+7}{8}\left(\frac{2\times 2+1}{2}-\frac{7}{8}\right)$$

Add 20 and 7 to get 27.

$$\frac{27}{8}\left(\frac{2\times 2+1}{2}-\frac{7}{8}\right)$$

Multiply 2 and 2 to get 4.

$$\frac{27}{8}\left(\frac{4+1}{2}-\frac{7}{8}\right)$$

Add 4 and 1 to get 5.

$$\frac{27}{8}\left(\frac{5}{2}-\frac{7}{8}\right)$$

Least common multiple of 2 and 8 is 8. Convert \frac{5}{2} and \frac{7}{8} to fractions with denominator 8.

$$\frac{27}{8}\left(\frac{20}{8}-\frac{7}{8}\right)$$

Since \frac{20}{8} and \frac{7}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{27}{8}\times \frac{20-7}{8}$$

Subtract 7 from 20 to get 13.

$$\frac{27}{8}\times \frac{13}{8}$$

Multiply \frac{27}{8} times \frac{13}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{27\times 13}{8\times 8}$$

Do the multiplications in the fraction \frac{27\times 13}{8\times 8}.

$$\frac{351}{64}$$

Factor

$$\frac{3 ^ {3} \cdot 13}{2 ^ {6}} = 5\frac{31}{64} = 5.484375$$