Solve (11/2+1/4)text{by}(11/2-1/4)

$$( 1 \frac { 1 } { 2 } + \frac { 1 } { 4 } ) \text { by } ( 1 \frac { 1 } { 2 } - \frac { 1 } { 4 } )$$

Evaluate

$$\frac{35by}{16}$$

Solution Steps

Multiply 1 and 2 to get 2.

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

Add 2 and 1 to get 3.

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

Least common multiple of 2 and 4 is 4. Convert \frac{3}{2} and \frac{1}{4} to fractions with denominator 4.

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

Since \frac{6}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

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

Add 6 and 1 to get 7.

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

Multiply 1 and 2 to get 2.

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

Add 2 and 1 to get 3.

$$\frac{7}{4}by\left(\frac{3}{2}-\frac{1}{4}\right)$$

Least common multiple of 2 and 4 is 4. Convert \frac{3}{2} and \frac{1}{4} to fractions with denominator 4.

$$\frac{7}{4}by\left(\frac{6}{4}-\frac{1}{4}\right)$$

Since \frac{6}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{4}by\times \frac{6-1}{4}$$

Subtract 1 from 6 to get 5.

$$\frac{7}{4}by\times \frac{5}{4}$$

Multiply \frac{7}{4} times \frac{5}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 5}{4\times 4}by$$

Do the multiplications in the fraction \frac{7\times 5}{4\times 4}.

$$\frac{35}{16}by$$

Expand

$$\frac{35by}{16}$$

Solution Steps

Multiply 1 and 2 to get 2.

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

Add 2 and 1 to get 3.

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

Least common multiple of 2 and 4 is 4. Convert \frac{3}{2} and \frac{1}{4} to fractions with denominator 4.

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

Since \frac{6}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

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

Add 6 and 1 to get 7.

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

Multiply 1 and 2 to get 2.

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

Add 2 and 1 to get 3.

$$\frac{7}{4}by\left(\frac{3}{2}-\frac{1}{4}\right)$$

Least common multiple of 2 and 4 is 4. Convert \frac{3}{2} and \frac{1}{4} to fractions with denominator 4.

$$\frac{7}{4}by\left(\frac{6}{4}-\frac{1}{4}\right)$$

Since \frac{6}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{4}by\times \frac{6-1}{4}$$

Subtract 1 from 6 to get 5.

$$\frac{7}{4}by\times \frac{5}{4}$$

Multiply \frac{7}{4} times \frac{5}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 5}{4\times 4}by$$

Do the multiplications in the fraction \frac{7\times 5}{4\times 4}.

$$\frac{35}{16}by$$