Write the Fraction in Simplest Form (2 1/2*2 3/4)^2

${(2 \frac{1}{2} \cdot 2 \frac{3}{4})}^{2}$

Step 1

Convert $2 \frac{1}{2}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

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

Add $2$ and $\frac{1}{2}$ .

To write $2$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Combine $2$ and $\frac{2}{2}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $2$ by $2$ .

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

Add $4$ and $1$ .

${(\frac{5}{2} \cdot 2 \frac{3}{4})}^{2}$

Step 2

Convert $2 \frac{3}{4}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

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

Add $2$ and $\frac{3}{4}$ .

To write $2$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

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

Combine $2$ and $\frac{4}{4}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $2$ by $4$ .

${(\frac{5}{2} \cdot \frac{8 + 3}{4})}^{2}$

Add $8$ and $3$ .

${(\frac{5}{2} \cdot \frac{11}{4})}^{2}$

Step 3

Multiply $\frac{5}{2} \cdot \frac{11}{4}$ .

Multiply $\frac{5}{2}$ by $\frac{11}{4}$ .

${(\frac{5 \cdot 11}{2 \cdot 4})}^{2}$

Multiply $5$ by $11$ .

${(\frac{55}{2 \cdot 4})}^{2}$

Multiply $2$ by $4$ .

${(\frac{55}{8})}^{2}$

Step 4

Apply the product rule to $\frac{55}{8}$ .

$\frac{55^{2}}{8^{2}}$

Step 5

Raise $55$ to the power of $2$ .

$\frac{3025}{8^{2}}$

Step 6

Raise $8$ to the power of $2$ .

$\frac{3025}{64}$

Write the Fraction in Simplest Form (2 1/2*2 3/4)^2

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