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Alex777 [14]
3 years ago
11

Which expression is equivalent to (21/2 x 2 3/4)^2

Mathematics
2 answers:
eimsori [14]3 years ago
8 0

\left(2\dfrac{1}{2}\cdot2\dfrac{3}{4}\right)^2=\left(\dfrac{2\cdot2+1}{2}\cdot\dfrac{2\cdot4+3}{4}\right)^2=\left(\dfrac{5}{2}\cdot\dfrac{11}{4}\right)^2=\left(\dfrac{55}{8}\right)^2\\\\=\dfrac{55^2}{8^2}=\dfrac{3025}{64}

sasho [114]3 years ago
4 0
ANSWER

(2 \frac{1}{2}  \times 2 \frac{3}{4} ) ^{2}  =  47 \frac{17}{64}


EXPLANATION

To find the expression that is equivalent to
(2 \frac{1}{2}  \times 2 \frac{3}{4} ) ^{2}

we need to simplify it.


We convert the mixed numbers to improper fraction as follows.



(2 \frac{1}{2}  \times 2 \frac{3}{4} ) ^{2}  = ( \frac{2 \times 2 + 1}{2}   \times  \frac{2 \times 4 + 3}{4} ) ^{2}


This will give us,

(2 \frac{1}{2}  \times 2 \frac{3}{4} ) ^{2}  = ( \frac{4 + 1}{2}   \times  \frac{8 + 3}{4} )^{2}


(2 \frac{1}{2}  \times 2 \frac{3}{4} ) ^{2}  = ( \frac{5}{2}   \times  \frac{11}{4} )^{2}


We multiply the expression in the parenthesis on the right hand side to obtain,

(2 \frac{1}{2}  \times 2 \frac{3}{4} ) ^{2}  = ( \frac{55}{8} )^{2}


We share the exponent for the numerator and the denominator separately.


(2 \frac{1}{2}  \times 2 \frac{3}{4} ) ^{2}  =  \frac{ {55}^{2} }{ {8}^{2} }



This simplifies to,


(2 \frac{1}{2}  \times 2 \frac{3}{4} ) ^{2}  =  \frac{ {3025} }{ {64}}


We write the final answer as a mixed number to obtain,

(2 \frac{1}{2}  \times 2 \frac{3}{4} ) ^{2}  =  47 \frac{17}{64}

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