Are the expressions you wrote in above question equivalent to the original expressions? Explain your reasoning.

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Solution

Step 1: Part{a}
$\frac{4}{5} (1 + 2) = (\frac{4}{5} + 2 \frac{4}{5}) {D i s t r i b u t i v e p r o p e r t y} = \frac{4}{5} + \frac{8}{5} {B e c a u s e 2 \frac{4}{5} = \frac{8}{5}}$
Yes they are equivalent.
Step 2: Part (b)
$\frac{1}{2} (3 x + 1) = (3 \frac{1}{2} x + \frac{1}{2}) {D i s t r i b u t i v e p r o p e r t y} = \frac{3}{2} x + \frac{1}{2} {B e c a u s e 3 \frac{1}{2} = \frac{3}{2}}$
Yes they are equivalent.
Step 3: Part (c)
$2.5 (x + 1.5 y) = (2.5 x + 2.5 \times 1.5 y) {D i s t r i b u t i v e p r o p e r t y} = 2.5 x 3.75 y {B e c a u s e 2.5 \times 1.5 = 3.75}$
Yes they are equivalent.
Final result: Yes they are equivalent.

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