Simplify $2- {\frac{a\left(1-(\frac{1}{2a})\right)}{0.25}}$

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Simplify:
$$2- {\frac{a\left(1-(\frac{1}{2a})\right)}{0.25}}$$

  1. I removed the parenthesis by filling it in. I got: $a(\frac{-a}{2a}).$ I multiplied a with $2a= 2a^2.$ So now I have $2a^2\div 2a= a.$

  2. Filling in a in the equation that I originally had gave me: $2- (\frac {a}{0.25}).$ To involve the $2$, I made: ${\frac{2(0.25)}{0.25}} - (\frac{a}{0.25}).$

  3. I calculated this so I got ${(2\times0.25)/0.25} =0.5$

  4. Filling in gave me: $\frac{0.5-a}{0.25}= 2-a$

Apparently this is not correct. Can anyone point out where I went wrong? Please don't give me the answer to the question.

  • Ok with help this is my second attempt:
  1. Filling the parenthesis ~~Thank you, mvw~~ 1-$(\frac{1}{2a}) = (2a-\frac{1}{2a}) = 2a$ cancel out so I'm left with $-1.$
  2. Filling in a in the equation that I originally had gave me: $2 - [a\times\frac{-1}{0.25}].$ $a$ times -1 is $-a$ $2- (\frac{-a}{0.25}).$
  3. To involve the 2, I again made: $\left[\frac{2(0.25)}{0.25}\right] - (\frac{-a}{0.25}).$ Minus + minus = plus. So $a\div 0.25= 4a.$
  4. This gave me: ${[2\times(0.25) \div 0.25] + 4a}.$ ~~~~ $(2 + 4a)$ or $(0.25 + 4a)$ or $(1 + 4a)$ If I divide $0.25$ by $0.25 = 1.$
  5. $2 + 4a = 2(1+2a)$ or $(0.25 + 4a)$ or $(1+4a)$

Again incorrect. Can anyone help me with the solution?

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The innermost two terms give $$ (1-(1/2a))=\frac{2a-1}{2a} $$ Stopping to not spoil more.

Full go: $$ 2 - \{a(1-(1/2a)) /0.25\} = \\ $$ writing out the fractions $$ 2 - \left\{a \left(1-\frac{1}{2a}\right)\frac{1}{1/4}\right\} = \\ $$ Using the common denominator $2a$ for the fraction in the inner parentheses and using that division by a fraction is multiplication by its inverse $$ 2 - \left\{a \left(\frac{2a-1}{2a}\right)\frac{4}{1}\right\} = \\ $$ shortening the fraction by $a$, dropping the $1$ denominator $$ 2 - \frac{2a - 1}{2} \cdot 4 = \\ $$ now multiplying by $4/2 = 2$ $$ 2 - 2(2a-1) = \\ $$ and adding the $2$'s $$ 4-4a = 4(1-a) $$

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Check what you are dividing by $0.25$ - be careful about the brackets - and note that $0.25$ is different from $0.5$ or $\frac 12$