Ralzereep9h

2022-10-14

How do I solve this fraction question?
If $a=-1/5$, how do I calculate:
$3a+2{a}^{2}$
I did $3×\left(-1/5\right)+\left(-1/5\right)×\left(-1/5\right)×2$, but can't figure out what the right way to solve this is.

Immanuel Brennan

A helpful tip: You can only add fractions with the same denominator (the numbers at the bottom). If the denominators are not equal, you have to multiply them by a constant number $k$ to add them.
Starting from
$\frac{3×-1}{5}+\frac{-1×-1×2}{5×5},$
since $+a×-b=-ab$, and $-a×-b=ab$ for arbitrary numbers $a,b$, we have:
$-\frac{3}{5}+\frac{2}{25}$
Since $\frac{1}{5}$ is $5$ times that of $\frac{1}{25}$, $k=5$, and we have to multiply both numerator and denominator by $5$ to simplify:
$-\frac{15}{25}+\frac{2}{25}$
Now you can simplify the expression by cancelling $\frac{10}{25}$ and adding the $2$ fractions together:
$-\frac{15}{25}+\frac{2}{25}=\frac{-15+2}{5}$
I'll leave the last step for you to figure out.

Martin Hart

That's the correct way.
$\begin{array}{rl}\left(3×\frac{-1}{5}\right)+\left(\frac{-1}{5}×2×\frac{-1}{5}\right)& =\frac{-3}{5}+\frac{2}{25}\\ & =\frac{-15}{25}+\frac{2}{25}\\ & =\frac{-13}{25}\end{array}$

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