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 $3\times (-1/5)+(-1/5)\times (-1/5)\times 2$, but can't figure out what the right way to solve this is.

If $a=-1/5$, how do I calculate:

$3a+2{a}^{2}$

I did $3\times (-1/5)+(-1/5)\times (-1/5)\times 2$, but can't figure out what the right way to solve this is.

Immanuel Brennan

Beginner2022-10-15Added 9 answers

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

$\frac{3\times -1}{5}+\frac{-1\times -1\times 2}{5\times 5},$

since $+a\times -b=-ab$, and $-a\times -b=ab$ 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.

Starting from

$\frac{3\times -1}{5}+\frac{-1\times -1\times 2}{5\times 5},$

since $+a\times -b=-ab$, and $-a\times -b=ab$ 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

Beginner2022-10-16Added 3 answers

That's the correct way.

$\begin{array}{rl}(3\times \frac{-1}{5})+(\frac{-1}{5}\times 2\times \frac{-1}{5})& =\frac{-3}{5}+\frac{2}{25}\\ & =\frac{-15}{25}+\frac{2}{25}\\ & =\frac{-13}{25}\end{array}$

$\begin{array}{rl}(3\times \frac{-1}{5})+(\frac{-1}{5}\times 2\times \frac{-1}{5})& =\frac{-3}{5}+\frac{2}{25}\\ & =\frac{-15}{25}+\frac{2}{25}\\ & =\frac{-13}{25}\end{array}$

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