Question

Pls help me out on this!

Answer 1

Answer:

$=-1\frac{5}{9}$

Step-by-step explanation:

We want to write:

$-1.\bar{5}$

As a mixed number in the simplest form.

We can use the following algebraic trick. First, we can ignore the negative and add it on the very end. So, we have the number:

$1.55555...$

Let's let this equal to n. So:

$1.55555...=n$

Now, we will multiply n by 10^x for the number of repeating digits x.

There is only one digit repeating (the 5). So, we will multiply both sides by 10^1 or just 10. This yields:

$15.55555...=10n$

Now, we will subtract n from both sides. This yields:

$15.5555...-n=10n-n$

On the right, we will just get 9n.

However, let's replace n with 1.5555... on the left. This yields:

$15.5555...-1.5555...=9n$

All of the repeatings 5s will cancel. 15-1 is 14. So:

$14=9n$

Now, divide both sides by 9. So, our n is:

$n=\frac{14}{9}$

And since we originally set n to be 1.5 repeating, this is equivalent to:

$n=1.\bar{5}=\frac{14}{9}$

And now, we can add back the negative:

$-1.\bar{5}=-\frac{14}{9}$

We can rewrite this as:

$=-(\frac{9}{9}+\frac{5}{9})$

So, as a mixed fraction, our decimal is:

$=-1\frac{5}{9}$

And we're done!