## Solving One Step Equations: (-3/5)a = 27

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brazil820
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### Solving One Step Equations: (-3/5)a = 27

Hello everyone. My daughter needs some help understanding some Algebra problems. The first problem that we need help with is:

$\dfrac{-3}{5}\, a\, =\, 27$

In the second step, they are multiplying both sides by 5 which we understand, but how are they getting -3a as the answer on the left after multiplying by 5?

\begin{align} \dfrac{-3}{5}\, a\, &=\, 27 \\ (5)\, \dfrac{-3}{5}\, a\, &=\, 27\,(5) \\ -3a\, =\, 135 \\ \dfrac{-3a}{-3}\, &=\, \dfrac{135}{-3} \\ a\, &=\, -45 \end{align}

Thank you!

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Joined: Sun Feb 22, 2009 11:12 pm

### Re: Solving One Step Equations: (-3/5)a = 27

The first problem that we need help with is:

$\dfrac{-3}{5}\, a\, =\, 27$

In the second step, they are multiplying both sides by 5 which we understand, but how are they getting -3a as the answer on the left after multiplying by 5?

\begin{align} \dfrac{-3}{5}\, a\, &=\, 27 \\ (5)\, \dfrac{-3}{5}\, a\, &=\, 27\,(5) \\ -3a\, =\, 135 \end{align}
They skipped a step that they probably expected you to know: 3/1 = 3, a = a/1, (3/1)(a/1) = (3a)/1, and (3a)/1 = 3a

$\dfrac{-3}{5}\, a\, =\, 27$

$(5)\, \dfrac{-3}{5}\, a\, =\, 27\,(5)$

$\left(\dfrac{5}{1}\right)\, \dfrac{-3}{5}\, \dfrac{a}{1}\, =\, 27\, (5)$

$\dfrac{-3}{1}\, \dfrac{a}{1}\, =\, 135$

$\dfrac{-3a}{1}\, =\, 135$

$-3a\, =\, 135$

It's the same process that lets you say that 135/(-3) = 45/-1 = -45/1 = -45.

brazil820
Posts: 4
Joined: Thu Sep 08, 2016 6:01 am
Contact:

### Re: Solving One Step Equations: (-3/5)a = 27

Thank you so much for the help!