Multiplication Property of Equality

[bobisaka]

Hi all,
In in the Multiply Step of the example below, why does the denominator change from negative to positive?


Below I initially done it a different way and got the same answer.. am i wrong in how i solved it?

1. y/-7 = -14

2. y/-7 * 1/-7 = -14 * -7

3. y = 98

Check:

4. 98/-7 = -14

Answer = 98

 

[Romsek]

you have one mistake which is probably just a typo.

in 2. you have [MATH]\dfrac{y}{-7} \cdot \dfrac{1}{-7} = -14 \cdot (-7)[/MATH]
I'm sure what you mean is

[MATH]\dfrac{y}{-7}\cdot (-7) = -14 \cdot (-7)[/MATH]

 

[bobisaka]

haha actually, no it wasn't a typo. I did think i was doing something incorrect. Thanks for the correction, it clears things up.

Do you know why in the example diagram, the denominator becomes a positive?

edit: perhaps i should have created a separate thread for separate questions.

 

[Romsek]

haha actually, no it wasn't a typo. I did think i was doing something incorrect. Thanks for the correction, it clears things up.

Do you know why in the example diagram, the denominator becomes a positive?

edit: perhaps i should have created a separate thread for separate questions.

actually their diagram has a typo.

across from "Multiply" should be \(\displaystyle \dfrac{-7y}{-7} = 98\)

 

[HallsofIvy]

As far a your question about the denominator becoming positive is concerned:
\(\displaystyle \frac{-a}{b}= \frac{a}{-b}= -\frac{a}{b}\).

 

[Dr.Peterson]

For the sake of clarity: The example you asked about is WRONG. There is NO valid reason the -7 was replaced with a 7; they just dropped the negative sign in copying, and the rest of the work is correct.

 

[bobisaka]

Thanks, that clarifies things.

I've had a bad experience with maths in the past, where i spent a good 6 months struggling to understand and complete a textbook given in class. Only to find out that the book the college had made was full of typos literally on every question..is this a common thing?

 

[HallsofIvy]

No, it is not common. But it does happen.