GCSE Rearranging formula - please help!

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Cruellla
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#1
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#1
b = 2a - 5c

Make c the subject

Sometimes I completely understand how to do these, and other times I'm just lost and utterly confused!

I have attached a picture of my working out, and I have used two methods but both with slightly different answers.

Can someone please talk me through step by step of how we would rearrange this formula and the mathematical explanation of why we follow these steps in order to get the final answer?

Much appreciated x
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Callicious
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#2
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Your working on the right hand side is fine, except that you messed up with a negative sign-

See when you divide? 2nd line on the RHS- where'd the negative sign on the -5c go?
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Cruellla
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#3
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#3
(Original post by Callicious)
Your working on the right hand side is fine, except that you messed up with a negative sign-

See when you divide? 2nd line on the RHS- where'd the negative sign on the -5c go?
So, what am I supposed to do with the -5 when I bring it to the other side to divide? Keep it or remove it? See, this is where I am getting confused, arghh!!!

It's like the P = A - 6D and you are making D the subject.
If you take A to the opposite side, it becomes P - A = 6D, and then you divide P - A by 6 and that equals to 6, right?
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ashvinsingh
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#4
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(Original post by Cruellla)
b = 2a - 5c

Make c the subject

Sometimes I completely understand how to do these, and other times I'm just lost and utterly confused!

I have attached a picture of my working out, and I have used two methods but both with slightly different answers.

Can someone please talk me through step by step of how we would rearrange this formula and the mathematical explanation of why we follow these steps in order to get the final answer?

Much appreciated x
First make the c positive by adding to the other side, then subtract b from both sides to get 5c on its own, then divide by 5 to get c on its own hope this helps
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Cruellla
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#5
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#5
(Original post by ashvinsingh)
First make the c positive by adding to the other side, then subtract b from both sides to get 5c on its own, then divide by 5 to get c on its own hope this helps
OK, so is this a strict rule I need to follow by making the c positive?

Can I not do what I did on the right and still get a correct answer?
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Callicious
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#6
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(Original post by ashvinsingh)
First make the c positive by adding to the other side, then subtract b from both sides to get 5c on its own, then divide by 5 to get c on its own hope this helps
They've already done this- they're asking about their other method.

(Original post by Cruellla)
So, what am I supposed to do with the -5 when I bring it to the other side to divide? Keep it or remove it? See, this is where I am getting confused, arghh!!!

It's like the P = A - 6D and you are making D the subject.
If you take A to the opposite side, it becomes P - A = 6D, and then you divide P - A by 6 and that equals to 6, right?
Just divide by -5

Consider another example (I can't give answers here.) I don't know what level you're at, but I'll try my best...

What is \alpha - \beta divided by -5?

\frac{\alpha - \beta}{-5}

Factor out the minus one.

\frac{\alpha - \beta}{-1\times{5}}

Now, take out a minus one from the top as well. You should be able to see that

-1\times(\beta) = -\beta

and you know that (I hope)

-1 \times -1 = 1

since a minus times a minus makes a plus. Consequently...

\frac{\left(-1\times{-1}\times\alpha\right) + \left(-1\times\beta\right)}{-1\times{5}}

Now, you should be able to see a common term.

\frac{-1}{-1} = 1

Divide all the top by -1, and all the bottom by -1. You're allowed to do that. And hey-presto, you get what you want.

\frac{\left({-1}\times\alpha\right) + \left(\beta\right)}{{5}}

Simplify this and you're done

\frac{-\alpha + \beta}{5}

All dividing by -5 does is multiply by -1, and divide by 5.
Last edited by Callicious; 1 week ago
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Cruellla
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#7
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#7
(Original post by Callicious)
They've already done this- they're asking about their other method.


Just divide by -5

Consider another example (I can't give answers here.) I don't know what level you're at, but I'll try my best...

What is \alpha - \beta divided by -5?

\frac{\alpha - \beta}{-5}

Factor out the minus one.

\frac{\alpha - \beta}{-1\times{5}}

Now, take out a minus one from the top as well. You should be able to see that

-1\times(\beta) = -\beta

and you know that (I hope)

-1 \times -1 = 1

since a minus times a minus makes a plus. Consequently...

\frac{\left(-1\times{-1}\times\alpha\right) + \left(-1\times\beta\right)}{-1\times{5}}

Now, you should be able to see a common term.

\frac{-1}{-1} = 1

Divide all the top by -1, and all the bottom by -1. You're allowed to do that. And hey-presto, you get what you want.

\frac{\left({-1}\times\alpha\right) + \left(\beta\right)}{{5}}

Simplify this and you're done

\frac{-\alpha + \beta}{5}

All dividing by -5 does is multiply by -1, and divide by 5.
OK, thank you for this.

So, what you're saying is both methods are actually OK because regardless they'll give the same answer?
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Callicious
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#8
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(Original post by Cruellla)
OK, thank you for this.

So, what you're saying is both methods are actually OK because regardless they'll give the same answer?
If done correct, yes. You just don't abandon the - sign in front of the -5c: you have to divide by -5.
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Cruellla
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#9
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(Original post by Callicious)
If done correct, yes. You just don't abandon the - sign in front of the -5c: you have to divide by -5.
Thank you so much, you're a live saver!

I'm going to try and experiment with both methods and just substitute the subject with a random number and see if I get the same answer.

Many thanks x
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Muttley79
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#10
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(Original post by Callicious)
They've already done this- they're asking about their other method.


Just divide by -5

Consider another example (I can't give answers here.) I don't know what level you're at, but I'll try my best...


All dividing by -5 does is multiply by -1, and divide by 5.
NOt a great idea to divide by a negative number
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Muttley79
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#11
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(Original post by Cruellla)
Thank you so much, you're a live saver!

I'm going to try and experiment with both methods and just substitute the subject with a random number and see if I get the same answer.

Many thanks x
Stick with the method I showed you - don't divide by a -ve number - this will lead to errors when you meet inequailities
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ashvinsingh
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#12
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(Original post by Muttley79)
NOt a great idea to divide by a negative number
It’s perfectly fine… just have to remember positives become negative and negatives become positive
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ashvinsingh
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#13
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(Original post by Muttley79)
Stick with the method I showed you - don't divide by a -ve number - this will lead to errors when you meet inequailities
Sometimes it’s essential to divide by a negative, with inequalities you simply flip the sign.
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Callicious
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#14
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(Original post by Muttley79)
NOt a great idea to divide by a negative number
Sorry-

I don't know what level the OP is at (I've gotten bamboozled by the division being a problem) and just tried to explain it the way I got taught (somewhat- iirc we just gunned straight for dividing by negatives.)
Last edited by Callicious; 1 week ago
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Muttley79
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#15
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(Original post by ashvinsingh)
Sometimes it’s essential to divide by a negative, with inequalities you simply flip the sign.
NOOOOOOO!!! This is incredibly bad advice ... NEVER divide by a -ve number
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Muttley79
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(Original post by ashvinsingh)
It’s perfectly fine… just have to remember positives become negative and negatives become positive
No - it leads to mistakes
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Cruellla
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#17
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(Original post by Muttley79)
Stick with the method I showed you - don't divide by a -ve number - this will lead to errors when you meet inequailities
Where is this method?
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ashvinsingh
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#18
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(Original post by Muttley79)
NOOOOOOO!!! This is incredibly bad advice ... NEVER divide by a -ve number
… in a level maths you divide through by negative numbers all the time.
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Muttley79
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#19
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(Original post by ashvinsingh)
… in a level maths you divide through by negative numbers all the time.
Not in my class - and this isn't A level!
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ashvinsingh
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#20
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(Original post by Muttley79)
Not in my class - and this isn't A level!
Dividing through by a negative number is perfectly valid maths. It may be more complex for some people but for others it’s easier. E.g. -5x = 5 + 25y + 125z, find x
I would divide by -5
To get x = -1-5y-25z
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