The Student Room Group
Competition - post a photo you've taken of nature >>
Competition - post a photo you've taken of nature >>
Competition - post a photo you've taken of nature >>

GCSE Rearranging formula - please help!

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
IMG_1123.jpg519.4KB

Scroll to see replies

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?
Reply 2
Avatar for Cruellla
Cruellla
OP
1
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?
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 :smile:
Reply 4
Avatar for Cruellla
Cruellla
OP
1
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 :smile:

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?
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 :smile:

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 :tongue:

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 α−β\alpha - \beta divided by -5?

α−β−5\frac{\alpha - \beta}{-5}

Factor out the minus one.

α−β−1×5\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×(β)=−β-1\times(\beta) = -\beta

and you know that (I hope)

−1×−1=1-1 \times -1 = 1

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

(−1×−1×α)+(−1×β)−1×5\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.

−1−1=1\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.

(−1×α)+(β)5\frac{\left({-1}\times\alpha\right) + \left(\beta\right)}{{5}}

Simplify this and you're done

−α+β5\frac{-\alpha + \beta}{5}

All dividing by -5 does is multiply by -1, and divide by 5.
(edited 2 years ago)
Reply 6
Avatar for Cruellla
Cruellla
OP
1
Original post by Callicious
They've already done this- they're asking about their other method.


Just divide by -5 :tongue:

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 α−β\alpha - \beta divided by -5?

α−β−5\frac{\alpha - \beta}{-5}

Factor out the minus one.

α−β−1×5\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×(β)=−β-1\times(\beta) = -\beta

and you know that (I hope)

−1×−1=1-1 \times -1 = 1

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

(−1×−1×α)+(−1×β)−1×5\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.

−1−1=1\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.

(−1×α)+(β)5\frac{\left({-1}\times\alpha\right) + \left(\beta\right)}{{5}}

Simplify this and you're done

−α+β5\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?
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.
Reply 8
Avatar for Cruellla
Cruellla
OP
1
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
Original post by Callicious
They've already done this- they're asking about their other method.


Just divide by -5 :tongue:

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
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
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
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.
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.)
(edited 2 years ago)
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
Original post by ashvinsingh
It’s perfectly fine… just have to remember positives become negative and negatives become positive

No - it leads to mistakes
Reply 16
Avatar for Cruellla
Cruellla
OP
1
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?
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.
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!
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

Quick Reply

Related discussions

Latest

Trending

Trending

Articles for you