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Help please on rearranging an equation
- Thread starter sarannie
- Start date
I am absolutely stuck on this question
I have to rearrange to make s the subject:
4s - 5t
2s + 3t = 1/4
Can anybody please help me to understand what to do?
Hi Sarannie:
We can help you get started, but then you need to show us your efforts.
We cannot make a variable the subject, as long as that variable appears in the denominator of a ratio.
Therefore, a first step is to get rid of the ratio, on the left-hand side.
Consider the following form.
A/B = C
To get rid of the ratio, we multiply both sides by the denominator.
AB/B = BC
On the left-hand side, the B in the numerator cancels with the B in the denominator.
A = BC
See what happened? We got rid of the ratio.
That's what you could do. Multiply both sides by the denominator, then continue.
Cheers :cool:
Thank you
Thank you for being so patient with me. I am in my 40s and am home educating my teenage daughter who has been very ill. I have always struggled with maths but am trying to keep ahead of the topics so that I can help her properly. We have expanded brackets before but I haven't come across one like this
Ok so this is where I have got to:
I have multiplied by 4:
4(4s - 5t) / (2s + 3t) = 1
16s - 20t /8s + 12t = 2s + 8t
Then if 2s = 8t s = 4t
Is this anywhere close?
Thank you very much for helping me.
Thank you for being so patient with me. I am in my 40s and am home educating my teenage daughter who has been very ill. I have always struggled with maths but am trying to keep ahead of the topics so that I can help her properly. We have expanded brackets before but I haven't come across one like this
Ok so this is where I have got to:
I have multiplied by 4:
4(4s - 5t) / (2s + 3t) = 1
16s - 20t /8s + 12t = 2s + 8t
Then if 2s = 8t s = 4t
Is this anywhere close?
Thank you very much for helping me.
I have multiplied by 4:
4(4s - 5t) / (2s + 3t) = 1
(16s - 20t) / (8s + 12t) = 2s + 8t
When typing algebraic ratios, please remember to always put grouping symbols around numerators and denominators. These grouping symbols are the only way to clearly show what's on the top and what's on the bottom.
Without the grouping symbols shown in red, the left-hand side above actually means this:
\(\displaystyle 16s - \dfrac{20t}{8s} + 12t\)
On the left-hand side, it appears that you multiplied both the numerator and the denominator by 4. That's incorrect.
On the right-hand side, I'm not sure how the 1 changed into 2s + 8t.
When we multiply a ratio by 4, we need to think of 4 in fractional form (4/1) because the rule for multiplying one ratio by another is: numerator times numerator over denominator times denominator.
Therefore, this is how we multiply both sides of the given equation by 4:
\(\displaystyle \dfrac{4}{1} \cdot \dfrac{4s + 5t}{2s + 3t} = \dfrac{4}{1} \cdot \dfrac{1}{4}\)
On the left-hand side, we multiply numerator times numerator. In other words, (4)(4s+5t)
We also multiply denominator times denominator. In other words, (1)(2s+3t)
On the right-hand side, we have (4/1)*(1/4). In other words, 4/4
Therefore, multiplying both sides of the given equation by 4 yields this:
\(\displaystyle \dfrac{16s + 20t}{2s + 3t} = 1\)
If this result is not clear, please ask your daughter to explain the confusing part(s).
Otherwise, let's continue.
You're trying to make s the subject (AKA: "solve for s").
As long as s appears in the denominator of a ratio, we cannot isolate it. We need to get rid of the ratio, on the left-hand side above.
We can do this by multiplying both sides by the denominator.
In other words, multiply both sides by \(\displaystyle \dfrac{2s + 3t}{1}\)
Please try that, and show us what your daughter gets.
If I wrote anything that you don't understand, please ask a specific question about it.
Cheers :cool: