How do I solve for B in this equation

Question

h=a/b

Answer 1

h = a/b

Multiply both sides by b (to eliminate the fraction)

Get bh = a

Divide both sides by h to isolate the b on the left side of the equation.

b = a/h

Another approach would be to re-write as h/1 = a/b and solve like any other proportion (cross-multiply)

Get a = hb, then divide both sides by h as before.

Answer 2

I like to point out there is a pattern that works well when there is a variable you are solving for that is in the bottom.

Suppose

some # = some # / something we'd like to know

Let's call the first "Some#" "S".

Let's call the second one on the right "N" for numerator.

Let's call the something we'd like to know "x" with a nod to tradition.

S = N/x

If we think about the individual steps, one thing we could do is make sure the variable we are solving for isn't in the denominator by multiplying both sides by it.

S * x = (N/x) * x = N

Sx = N

Then we can isolate the variable we are solving for by dividing by S.

x = N / S

Or we could have multiplied both sides by x/S all at once.

In effect, the overall combined effect of both operations was to swap the S and the x.

This is a mental shortcut which can very effective (save time) if you are aware that it works when

a fraction equals another fraction. S can be considered S/1 (after all you can think of any number as a ratio of itself versus one if you choose to).

So if T= J/ B, then B = J/T.

Or if G=x/y, then y=x/G.

Caution though.

What if you have

B

A = -------- or in another style of typing , what if A = B/ (C+x)

C + x

Now you have to swap the entire (C+x) with A. That entire (C+x) is what you would multiply by, then divide by A, or do both at once.

Which would take you to:

C+ x = B/A

then you'd have to subtract C to finish isolating by X. Make sense?

Thank you for reading this explanation.

Please comment your conclusion about your problem, so I can congratulate you on what you've learned, or improve the explanation if it misled you.