# How to write that per that in mathematical terms?

1. Jan 11, 2010

### Juwane

How to write "this per that" in mathematical terms?

What is the mathematical equivalent of saying, for example, meters per second?

If we want to say that something moves with the rate of 50 meters per 30 seconds--do we write this as a fraction or as an equation, or we can write as both?

I mean what is the difference between saying "50 m/30 sec" and "50 m = 30 sec"? I'm confused.

Last edited: Jan 11, 2010
2. Jan 11, 2010

### tuoni

Re: How to write "that per that" in mathematical terms?

You would write:

$1 + \frac{2}{3} \; \frac{m}{s}$ or $\frac{5}{3} \; \frac{m}{s}$ or $\frac{50}{30} \; \frac{m}{s}$

or in indefinite form:

$1.6... \; \frac{m}{s}$

The general syntax being, "change in y over change in x":

$\frac{\delta y}{\delta x}$

"50 m = 30 s" is not possible, = indicates equality, and 50 m is NOT equal to 30 s.

Last edited: Jan 11, 2010
3. Jan 11, 2010

### Juwane

Re: How to write "that per that" in mathematical terms?

How can we I set the fraction to an equal something? Can I say something like:

$\frac{50 m}{30 s} = \frac{5}{3}$

4. Jan 11, 2010

### espen180

Re: How to write "that per that" in mathematical terms?

You cannot. Since the units don't match on each side of your equation, the equation is nonphysical.

You can say $$\frac{50m}{30s}=\frac{5m}{3s}$$

5. Jan 11, 2010

### Tac-Tics

Re: How to write "this per that" in mathematical terms?

Compare these two sentences.

"The man walked over the hill."

"The man with no hair."

The first one is a sentence. The second isn't.

The same is true of "50m = 30sec" and "50 m/30 sec". The equals sign makes a statement about two values. It says the value on the left is equal to the value on the right. The second one is just a value.... with no equals sign. The equals sign is the verb. Without one, you just have a meaningless noun.

What you want to express can't be put into symbols. Use words to describe it: "the man ran 50m in 30sec" or "His velocity was 50m/30sec".

Last edited: Jan 11, 2010