I actually paid attention in math class when I was in school. Though I came out of the educational system as a musician, I still understood the importance of what math brought to me. Today I’m going to try to share one little tidbit that I think is one of the most important things a finisher uses.
Proportion is really important to us. Whether we are mixing up a post-cat or enlarging a wipe stain recipe, we need to be able to understand and use proportion to correctly do that.
To get started, then, let’s say that you have a product to catalyst ratio of 1 to 10 for the product that you are going to mix up. You need 35 ounces of product. How many ounces of catalyst do you need at that ratio?
Think it through in your head first. One is to ten as X is to thirty-five. Right? Now, let’s put that into equation form that we can work with. Please note how my equation sentence above translates onto the page. Don’t get the numbers mixed up or this won’t work. One over ten is equal to X over thirty-five.
1/10 = X/35
The issue now is solving this so that you find out what X equals. You do that by cross multiplying the numbers on each side of the equal sign. Cross multiplying is essential to making this work. Look at how I do that so that you understand the concept of “cross” in this process.
1 ∙35 =X ∙10
See how I created a cross as I did that? Now, in simpler form, that same information looks like this
So, if ten Xs equal 35, how much does one X equal? To keep things even, you have to divide both sides of the equation by ten…like this.
35/10 = 10X/10
To cut to the chase, the two issues are:
- what ten divided by ten equals and
- what thirty-five divided by ten equals.
Remember your math teacher drilling this into your head? Any number divided by that same number always equals one. So…
10/10 = 1
Then, on the other side of the equal sign, you’re dividing by ten so just slide that decimal point one place to the left and voila!
35/10 = 3.5/1
In other words…or numbers…
3.5 = X
You need 3.5 ounces of catalyst.
The reason that I paid attention to this little tidbit in class is that I could see that this process would be something that I could use in so many ways and times throughout my life. If you have a ratio of some kind that you need to blow up into something bigger or one that you need to cut down, this is how you do that. And I found that once I had this thought process committed to memory that I could pretty much do it in my head. But, whenever I did, the voices of my math teachers past would echo between my ears…ALWAYS SHOW YOUR WORK!!!! So I still go through lots of scratch paper because I find that they were right. It is important to think through this kind of thing in a logical progression that involves mind, eyes, and fingers.
Come back next week when I will give you another ratio problem to solve.
Until next time…spray on!