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Defining Variables - Problem 3
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Read the word sentence and take note of the keywords to help you in writing it as a mathematical sentence. In the sentence "The product of some number and 5 is 80", the word "product" indicates that two numbers are being multiplied. One of those numbers is 5 and the other is "some number", which is the unknown value, or the variable. The product of the two numbers equals 80. This is written mathematical as (x)(5) = 80 or 5x = 80. 5x is another way of writing 5 times x, or 5 times some number.

It's really important when you're learning variables to be able to move back and forth between Math symbols and words. It will help you keep straight in your head what's actually going on mathematically. Look at this example, write the following using mathematical symbols, the product of some number and 5 is 80.

So let's go through it and decode what the sentence is saying. The first important vocabulary word is product. Hopefully you guys remember that product means the answer to a multiplication problem so I know I'm going to have some kinds of multiplication. However instead of using that little x, that little cross, a lot of times in Algebra you'll use either a dot between two numbers or else you'll use parentheses and the reason why is when you start doing something like x times x, it's really ugly and confusing when you have x x x so we'll be using some other different types of notation for multiplying.

Okay so the product of some number, some number means I'm going to have a variable, you can choose any letter you want to. You can choose the first letter of your name, you can choose the first letter of your dog's name, I'm going to use the letter a because that's the first letter of my name and 5. So some number a, is getting multiplied by 5 and the answer is 80. So what I'm going to write is some number being multiplied by 5 gives me the answer of 80. That's one way to write it with a dot in the middle. You could also write this like 5a like that even though there's no little cross sign or dot or parentheses or anything, in Math if you just have a number next to a letter or variable, that means multiply.

So either one of these is fine, these are both mathematically valid statements and then I'm done. I've taken this sentence and turned it into Math symbols. I personally like Math because this stuff that takes forever to write, it's like a whole sentence, you can write it in 3 or 4 different symbols and it's done. You don't have to write out like your hand gets tired so Math's kind of cool in that way.

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