Translating Math Sentences into Equations

In our last video lesson, we just learned how to translate math expressions. Now we're going to look at translating math equations. What's the difference between a math expression versus a Math equation?

Math expressions, when we see them written in words, they do not have a verb. Just like when we're writing with words and we don't have a verb, we call that a sentence fragment. It's like saying the red car. Well, there's no action, there's no verb there.

So we would just call that a phrase. In math that's the same thing as saying an expression. Now, when we write it in math expressions do not have an equal sign. That's how we'll be able to tell whether it's an expression or not.

In Math equations, when we see it written in words, they will have some type of verb. Normally it's the verb is. So this is kind of like having a complete sentence. Instead of saying the red car, we're saying the red car is driving fast. Now it's a complete sentence. So when we see equations in math, they will have an equal sign. So just think of an expression as being a sentence fragment and an equation being a complete sentence.

Let's look at how to translate this one. We have a number increased by eight is twelve. And because we have that word is in there, we have our verb. This tells us that we're going to have a complete sentence or an equation. Now we know that when we have an unknown number, we're going to translate that into some variable. We can use whatever letter we want.

When we have the words increased by that means we're performing some addition. And we also now know that the word is is going to translate into an equal sign. So now we just have to make sure that we understand exactly what we are adding. Here it says the number increased by eight is twelve.

So we're taking our variable, our number, adding eight to it because it's being increased by eight. And then is twelve will become equal sign twelve. We put that all together. We have some variable. In this case, x plus eight equals twelve. A number increased by eight is twelve.

And this one we have the difference between 15 and the number is ten. We know that difference between indicates subtraction and we have some unknown number that will be a variable. And we also have is. So we know that we'll have an equal sign in there, making it a complete equation. So let's put all this together.

The difference between 15 and a number. So that means we're going to have 15 minus our variable and then is ten will become equals ten. So we can write it like this 15 minus x that represents the difference between 15 and some number variable equals ten. That's from is ten. So we just had to put it all together. Each part of our sentence in words represents some part in that equation.

Now we have the quotient of a number and six is negative seven. Quotient of indicates division. We have an unknown number. Again, we'll represent that with a variable and we have is. So now we know that we have an equal sign in there, making it an equation.

So let me start off with the quotient of a number and six. So that means we're going to be dividing some number or variable by six and then is negative seven will become equals negative seven. Putting it all together, we have x divided by six, which we're representing as a fraction equals negative seven.

And let's look at one more. 34 is twice a number. Now notice in this one we have our number written in words as well. So be careful with that. Sometimes we get so used to looking for actual numbers that we forget that some words represent numbers as well.

So the words 34 we'll just write with the numbers 34 is will become an equal sign and then twice a number. Remember, twice means multiplying by two and we have our unknown number that will represent with a variable. So we're going to take each part of that sentence up top in words and translate it down into our equation. So we have 34 equals which is from the word is twice a number. So two times our variable x 34 equals two x.

So there you go. That's how you translate math words into equations. Now in these examples, we wanted to focus just on the translating part, so we didn't actually finish these equations by solving them. So sometimes when you come across those problems, they will ask you to take that extra step and actually solve for the variables. So just make sure that you read your directions carefully when you come across these problems.