- Now that you are familiar with algebraic expressions, we will begin to write expressions so that we can solve real-world problems. There are many common words or phrases that are used in mathematics. Many of those words represent addition, subtraction, multiplication, and division. I'd like you to take a minute to think about any words that you think might represent these operations. In your exercise files, you've a worksheet. You can use this worksheet to record your answers and as we go over these answers, you will be able to fill in more words that represent these operations.

There's a few words that I came up with for addition. Plus, Sum, which is the answer to an addition problem, Increased by, and More than. For subtraction, you might see Minus, Difference, which is the answer to a subtraction problem, Decreased by or Less than. When you multiply, you might see the word Times, Product, which is the answer to a multiplication problem, Multiplied by, Twice, which means times two, Triple, which means times three, and key words like "of" or "per", that will represent multiplication as well.

And when dividing, you might see the words Divided by, or Quotient. Now let's use our chart to help us translate the following statements into algebraic expressions. The first problem says, "A number increased by five." A number, we don't know exactly what number, so we must use a variable. In this case, you can choose any variable that you like. I'm going to use n for number. So a number increased by five.

"Increased" is a key word, and that word typically means "to add", so we're going to add five. So this algebraic expression means a number increased by five. The second problem says "Twice a "number decreased by four." "Twice" is a key word for multiplication. That means multiplied by two. So we're multiplying a number by two.

This time I'm going to use x as my variable. So twice a number means two times x. And that is decreased by four. "Decreased" means to subtract. So we're going to subtract four. Therefore, this algebraic expression means Two times a number, or twice a number, decreased by four. "The quotient of 36 and a number." "Quotient" is a tricky word.

But that's the answer to a division problem. So the quotient of 36 and a number is 36 divided by, and I'm going to use y this time, you can use this symbol that's on a slant, or if you choose to, you can write it like a fraction. This also means divided by. If you really wanted to, you could also use the division symbol. We don't see this symbol as much in algebra, however you can still use it.

36 divided by y. Our next problem says, "One half "of a number increased by two." One half is a fraction, and we're taking half of a number. So I'm going to write this as one-half times, and this time I will use n again, one-half n increased, increased means to add, and we're increasing it by two. So one-half n plus two is the algebraic expression.

Our last problem is really tricky because it says, "Five less than a number." Most students would start with a number five, less than typically means to subtract, and then a number n. Five minus n. Does five minus n mean five less than a number? Actually, it does not in this situation. This is five minus a number, but not five less than a number.

So even though it's written in this order, we actually have to write n minus five, because this is five less than a number. So that one's a little tricky, so you may want to read through the statement first, before deciding which order you need to write the numbers and the variables in. Hopefully, we now have your mind thinking about these special math words and how they can help us to write algebraic expressions. In our next lesson, we will look at real-world problems.

###### Released

8/4/2015This course includes practice challenges and worksheets, as well as tips for educators who are helping students master pre-algebra for Common Core. Karin Hutchinson also helps you evaluate, write, and simplify expressions, and solve word problems and complex algebraic expressions.

- Adding integers
- Subtracting
- Multiplying and dividing
- Understanding the order of operations
- Evaluating expressions
- Breaking down word problems and algebraic expressions
- Distributing positive and negative numbers
- Simplifying expressions

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Video: Introduction to common mathematical words