# Welcome to Algebra I: Translating Expressions

15 minutes

Hey, guys. Welcome to Algebra I. Today we're gonna get started translating expressions. You've actually been translating expressions since elementary school, but I bet you didn't realize that you were.

(Describer) She activates a screen which has the word "six".

I bet when you see that word, I bet you know it means this number.

(Describer) She writes 6.

You just translated an expression from verbal to numeric. Look at that next number.

(Describer) 11.

I bet you know that it means this word.

(Describer) She writes.

You just translated an expression from numeric to verbal. Look at that last one, "Twelve more than a number." That's when we step it up to Algebra I. How exactly do you translate something like that? You've got to know key words and what they're telling you you need to do. When you see plus, and, sum, increased by, greater than, more than, all of those phrases are telling you to add. If you run into a problem, for example, "Three more than number," you see "more than" in there. That's telling me I'm gonna be adding two things together. In algebra, when we don't know what something is, we assign it a variable. Pick any letter in the alphabet. Normally, we use x. Three more than some number, and I don't know what that number is. I can represent that as 3 plus x. I have some value that I'm unsure of, and I'm increasing it by 3. Now, there's another way you could write that expression. If you remember from middle school, you can add numbers in any order that you want. Right now I have 3 plus x. I could've also written it as x plus 3. Either one is fine. They're both acceptable. Let's take a look at some more. "Subtract, less, minus, difference of." I bet you knew from the first word that those were telling you to subtract. When you see something like two less five, it sounds a little awkward. Just swap out "less" and think "subtract" instead. So, 2 subtract 5. 2 subtract 5. You just represented that verbal expression as something numeric. Let's keep going. "Less than, subtracted from." Those also mean subtract. So, two less than five. I have a value of 5, and I need 2 less than that. So, 5 subtract 2. That's exactly what that means numerically. I have some value of 5, and I need 2 less than that. "Product, times, multiply by." Those are all telling you to multiply, and in algebra, we use the dot symbol to show that we're multiplying. So, 7 times a number. 7 times a number. That's showing me the product of 7 and some value of x. If you want, you can completely disregard the dot and just write 7x. Both of those expressions are telling you you're multiplying 7 times x. Let's keep going. "Quotient, divided by." I bet you knew those were telling you to divide. An example like, "The quotient of a number and nine." You have some number that you don't know the value of, and you're dividing it by 9. In Algebra 1-- in all math classes-- it's easier if you use the horizontal fraction bar and not the slanted one. As you keep going through the course, you'll learn why. It makes some problems difficult to read. From now, go ahead and use that horizontal bar when you're dividing. Okay. Now it's your turn. Look at these examples. Pause the tape and try and see if you can get through these. You'll never know for sure if you got it till you try it yourself. Then press play, and we'll check our answers.

(female describer) Title: Match.

(Describer) Title: Match. In one column are five verbal expressions. In the other are five algebraic expressions. In the verbal column: Number One: Five more than a number Number Two: A number divided by five Number Three: The product of five and a number Number Four: Five less a number Number Five: Five less than a number In the algebraic column: Letter A: 5 minus x Letter B: x over 5 Letter C: x minus 5 Letter D: x plus 5 Letter E: 5x

In one column are five verbal expressions. In the other are five algebraic expressions. In the verbal column, number one: Five more than a number. Number two: A number divided by five. Number three: The product of five and a number. Number four: Five less a number. Number five: Five less than a number. In the algebraic column, letter A: 5 minus x. Letter B: x over 5. Letter C: x minus 5. Letter D: x plus 5. Letter E: 5x.

(instructor) Let's go over these. "Five more than a number." Did you catch that "more than"? That's telling you you need to add. That has to be D. I'm adding 5 to a number I don't know the value of.

(Describer) X plus 5

"A number divided by 5." So, "divided by." I'm looking for division. Straight across. That one's B.

(Describer) X over 5.

"The product of five and a number." So, "product." I know I'm multiplying, so look for your multiplication. That one's E.

(Describer) 5x

"Five less a number." Remember we said that was the one that sounded awkward? So, instead of saying "less," just say "subtract." So, 5 subtract a number. That one's A.

(Describer) 5 minus x.

"Five less than a number." Either process of elimination, you know that one is C, or you really did translate it. There we go, x minus 5. Let's step up our operations a bit. See if we can handle these. Anytime you see "to the power of," that is a signal there's an exponent involved. Look at that example. "A number to the power of five." I don't know my value, but I'm gonna raise it to the fifth power. So, I'll write x, and then my exponent's 5. Some value I'm unsure of. I've raised to the fifth power. Let's keep going. "Squared to the power of two to the second power." This is still telling me I have an exponent, but in this case, the exponent is 2. Anytime you see phrases like that, your exponent is gonna be 2. A number squared. "Squared" is telling me 2. I've got x to the second power. Let's keep going. "Cubed to the power of three to the third power." All right, got an exponent. And I bet you figured it out that in this case that exponent's 3. A number to the third power. Don't know what that number is, so that's my variable that I'm gonna raise to the third power. Okay? We got a few for you to try. Pause me again. Give yourself a shot at these. Then we'll check our answers.

(describer) Number one: A number to the second power.

(Describer) Number One: A number to the second power Number Two: A number cubed Number Three: A number to the power of four

Number two: A number cubed. Number three: A number to the power of four.

(instructor) Okay. "A number to the second power." Let's see what you got. Gonna have to switch to my pointer tool. All right, x-squared for that one. "A number cubed." X-cubed for that one. "A number to the power of four." X to the 4th power for that one. Let's keep going. Let me get my pen back. Okay. "One-half of a number." I know nobody likes fractions. We see them and say, "What do I do?" You can't avoid them in math, so learn to handle them. Eventually, they won't bother you. So, "one-half of a number." That "of" is telling me I've got to multiply. I'm taking one half of some value that I don't know. So, I've got 1/2 times a number. Don't know what that number is. I'm calling it x. If you feel fancy, you could also represent this this way: x divided by 2. Because multiplying a number by 1/2 is the same as dividing it by 2. Whichever one you want to write, they're both acceptable. Let's keep going. "Three-fourths of a number." Different fraction, but it's the same idea. I've got 3/4 times a number. Or, in this case, if you want to write it differently, you could represent that as 3x divided by 4. They're both acceptable. It's a matter of which one you want to write. Let's keep moving. "Twice a number." This one isn't a fraction, but it's a little funky. I want to make sure you can handle it. "Twice a number." You're multiplying it by 2. Whatever number that is, I multiply it by 2. I could represent that as 2x, and you've translated that expression. Let's take a look at these. Go ahead and pause. Try this, see how you work it out. Then we'll get back together and we'll check our answers.

(describer) Number one: Four-fifths of a number.

(Describer) Number One: Four-fifths of a number Number Two: One-third of a number Number Three: Triple a number

Number two: One-third of a number. Number three: Triple a number.

(instructor) Let's see how you did. So, "four-fifths of a number." Either you wrote 4 divided by 5 times x, or 4x divided by 5. Either one is fine. "One-third of a number." Either one of those are fine. 1/3 times x or x divided by 3. And triple a number: 3 times x. Okay. Let's keep going. "Three times the sum of five and a number." That sounds like a mouthful, but we'll break it down, and then it won't be so bad. "Three times the sum of five and a number." Handle this part first. Let me get my pen back. You want to handle that sum of five and a number. Throw back to middle school a bit, order of operations. You remember whatever was in the parentheses you'd do first? Same idea here. Because I want to handle that sum of five and a number first, I'm gonna put it in parentheses. So, the sum--I know I'm adding-- of 5 and a number. And then I need three times that sum. So, three times the sum of five and a number, and you've translated that expression. Let's keep going. Get the pointer tool back. All right. "One-half the product of six and seven." It sounds like a lot again, but let's do exactly what we did before. We're gonna start with the second half of that first, that product of 6 and 7. In this case, I'm gonna put my dot. Because I'm multiplying, and if I don't show that dot, it's gonna look like 67. You don't want to take the product. Don't multiply 6 and 7 together. Represent it just like you did: 6 times 7. Then I have one-half of that product. I know I'm gonna be multiplying by one-half out front. All right? Not too bad. A couple for you to try. So, press pause. Then we'll get back together and check our answers.

(Describer) Number One: Four times the product of nine and a number Number Two: One-fourth the sum of three and a seven

(describer) Number one: Four times the product of nine and a number. Number two: One-fourth the sum of three and a seven.

(instructor) Okay. "Four times the product of 9 and a number." You've got your 9 times x in parentheses, and you're multiplying it by four. "One-fourth the sum of three and a seven." You're adding 3 plus 7, and then 1/4 times that.

(Describer) Three plus seven is in parentheses.

All right. Okay. So, you've had some practice translating expressions. I hope you got comfortable working with fractions. And I bet you now are feeling more comfortable with all of this altogether. See you next time.

(Describer) Accessibility provided by the US Department of Education.

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In this program, students learn how to translate algebraic expressions that contain ordinary numbers, variables (x, y), and operators (add, subtract, multiply, and divide). Part of the "Welcome to Algebra I" series.

## Media Details

Runtime: 15 minutes