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Algebra I: High School20 chapters | 168 lessons | 1 flashcard set

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Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Watch this video lesson to learn how you can write a simple math equation when you are given a word problem. Learn how to translate words into math symbols. Learn the shortcuts to remember.

**Translating** word problems into math equations involves exchanging words for the proper math symbols. A math **equation** tells you something is equal to something else. What this means is that we will have an equals sign somewhere in our problem. Also, our word problem will use keywords that let us know how to write our math equation.

This doesn't sound so hard, does it? Still, some consider word problems the most difficult of all math problems. But, I don't want you to think like that. Once you know the keywords to look out for, translating your word problems into easy to solve math equations becomes easy. Let's go over some of these keywords before we look at a few examples. What these keywords tell you is that whenever you see these words, you will write its math equivalent instead:

- The first set of words include the words
**is, are, will be, gives**, and similar words that show one thing matching up or being identified with another thing. When you see one of these words, you will write the equals symbol (=) for equality. - The next set of words include the words
**more, total, sum, plus, combine, increased**, and similar words that show things are being added together. When you see one of these words, write the plus symbol (+) for addition. - Another set includes the words
**decreased, minus, less, fewer, takes**, and similar words that show things are being taken away. Write the minus symbol (-) for subtraction when you see these words. - The next set includes the words
**of, multiplied, product, times**, and similar words that show things are being made larger by multiplication. Use the multiplication symbol (*) for these words. - The last group of words includes the words
**per, out of, ratio of**, and similar words that show things are divided. Use either the division symbol or the division slash (/) for these words.

Now, let's see how we can use these keywords in the following examples.

Our problem: Sarah has two apples in her bag. Jordan has five apples in his bag. If Sarah and Jordan combined their apples into one big bag, how many apples would be in the big bag?

The solution: As we read our problem, we identify the keywords of 'combined' and 'will be.' How will our equation look? Well, what are we trying to accomplish here? The problem asks us what will happen when Sarah's and Jordan's apples are combined. What math operation is that?

The keyword here is 'combined,' and this tells me to write a plus sign for addition. What am I adding together? The number of apples Sarah has and the number of apples Jordan has. So I have 2 + 5.

Now what? Well, the problem then asks what will be the answer after they are combined. I see a keyword of 'will be,' which tells me to write an equals sign. Now I have 2 + 5 =.

What goes on the other side of my equal sign? That will be my answer. I will use the variable *x* for that. So now I have my finished math equation: 2 + 5 = *x*. Now I can go ahead and solve it to find my answer. 2 + 5 = *x*. And so *x* = 7. Aaah, so 7 apples is my answer.

Let's look at another example. Our problem: What is three times five?

The solution: After reading this problem, we identify the keywords of 'is' and 'times.' Is translates to equals, and times translates to the multiplication symbol for multiplication. My 'what' will be my variable *x*.

So my problem written using math symbols now reads *x* = 3 * 5. Solving it, I get *x* = 15 as my answer.

Here is one last example. Our problem: A box has twenty candies inside it. Alex comes and takes five candies out of the box. How many candies are left?

The solution: To start, what are my keywords? They are 'takes' and 'are.' The keyword 'takes' translates to minus for subtraction, and the keyword 'are' translates to equals.

What is being subtracted? The 5 is being subtracted from the 20. The equals sign goes after this operation, and my *x* goes on the other side of that since it is what I want to find out. I get 20 - 5 = *x*. Solving this, I get *x* = 15. So I have 15 candies left.

What have we learned? We've learned that **translating** word problems into math equations involves exchanging words for the proper math symbols. A math **equation** tells you something is equal to something else. When translating word problems into math equations, we look for keywords:

- Keywords such as
**is, are, will be**, and**gives**translate into the equals sign (=). - Keywords such as
**more, total, sum, plus, combine**, and**increased**translate into addition (+). - Keywords such as
**decreased, minus, less, fewer**, and**takes**translate into subtraction (-). - Words such as
**of, multiplied, product**, and**times**translate into multiplication (*). - For division (/), look for such words as
**per, out of**, and**ratio of**.

As you read the word problem, in addition to looking for these keywords, also read to find out what the problem is asking so you know where to put the equals sign.

Following this lesson, you should have the ability to:

- Describe the general steps for translating word problems into math equations
- Identify important keywords that will help you make equations out of the word problems

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Algebra I: High School20 chapters | 168 lessons | 1 flashcard set

- What is the Correct Setup to Solve Math Problems?: Writing Arithmetic Expressions 5:50
- Understanding and Evaluating Math Formulas 7:08
- Expressing Relationships as Algebraic Expressions 5:12
- Evaluating Simple Algebraic Expressions 7:27
- Combining Like Terms in Algebraic Expressions 7:04
- Practice Simplifying Algebraic Expressions 8:27
- Negative Signs and Simplifying Algebraic Expressions 9:38
- Writing Equations with Inequalities: Open Sentences and True/False Statements 4:22
- Common Algebraic Equations: Linear, Quadratic, Polynomial, and More 7:28
- Defining, Translating, & Solving One-Step Equations 6:15
- Solving Equations Using the Multiplication Principle 4:03
- Solving Equations Using Both Addition and Multiplication Principles 6:21
- Collecting Like Terms On One Side of an Equation 6:28
- Solving Equations Containing Parentheses 6:50
- Solving Equations with Infinite Solutions or No Solutions 4:45
- Translating Words to Algebraic Expressions 6:31
- How to Solve One-Step Algebra Equations in Word Problems 5:05
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- How to Solve Multi-Step Algebra Equations in Word Problems 6:16
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