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Defining, Translating, & Solving One-Step Equations

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  • 0:01 Translating Equations
  • 2:11 Example 1
  • 3:41 Example 2
  • 4:13 Example 3
  • 5:03 Lesson Summary
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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 Equations

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.

Example 1

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.

Example 2

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.

Example 3

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?

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