Translating a Division Statement into an Algebraic Expression

Translating a Division Statement into an Algebraic Expression
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  • 0:01 A Division Statement
  • 1:06 Translating It
  • 2:47 Example 1
  • 3:35 Example 2
  • 4:11 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.

In this video lesson, you will see that when it comes to math and the real world, there will be situations when you have to translate a statement that you hear or read in words into a math problem that you can solve.

A Division Statement

In this video lesson, we talk about translating a division problem from words into an algebraic expression. An algebraic expression is a mathematical statement using numbers and symbols. In the real world, there are many instances where you are asked a problem that you need to solve. But before you can solve it, you will need to translate the problem into an algebraic expression that you can solve.

In this video lesson, we look at just the translating process; how to solve the resulting algebraic expression is covered in other lessons. Let's take a look at a possible circumstance.

Imagine that you are working at a candy shop. You have a bag of candies that you need to separate equally into 12 different bowls. The bag of candies contains a total of 108 candies. You ask yourself this question to figure out how many candies will go into each bowl: 'What is one hundred eight divided by twelve?'

Translating It

Before you can answer your question, you need to translate your question (your problem) into an algebraic expression. How can you do this? You can do this by focusing on your key words and on what your problem is really saying. Looking at your question, your key words are 'what', 'is', 'one hundred eight', 'divided by', and 'twelve'. In this case, all of your words are key words. This won't happen in all cases though. These key words tell you your numbers and the kind of operation to use, and what is equal to what.

Your number words will tell you the numbers as well as your unknown numbers that you need to find. You will typically only have one operation word. The word 'is' tells you where your equal sign goes by telling you what equals what. The word 'what' in your question represents an unknown number. When you write your algebraic expression, you write down 'x' for it. Seeing how your key words are arranged and what they mean, you go ahead and write your algebraic expression as x = 108 / 12. This is an algebraic expression that you can solve.

Of course, there are other key words out there. Just think about what other words can represent the division operation? One word I can think of is 'out of'. What other words can you think of? Another word that represents the same thing as the word 'is' in your question is the word 'equals'. Because there are other key words out there, it is important to fully understand what your problem is really telling you.

Let's look at a couple more examples.

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