Math Lesson 9.1.1 - What is a Mathematical Sentence?

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Welcome to our Math lesson on What is a Mathematical Sentence?, this is the first lesson of our suite of math lessons covering the topic of Variables, Coefficients and Constants. First Order Equations with One Variable, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.

What is a Mathematical Sentence?

In spoken language, we express facts through wordy sentences. For example, by saying "Today is Monday", we are expressing a fact, which may be true or false. Likewise, a mathematical sentence is a sentence that tells something written in math symbols. For example, if we write 4 + 7 = 11, we are expressing a (true) fact in math symbols. On the other hand, when writing 20 - 3 = 4, we are expressing another fact in math symbols, which this time is false.

By definition, a mathematical sentence, also called a mathematical statement, is a sentence written using math symbols which can be identified as either true or false.

Obviously, the quantities included in a mathematical sentence must be measurable. Otherwise the sentence may be subjective and its worth may depend on the opinion of its author. For example, the sentence "Today I feel 100 times healthier than when I was ill" is not a mathematical one despite the number 100 contained in it. This is because this sentence represents a subjective opinion of the author.

Example 1

From the list below, identify the sentences that are suitable to be written as mathematical sentences:

1. My brother is three years older than me.
2. This painting looks much clearer than that one.
3. It is 1000 times better to have a good friend than 1 million dollars in the account.
4. Today I earned $70 more than yesterday.
5. The factory where I work produced the same number of items last year as it produced in the previous two years combined together.

Solution 1

1. This sentence can be expressed as a mathematical one. We can denote the author's age by x and that of his/her brother by y. Hence, the sentence is written in the form
   x = y - 3
2. This sentence cannot be written as a mathematical one as the opinion expressed is subjective.
3. Despite two numbers appearing in this sentence it still represents a subjective opinion. Therefore, it cannot be written as a mathematical sentence.
4. This sentence is similar to the first one. It can be written as a mathematical sentence when expressing the amounts earned in the last two days by different letters, for example T for today and Y for yesterday. Hence, we can write
   T = Y + 70
5. This too, can be written as a mathematical sentence despite there being no numbers in the statement. Thus, if we denote the amount of items produced in the current year by x, and those of the items produced in the last two years by y and z respectively, we can write the following formula using the information givin.
   x = y + z

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