Numerical Sentences
Before you learn to deal with algebraic sentences, let's look at numerical sentences. These are math sentences (equations or inequalities) that do not contain variables. They only contain numbers. Because of this, numerical statements are either true all the time or false all the time.
Expressions such as 2 6 = 12 and 6 > 4, are numerical sentences. Ask yourself, "Are these statements true or false?" In this case, both statements are true.
6 > 10 is a numerical sentence; however, it is a false statement. Another example of a false statement is 8 = 5. The goal for this lesson is to determine if any given numerical statement is true or false.
Properties of Zero
Mathematical sentences including zero are common. Several properties of zero are important in working with numerical sentences.
1. Any number times zero equals zero.
2. Zero divided by any non-zero number equals zero.
3. Zero cannot be used as a divisor.
4. Zero added to a number equals that number.
5. A number added to its opposite equals zero.
Example 1:
7 0 = 0 and 0 x = 0
Example 2:
= 0 and = 0 if y 0.
Example 3:
is impossible, and is impossible.
These quotients are undefined.
Example 4:
8 + 0 = 8 and 0 + b = b
Example 5:
3 + (-3) = 0 and -c + c = 0
Properties of One
We will now discuss the mathematical properties involving the number "one." These properties can also be helpful in working with numerical sentences.
1. One times any number equals the number.
2. Any non-zero number divided by itself equals one.
3. Any number divided by one equals the number.
Example 1:
12 1 = 12 and 1 R = R
Example 2:
= 1 and = 1 if T 0
Example 3:
= 9 and = N
Models:
4(1 - 0) = 4(1) = 4
- A 0 = A - 0 = A
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