Q4. - Algebra 1

Question

State whether each sentence is true or false. If false, replace the underlined word, phrase, expression, or number to make a true sentence.

 

A rational expression is a fraction in which the numerator and denominator are fractions.

Step-by-Step Solution

Answer

The given statement is false.

The corrected statement is “A rational expression is a fraction in which the numerator and denominator are polynomials.”

Step 1. State the concept.

A rational expression is an algebraic expression whose numerator and denominator are polynomials. Also, division by 0 is undefined, so therefore, the polynomials in the denominator cannot be zero and the values for which the denominator is zero is termed as excluded values for the respective rational expression.

Step 2. Explanation of the statement.

When the values of numerator and denominator are polynomials, then the ratio calculated by these values is nothing but rational expression. 

Hence, the ratio of numerator and denominator value as polynomials gives a rational expression. 

So, the given statement is false.

Step 3. State the correct statement.

The corrected statement is “A rational expression is a fraction in which the numerator and denominator are polynomials.”