Problem 147 - Introductory Algebra for College Students

Question

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Every fraction has infinitely many equivalent fractions.

Step-by-Step Solution

Answer

The statement is true. Every fraction does indeed have an infinite number of equivalent fractions.

Step 1: Understand the Definition of Equivalent Fractions

An equivalent fraction is created by multiplying or dividing both the numerator and the denominator by the same nonzero whole number. Allowed values for this multiplier or divisor range from 2 to infinity, as long as it does not result in a denominator of zero.

Step 2: Evaluate the Statement

Applying the definition from the previous step, it can be seen that every fraction indeed has an infinite number of equivalent fractions. For example, the fraction 1/2 can be multiplied by 2 to get 2/4, multiplied by 3 to get 3/6, and so on infinitely.

Step 3: Confirm the Statement

The statement 'Every fraction has infinitively many equivalent fractions' is true.