In this lesson, the student will learn that any fraction can made to look different but still represent the same value. This is called renaming fractions, and is used in the process of finding a common denominator when adding fractions in later lessons.
First, the student is taught that any fraction can be renamed by multiplying the numerator and denominator by the same number. In this way, the fraction is still balanced and still represents the same value.
Next, we work several example problems where the student gains practice in renaming fractions. In all cases, the fraction represents the same number, but it is just "renamed" to look slightly different.
This process is used constantly when we learn to add fractions in subsequent lessons because the process of finding a common denominator between two fractions is very similar.