Mathematics ACT Aspire Practice Test

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What is the first step in adding unlike fractions?

Add the numerators directly
Rename the fractions using the least common denominator
Convert the fractions to decimals
Find the greatest common factor

The correct answer is: Rename the fractions using the least common denominator

When adding unlike fractions, the first step involves renaming them using the least common denominator (LCD). Unlike fractions have different denominators, which makes it impossible to directly combine their numerators and denominators. To effectively add these fractions, you need to convert them to equivalent fractions that share a common denominator. The least common denominator is the smallest multiple that the denominators of the fractions can both divide into. By finding the LCD, you can rewrite each fraction as an equivalent fraction with that common denominator. Once this step is completed, you can easily add the numerators of the updated fractions while keeping the common denominator the same. This process ensures that the fractions are compatible for addition and yields a correct and simplified sum. Other approaches, such as converting to decimals or finding the greatest common factor, do not address the immediate requirement of creating a common base for the addition and would complicate the process. Therefore, renaming the fractions using the least common denominator is essential for successfully adding unlike fractions.