Mathematics ACT Aspire Practice Test

How should you handle terms with unlike denominators before subtraction?

1. Convert them to like fractions

2. Just subtract the numerators

3. Leave them as is

4. Convert them to decimals

The correct answer is: Convert them to like fractions

When dealing with terms that have unlike denominators in subtraction, the correct approach is to convert them to like fractions. This is essential because in order to perform subtraction accurately, the denominators must be the same. When fractions have different denominators, subtracting the numerators directly would not yield the correct result because the fractions represent different parts of a whole. For example, when you have \( \frac{a}{b} - \frac{c}{d} \), you cannot simply subtract \( a - c \) because \( b \) and \( d \) scale the values differently. To convert the fractions to like fractions, you need to find a common denominator, which is typically the least common multiple (LCM) of the two denominators. Once the fractions have the same denominator, you can easily subtract the numerators while keeping the common denominator intact. This process ensures that the subtraction reflects accurate values proportional to each original fraction. Options that suggest leaving the fractions as they are or converting them merely into decimals do not allow for proper subtraction of unlike fractions, as they either lack the necessary adjustment to align denominators or alter the representation in a way that can lead to inaccuracies in calculations.