Assessment and Learning in Knowledge Spaces (ALEKS) Basic Math Placement Practice Test

What method do you use to simplify fractions after multiplication?

1. Just leave them as is

2. Add both fractions to simplify

3. Combine numerators only

4. Simplify both the numerator and denominator

The correct answer is: Simplify both the numerator and denominator

When simplifying fractions after multiplication, the appropriate method is to simplify both the numerator and the denominator. This process involves reducing the fraction to its simplest form by finding the greatest common factor (GCF) of the numerator and denominator. Once you have multiplied the fractions together, the resulting fraction's numerator and denominator may have common factors that can be divided out, resulting in a simplified fraction. For example, if you multiply two fractions \( \frac{a}{b} \) and \( \frac{c}{d} \), you get a new fraction \( \frac{a \cdot c}{b \cdot d} \). After performing this multiplication, you should check if the new numerator \( (a \cdot c) \) and the new denominator \( (b \cdot d) \) can be simplified. By dividing both the numerator and the denominator by their GCF, you can present the fraction in its simplest form. Using this method ensures that fractions are expressed in the simplest possible way, making them easier to work with in further calculations or comparisons.