Answer Key for Lesson 3.2 Adding Rational Numbers with Step-by-Step Solutions

To begin, align the fractions by their denominators. If the denominators are different, find the least common denominator (LCD) and adjust both fractions accordingly. This ensures that the fractions are expressed with a common base for easier addition.

Next, convert the fractions to equivalent forms with the LCD. After this, add the numerators together while keeping the denominator unchanged. For instance, when adding 3/4 and 5/6, the LCD is 12, and you would rewrite the fractions as 9/12 and 10/12, then add them to get 19/12.

If the resulting fraction is improper, convert it to a mixed number by dividing the numerator by the denominator. For example, 19/12 becomes 1 7/12. Simplify if possible by reducing the fraction to its lowest terms.

Be sure to check for any common factors between the numerator and denominator before finalizing your answer. This will ensure the result is in its simplest form.