Question

As you have discovered, any fraction can be rewritten in many equivalent ways. When choosing a denominator that will work to add two fractions, there is no single correct choice. Often, people find it convenient to use the smallest whole number that all denominators divide into evenly. This number is called the lowest common denominator. For each of the following sums, first rewrite each fraction using the lowest common denominator. Then add.

a. +
b. $

Answer 1

To add fractions, find the lowest common denominator, rewrite each fraction using this denominator, and then add the numerators while keeping the denominator the same.

Step-by-step explanation:

Adding fractions requires a common denominator to combine the numerators. The lowest common denominator (LCD) is the smallest whole number into which all the denominators can evenly divide. To select the LCD when adding fractions, you analyze the denominators of the fractions involved and look for the smallest multiple they both share. Once the fractions are rewritten with the same LCD, their numerators can be added while the denominator remains the same. For example, adding ½ and ⅓ requires the LCD of 6. Rewriting ½ as 3/6 and ⅓ as 2/6 allows you to add directly to get 5/6. Unlike multiplication of fractions, where you simply multiply the numerators and denominators together, addition requires a common base to perform the operation correctly.