# Operations with Unlike Fractions Worksheets

### About These 15 Worksheets

These worksheets are dedicated resources that focus on teaching students how to perform various mathematical operations (addition, subtraction, multiplication, and sometimes division) with fractions that do not share the same denominator. Unlike fractions pose an added layer of complexity, especially when adding or subtracting, because they cannot be combined directly until they’re converted to have a common denominator. These worksheets guide students through this process, providing ample practice to cement understanding.

### Types of Exercises on These Worksheets

**Finding the Least Common Denominator (LCD)** – Exercises that solely focus on determining the LCD for a pair or set of unlike fractions. This is a foundational skill, as the LCD is crucial for adding or subtracting unlike fractions. Students become adept at quickly identifying the smallest number into which all the denominators can evenly divide.

**Rewriting Fractions with the LCD** – Once the LCD is identified, students are tasked with converting the given fractions to equivalent fractions using this denominator. This step is vital for making unlike fractions compatible for addition or subtraction. Students grasp how to make equivalent fractions with a desired denominator, preserving the fraction’s value.

**Addition of Unlike Fractions** – Students add two or more fractions with different denominators. These are super helpful to practice the skill of converting unlike fractions to like fractions and then adding them. Mastery in adding fractions with different denominators.

**Subtraction of Unlike Fractions** – Exercises that require students to subtract one unlike fraction from another. Similar to addition, but practicing the skill of subtraction.

**Multiplication of Fractions** – While the denominators don’t need to be the same for multiplication, worksheets might still include multiplication exercises to provide comprehensive practice. These are used to teach students that unlike fractions can be directly multiplied without needing a common denominator. This improves your understanding of the straightforward nature of fraction multiplication irrespective of denominators.

**Division of Fractions** – Exercises that involve dividing one fraction by another, guiding students to multiply by the reciprocal. To elucidate the process of fraction division and its relation to multiplication. Students learn the trick of flipping and multiplying when faced with fraction division.

### How Do You Perform Operations with Unlike Fractions

Operations with unlike fractions primarily require attention to the denominators. Ensuring they are the same (or finding a common denominator) is crucial for addition and subtraction. Once that’s achieved, the operations are straightforward. On the other hand, multiplication and division do not require a common denominator but do follow their unique set of rules. Always remember to simplify the resulting fraction, if possible, to ensure your answer is in its most reduced form.

**Step #1 – Finding the Least Common Denominator (LCD)**

When the denominators of the fractions are not the same (i.e., they are “unlike” or “different”), the first step is to find the least common denominator (LCD). The LCD is the smallest number that both denominators can divide into evenly. It’s essentially the least common multiple (LCM) of the two denominators.

**Step #2 – Rewriting the Fractions with the LCD**

Once you find the LCD, you can rewrite each fraction so that they both have this common denominator.

Example: To add 1/3 and 2/5 or 1/3 + 2/5.

Step #1 – Find the LCD: The LCM of 3 and 5 is 15. So, the LCD is 15.

Step #2 – Rewrite each fraction with the LCD

For 1/3: Multiply the numerator and the denominator by 5.

1/3 x 5/5 = 5/15

For 2/5: Multiply the numerator and the denominator by 3.

2/5 c 3/3 = 6/15

The two fractions become 5/15 and 6/15, respectively.