Adding Fractions with Unlike Denominators Made Easy

Understanding the Basics of Adding Fractions with Unlike Denominators

Adding fractions with unlike denominators can seem daunting, but with a clear understanding of the underlying principles, it can be made easy. In this article, we will delve into the world of fractions, exploring the concept of unlike denominators and providing a step-by-step guide on how to add them with ease.

What are Unlike Denominators?

Unlike denominators refer to fractions that have different denominators. For example, ¹⁄₄ and ¹⁄₆ are fractions with unlike denominators. When adding fractions with unlike denominators, we cannot simply add the numerators and keep the same denominator. Instead, we need to find a common denominator that both fractions can share.

Step 1: Find the Least Common Multiple (LCM)

To add fractions with unlike denominators, we need to find the least common multiple (LCM) of the two denominators. The LCM is the smallest multiple that both denominators can divide into evenly. For example, the LCM of 4 and 6 is 12.

🤔 Note: Finding the LCM can be done by listing the multiples of each denominator and finding the smallest multiple they have in common.

Step 2: Convert the Fractions to Have the Same Denominator

Once we have found the LCM, we need to convert each fraction to have the same denominator. We do this by multiplying the numerator and denominator of each fraction by the necessary multiple. For example:

• ¹⁄₄ = ³⁄₁₂ ( multiply numerator and denominator by 3)
• ¹⁄₆ = ²⁄₁₂ ( multiply numerator and denominator by 2)

Step 3: Add the Fractions

Now that both fractions have the same denominator, we can add them by adding the numerators and keeping the same denominator.

• ³⁄₁₂ + ²⁄₁₂ = ⁵⁄₁₂

Example Problems

Let’s try some example problems to put our newfound knowledge into practice:

Example 1: Add ²⁄₅ and ³⁄₇

• Find the LCM: 5 and 7 are relatively prime, so the LCM is 35.
• Convert the fractions: ²⁄₅ = ¹⁴⁄₃₅ and ³⁄₇ = ¹⁵⁄₃₅
• Add the fractions: ¹⁴⁄₃₅ + ¹⁵⁄₃₅ = ²⁹⁄₃₅

Example 2: Add ¹⁄₃ and ²⁄₉

• Find the LCM: 3 and 9 have a common multiple of 9, so the LCM is 9.
• Convert the fractions: ¹⁄₃ = ³⁄₉ and ²⁄₉ = ²⁄₉
• Add the fractions: ³⁄₉ + ²⁄₉ = ⁵⁄₉

Table of Common Denominators

Here is a table of common denominators for reference:

Adding fractions with unlike denominators may seem daunting at first, but by following the steps outlined above, it can be made easy. Remember to find the least common multiple, convert the fractions to have the same denominator, and then add the fractions. With practice, you’ll be a pro in no time!

In essence, adding fractions with unlike denominators is a straightforward process that requires attention to detail and a basic understanding of the underlying principles. By breaking down the process into manageable steps and using the least common multiple to find a common denominator, you can easily add fractions with unlike denominators.

Related Terms:

• Fraction addition and subtraction worksheet
• Adding unlike fractions Worksheet PDF