Adding fractions is a fundamental arithmetic operation that often arises in everyday life, from dividing pizzas among friends to calculating recipe measurements in the kitchen. While adding fractions with the same denominators is relatively straightforward, adding fractions with different denominators requires a slightly different approach. In this article, we’ll explore examples of adding fractions with different denominators, providing step-by-step explanations to demystify this essential math skill.
Example 1: Adding Fractions with Common Multiples
Let’s consider the following example:
1/3 + 2/5
Step 1: Find a Common Denominator
To add fractions with different denominators, we need to find a common denominator. In this case, the least common multiple (LCM) of 3 and 5 is 15.
Step 2: Convert Fractions to Equivalent Fractions
Next, we’ll rewrite each fraction with the common denominator of 15:
1/3 = (1 * 5) / (3 * 5) = 5/15
2/5 = (2 * 3) / (5 * 3) = 6/15
Step 3: Add the Fractions
Now that both fractions have the same denominator, we can add them together:
5/15 + 6/15 = (5 + 6) / 15 = 11/15
So, 1/3 + 2/5 = 11/15.
Example 2: Adding Fractions with Prime Denominators
Now, let’s tackle an example with prime denominators:
1/2 + 1/3
Step 1: Find a Common Denominator
Since 2 and 3 are prime numbers, their least common multiple is simply their product: 2 * 3 = 6.
Step 2: Convert Fractions to Equivalent Fractions
Rewrite each fraction with the common denominator of 6:
1/2 = (1 * 3) / (2 * 3) = 3/6
1/3 = (1 * 2) / (3 * 2) = 2/6
Step 3: Add the Fractions
Add the fractions together:
3/6 + 2/6 = (3 + 2) / 6 = 5/6
Thus, 1/2 + 1/3 = 5/6.
Example 3: Adding Mixed Numbers with Different Denominators
Now, let’s consider an example involving mixed numbers:
1 1/4 + 2 1/3
Step 1: Convert Mixed Numbers to Improper Fractions
Convert the mixed numbers to improper fractions:
1 1/4 = (4 * 1 + 1) / 4 = 5/4
2 1/3 = (3 * 2 + 1) / 3 = 7/3
Step 2: Find a Common Denominator
The least common multiple of 4 and 3 is 12.
Step 3: Convert Fractions to Equivalent Fractions
Rewrite each fraction with the common denominator of 12:
5/4 = (5 * 3) / (4 * 3) = 15/12
7/3 = (7 * 4) / (3 * 4) = 28/12
Step 4: Add the Fractions
Add the fractions together:
15/12 + 28/12 = (15 + 28) / 12 = 43/12
Step 5: Convert Improper Fraction to Mixed Number (Optional)
If desired, convert the improper fraction back to a mixed number:
43/12 = 3 7/12
Thus, 1 1/4 + 2 1/3 = 3 7/12.
Adding fractions with different denominators may initially seem daunting, but with practice and a clear understanding of the steps involved, it becomes a manageable task. By finding a common denominator, converting fractions to equivalent forms, and adding the fractions together, we can accurately calculate the sum of fractions with different denominators. These examples serve as valuable illustrations of the process, empowering learners to master the skill of fraction addition and apply it confidently in various mathematical contexts.