Understanding Mixed Numbers and Unlike Denominators
When dealing with fractions, we often encounter mixed numbers, which are a combination of a whole number and a fraction. Subtracting mixed numbers with unlike denominators can seem like a daunting task, but with the right approach, it can be made easy. In this article, we will break down the steps to subtract mixed numbers with unlike denominators and provide examples to illustrate the process.
The Step-by-Step Process
To subtract mixed numbers with unlike denominators, follow these steps:
- Convert the mixed numbers to improper fractions: To do this, multiply the whole number part by the denominator and add the numerator. Then, write the result as an improper fraction.
- Find the least common multiple (LCM) of the denominators: The LCM is the smallest number that both denominators can divide into evenly. This will be the new denominator for the fractions.
- Convert both fractions to have the LCM as the denominator: To do this, multiply the numerator and denominator of each fraction by the necessary multiple to get the LCM.
- Subtract the fractions: Now that both fractions have the same denominator, subtract the numerators to get the final result.
- Simplify the result: If possible, simplify the fraction to its simplest form.
🤔 Note: Make sure to check if the result is in its simplest form. If not, simplify it before moving on to the next step.
Example 1: Subtracting Mixed Numbers with Unlike Denominators
Suppose we want to subtract 2 1⁄4 from 3 3⁄6.
Step 1: Convert the mixed numbers to improper fractions
- 2 1⁄4 = (2 x 4) + 1 = 9⁄4
- 3 3⁄6 = (3 x 6) + 3 = 21⁄6
Step 2: Find the LCM of the denominators
- The LCM of 4 and 6 is 12.
Step 3: Convert both fractions to have the LCM as the denominator
- 9⁄4 = (9 x 3)/(4 x 3) = 27⁄12
- 21⁄6 = (21 x 2)/(6 x 2) = 42⁄12
Step 4: Subtract the fractions
- 42⁄12 - 27⁄12 = 15⁄12
Step 5: Simplify the result
- 15⁄12 = 1 3⁄12 (which is the final result)
Example 2: Subtracting Mixed Numbers with Unlike Denominators
Suppose we want to subtract 1 2⁄3 from 2 5⁄8.
Step 1: Convert the mixed numbers to improper fractions
- 1 2⁄3 = (1 x 3) + 2 = 5⁄3
- 2 5⁄8 = (2 x 8) + 5 = 21⁄8
Step 2: Find the LCM of the denominators
- The LCM of 3 and 8 is 24.
Step 3: Convert both fractions to have the LCM as the denominator
- 5⁄3 = (5 x 8)/(3 x 8) = 40⁄24
- 21⁄8 = (21 x 3)/(8 x 3) = 63⁄24
Step 4: Subtract the fractions
- 63⁄24 - 40⁄24 = 23⁄24
Step 5: Simplify the result
- 23⁄24 (which is the final result)
Table of Common Denominators for Fractions
| Denominators | LCM |
|---|---|
| 2, 3 | 6 |
| 4, 6 | 12 |
| 3, 8 | 24 |
| 5, 10 | 10 |
By following these steps and using the table of common denominators, subtracting mixed numbers with unlike denominators becomes a straightforward process.
In conclusion, subtracting mixed numbers with unlike denominators requires a few simple steps: converting to improper fractions, finding the LCM, converting to equivalent fractions, subtracting, and simplifying. By mastering these steps and using the table of common denominators, you can easily tackle any subtraction problem involving mixed numbers with unlike denominators.
What is the LCM of two numbers?
+The least common multiple (LCM) of two numbers is the smallest number that both numbers can divide into evenly.
How do I convert a mixed number to an improper fraction?
+To convert a mixed number to an improper fraction, multiply the whole number part by the denominator and add the numerator. Then, write the result as an improper fraction.
What is the purpose of finding the LCM in subtracting mixed numbers with unlike denominators?
+The purpose of finding the LCM is to convert both fractions to have the same denominator, making it possible to subtract the fractions.
