Converting Mixed Numbers to Improper Fractions
When working with mixed numbers, it's essential to understand how to convert them to improper fractions. In this article, we'll explore how to subtract two mixed numbers, specifically 5 1/6 - 7 1/3, and convert the result to an improper fraction.
Step 1: Convert Mixed Numbers to Improper Fractions
To begin, let's convert each mixed number to an improper fraction:
5 1/6
- The whole number part is 5, and the fraction part is 1/6.
- To convert, multiply the whole number by the denominator (6) and add the numerator (1):
- 5 × 6 = 30
- 30 + 1 = 31
- So, 5 1/6 = 31/6
7 1/3
- The whole number part is 7, and the fraction part is 1/3.
- To convert, multiply the whole number by the denominator (3) and add the numerator (1):
- 7 × 3 = 21
- 21 + 1 = 22
- So, 7 1/3 = 22/3
Step 2: Subtract the Improper Fractions
Now that we have the improper fractions, we can subtract them:
31/6 - 22/3
To subtract these fractions, we need to find the least common multiple (LCM) of the denominators, which is 6 and 3. The LCM is 6.
- Convert 22/3 to have a denominator of 6 by multiplying both the numerator and denominator by 2:
- 22 × 2 = 44
- 3 × 2 = 6
- So, 22/3 = 44/6
- Now, subtract the fractions:
- 31/6 - 44/6 = -13/6
The Result
The result of subtracting 5 1/6 and 7 1/3 is -13/6. This is an improper fraction, where the numerator (-13) is greater than the denominator (6).
Remember, when working with mixed numbers, it's essential to convert them to improper fractions to perform arithmetic operations like subtraction. By following these steps, you can easily subtract mixed numbers and convert the result to an improper fraction.
