Adding Mixed Numbers with Different Denominators
When dealing with mixed numbers, it's essential to understand how to add them together, especially when they have different denominators. In this article, we'll explore how to add 7 5/6, 4 1/3, and 1 3/5 as fractions.
Step 1: Convert Mixed Numbers to Improper Fractions
To add these mixed numbers, we need to convert them into improper fractions. An improper fraction is a fraction where the numerator is greater than or equal to the denominator.
7 5/6
- Numerator: 7 × 6 + 5 = 47
- Denominator: 6
- Improper fraction: 47/6
4 1/3
- Numerator: 4 × 3 + 1 = 13
- Denominator: 3
- Improper fraction: 13/3
1 3/5
- Numerator: 1 × 5 + 3 = 8
- Denominator: 5
- Improper fraction: 8/5
Step 2: Find the Least Common Multiple (LCM) of the Denominators
To add these improper fractions, we need to find the least common multiple (LCM) of their denominators, which are 6, 3, and 5.
- Multiples of 6: 6, 12, 18, 24, 30, ...
- Multiples of 3: 3, 6, 9, 12, 15, ...
- Multiples of 5: 5, 10, 15, 20, 25, ...
The LCM of 6, 3, and 5 is 30.
Step 3: Convert Each Fraction to Have a Denominator of 30
Now, we'll convert each improper fraction to have a denominator of 30:
47/6
- Multiply numerator and denominator by 5: (47 × 5)/(6 × 5) = 235/30
13/3
- Multiply numerator and denominator by 10: (13 × 10)/(3 × 10) = 130/30
8/5
- Multiply numerator and denominator by 6: (8 × 6)/(5 × 6) = 48/30
Step 4: Add the Fractions
Now that all fractions have the same denominator, we can add them:
235/30 + 130/30 + 48/30 = (235 + 130 + 48)/30 = 413/30
Step 5: Simplify the Result
To simplify the result, we can divide both the numerator and the denominator by their greatest common divisor (GCD):
GCD of 413 and 30 is 1, so the result remains:
413/30
Conclusion
The result of adding 7 5/6, 4 1/3, and 1 3/5 as fractions is 413/30.
