Adding Fractions: 1 1/2 + 1/3
Adding fractions can seem tricky, especially when dealing with mixed numbers like 1 1/2. But with the right steps, it becomes a breeze! Let's break down how to add 1 1/2 and 1/3:
1. Convert Mixed Number to a Fraction
First, we need to convert the mixed number 1 1/2 into a fraction.
- Multiply the whole number (1) by the denominator (2): 1 * 2 = 2
- Add the numerator (1): 2 + 1 = 3
- Keep the same denominator (2): 3/2
Now we have our problem as 3/2 + 1/3.
2. Find a Common Denominator
To add fractions, they need to have the same denominator. The smallest common denominator for 2 and 3 is 6.
- Multiply 3/2 by 3/3: (3 * 3) / (2 * 3) = 9/6
- Multiply 1/3 by 2/2: (1 * 2) / (3 * 2) = 2/6
Now our problem is 9/6 + 2/6.
3. Add the Numerators
Since the denominators are the same, we can simply add the numerators: 9 + 2 = 11
4. Keep the Denominator
The denominator stays the same: 11/6
5. Simplify (if possible)
The fraction 11/6 is an improper fraction (the numerator is larger than the denominator). We can simplify it by converting it back to a mixed number:
- Divide the numerator (11) by the denominator (6): 11 / 6 = 1 with a remainder of 5
- The whole number is 1, the numerator is the remainder (5), and the denominator stays the same (6): 1 5/6
Conclusion
Therefore, 1 1/2 + 1/3 is equal to 1 5/6.