Adding Fractions: 1 1/3 + 1/2
Adding fractions can be a bit tricky, especially when dealing with mixed numbers. Let's break down how to solve 1 1/3 + 1/2.
Step 1: Convert Mixed Number to Improper Fraction
First, we need to convert the mixed number 1 1/3 into an improper fraction.
- Multiply the whole number (1) by the denominator of the fraction (3): 1 x 3 = 3
- Add the numerator (1): 3 + 1 = 4
- Keep the same denominator (3): 4/3
Now we have the equation: 4/3 + 1/2
Step 2: Find a Common Denominator
Before we can add fractions, they need to have the same denominator. The least common multiple of 3 and 2 is 6.
- To get 6 as the denominator for 4/3, multiply both numerator and denominator by 2: (4 x 2) / (3 x 2) = 8/6
- To get 6 as the denominator for 1/2, multiply both numerator and denominator by 3: (1 x 3) / (2 x 3) = 3/6
Now our equation looks like this: 8/6 + 3/6
Step 3: Add the Numerators
With the same denominator, we can now simply add the numerators:
8/6 + 3/6 = 11/6
Step 4: Simplify to a Mixed Number (Optional)
The answer 11/6 is an improper fraction. We can convert it back to a mixed number.
- Divide the numerator (11) by the denominator (6): 11 ÷ 6 = 1 with a remainder of 5
- The quotient (1) becomes the whole number part of the mixed number
- The remainder (5) becomes the numerator of the fraction, with the same denominator (6): 1 5/6
Therefore, 1 1/3 + 1/2 = 11/6 or 1 5/6.