Multiplying Mixed Numbers: 1 1/3 x 2 1/2
Multiplying mixed numbers might seem daunting at first, but with the right steps, it becomes a breeze! Let's break down how to solve 1 1/3 x 2 1/2.
Step 1: Convert Mixed Numbers to Improper Fractions
- 1 1/3: Multiply the whole number (1) by the denominator (3), then add the numerator (1). Keep the same denominator. This gives us (1 * 3 + 1)/3 = 4/3.
- 2 1/2: Multiply the whole number (2) by the denominator (2), then add the numerator (1). Keep the same denominator. This gives us (2 * 2 + 1)/2 = 5/2.
Step 2: Multiply the Fractions
Now we have (4/3) x (5/2). To multiply fractions, we multiply the numerators and the denominators:
- (4 x 5) / (3 x 2) = 20/6
Step 3: Simplify the Result
The fraction 20/6 can be simplified. Find the greatest common factor (GCD) of 20 and 6, which is 2. Divide both the numerator and denominator by 2:
- 20/2 = 10
- 6/2 = 3
Therefore, 20/6 simplifies to 10/3.
Step 4: Convert Back to a Mixed Number (Optional)
To express the answer as a mixed number, divide the numerator (10) by the denominator (3):
- 10 ÷ 3 = 3 with a remainder of 1
This means the mixed number equivalent is 3 1/3.
Conclusion
Therefore, 1 1/3 x 2 1/2 is equal to 10/3 or 3 1/3. Remember, the key is to convert mixed numbers into improper fractions, multiply, simplify, and then convert back to a mixed number if desired. Practice makes perfect, so don't be afraid to work through more examples!