Multiplying Fractions: 1 1/3 x 1/2
This article will guide you through multiplying the mixed number 1 1/3 by the fraction 1/2.
Understanding Mixed Numbers
A mixed number, like 1 1/3, represents a whole number plus a fraction. To multiply mixed numbers, it's helpful to convert them into improper fractions first.
Converting to Improper Fractions
- 1 1/3: 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): This gives us 4/3.
Now we have the equation: 4/3 x 1/2
Multiplying Fractions
To multiply fractions, we multiply the numerators and the denominators:
- Numerators: 4 x 1 = 4
- Denominators: 3 x 2 = 6
This gives us the result: 4/6
Simplifying the Fraction
The fraction 4/6 can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 2:
- 4 ÷ 2 = 2
- 6 ÷ 2 = 3
Therefore, the simplified answer is 2/3.
Conclusion
The product of 1 1/3 and 1/2 is 2/3. By converting the mixed number to an improper fraction and applying the rules of fraction multiplication, we arrived at the simplified answer.