Multiplying Mixed Numbers: 1 1/3 x 2 1/3
This article will guide you through the steps of multiplying two mixed numbers: 1 1/3 and 2 1/3.
Understanding Mixed Numbers
Mixed numbers are a combination of a whole number and a fraction. For example, 1 1/3 represents one whole and one-third. To multiply mixed numbers, we need to convert them into improper fractions.
Converting Mixed Numbers to Improper Fractions
To convert 1 1/3 to an improper fraction, follow these steps:
- Multiply the whole number by the denominator: 1 x 3 = 3
- Add the numerator: 3 + 1 = 4
- Keep the same denominator: 4/3
Similarly, 2 1/3 converts to 7/3.
Multiplying Improper Fractions
Now that we have improper fractions, we can multiply them:
(4/3) x (7/3) = (4 x 7) / (3 x 3) = 28/9
Converting Back to a Mixed Number
The answer, 28/9, is an improper fraction. To convert it back to a mixed number:
- Divide the numerator by the denominator: 28 ÷ 9 = 3 with a remainder of 1.
- The quotient (3) becomes the whole number part of the mixed number.
- The remainder (1) becomes the numerator of the fraction.
- Keep the same denominator: 3 1/9
Conclusion
Therefore, 1 1/3 x 2 1/3 = 3 1/9.