Multiplying Fractions: 1 1/3 x 2/3
This article will guide you through the steps of multiplying the mixed number 1 1/3 by the fraction 2/3, and simplifying the result to its simplest form.
Converting Mixed Numbers
First, we need to convert the mixed number 1 1/3 into an improper fraction.
To do this, we multiply the whole number (1) by the denominator of the fraction (3), and then add the numerator (1). This gives us 1 * 3 + 1 = 4. We keep the same denominator (3), resulting in the improper fraction 4/3.
Multiplication
Now we can multiply the two fractions:
4/3 x 2/3
To multiply fractions, we simply multiply the numerators and the denominators:
(4 x 2) / (3 x 3)
This simplifies to 8/9.
Simplest Form
The fraction 8/9 is already in its simplest form. This is because the greatest common factor (GCD) of 8 and 9 is 1. A fraction is in its simplest form when its numerator and denominator have no common factors other than 1.
Conclusion
Therefore, 1 1/3 x 2/3 is equal to 8/9.