Multiplying Mixed Numbers: 1 2/3 x 1 2/3 x 1 2/3
This article will walk you through how to multiply the mixed number 1 2/3 by itself three times, resulting in a fraction.
Understanding Mixed Numbers
A mixed number combines a whole number and a fraction. In the case of 1 2/3, we have one whole unit and two-thirds of another unit.
Converting to Improper Fractions
To multiply mixed numbers, the first step is to convert them into improper fractions. An improper fraction has a numerator that is greater than or equal to the denominator.
To convert 1 2/3 to an improper fraction:
- Multiply the whole number by the denominator: 1 x 3 = 3
- Add the numerator: 3 + 2 = 5
- Keep the same denominator: 5/3
Now we have 5/3 representing the mixed number 1 2/3.
Multiplication
We are multiplying 1 2/3 by itself three times, which is equivalent to:
(5/3) x (5/3) x (5/3)
To multiply fractions, we multiply the numerators and the denominators:
(5 x 5 x 5) / (3 x 3 x 3) = 125/27
Final Result
The product of 1 2/3 x 1 2/3 x 1 2/3 is 125/27. This is an improper fraction, but it can be represented as a mixed number if desired.
To convert 125/27 to a mixed number, divide 125 by 27:
- 125 ÷ 27 = 4 with a remainder of 17
Therefore, 125/27 is equivalent to 4 17/27.