Multiplying a Mixed Number by a Whole Number: 1 2/3 x 2
This article will guide you through the process of multiplying a mixed number, 1 2/3, by a whole number, 2.
Converting the Mixed Number to an Improper Fraction
First, we need to convert the mixed number, 1 2/3, into an improper fraction. To do this:
- 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 the equivalent improper fraction for 1 2/3, which is 5/3.
Multiplying the Fractions
We can now multiply the improper fraction, 5/3, by the whole number, 2. Remember that a whole number can be written as a fraction by placing it over 1:
5/3 x 2/1
To multiply fractions, we multiply the numerators and the denominators:
(5 x 2) / (3 x 1) = 10/3
Simplifying the Result
The fraction 10/3 is an improper fraction. We can convert it back to a mixed number:
- Divide the numerator by the denominator: 10 ÷ 3 = 3 with a remainder of 1
- The quotient becomes the whole number: 3
- The remainder becomes the numerator: 1
- Keep the same denominator: 3
Therefore, 1 2/3 x 2 = 3 1/3.