Multiplying Mixed Numbers: 1 2/3 x 4
This article will guide you through multiplying the mixed number 1 2/3 by the whole number 4.
Understanding Mixed Numbers
A mixed number is a combination of a whole number and a fraction. For example, 1 2/3 represents one whole and two-thirds of another.
Converting to Improper Fractions
To multiply mixed numbers, it's easier to first convert them to improper fractions. An improper fraction has a numerator larger than or equal to its denominator.
Here's how 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 1 2/3 as 5/3.
Multiplying Fractions
Multiplying fractions is simple:
- Multiply the numerators: 5 x 4 = 20
- Multiply the denominators: 3 x 1 = 3
- Simplify the result: 20/3
Therefore, 1 2/3 x 4 = 20/3.
Converting Back to a Mixed Number (Optional)
The answer 20/3 is an improper fraction. To convert it back to a mixed number:
- Divide the numerator by the denominator: 20 ÷ 3 = 6 with a remainder of 2
- The quotient (6) becomes the whole number part of the mixed number.
- The remainder (2) becomes the numerator of the fraction.
- Keep the same denominator (3): 6 2/3
So, 1 2/3 x 4 can also be expressed as 6 2/3.
Conclusion
By converting mixed numbers to improper fractions, we can easily multiply them. Remember to simplify the result and optionally convert it back to a mixed number if desired.