Multiplying Mixed Numbers: 1 1/3 times 1 1/3
This article will guide you through multiplying mixed numbers, focusing on the specific example of 1 1/3 times 1 1/3.
Understanding Mixed Numbers
Before diving into multiplication, let's recap what mixed numbers represent:
- Mixed numbers combine a whole number and a fraction. For example, 1 1/3 represents one whole unit plus one-third of another unit.
Converting to Improper Fractions
The easiest way to multiply mixed numbers is to convert them into improper fractions:
- Multiply the whole number by the denominator of the fraction: 1 x 3 = 3
- Add the numerator: 3 + 1 = 4
- Keep the same denominator: 4/3
So, 1 1/3 is equivalent to 4/3.
Multiplying Fractions
Now that both numbers are improper fractions, we can proceed with multiplication:
- Multiply the numerators: 4 x 4 = 16
- Multiply the denominators: 3 x 3 = 9
This gives us the answer: 16/9.
Converting Back to a Mixed Number (Optional)
The answer 16/9 is an improper fraction. To convert it back to a mixed number:
- Divide the numerator (16) by the denominator (9): 16 ÷ 9 = 1 with a remainder of 7
- The whole number of the mixed number is the quotient: 1
- The numerator of the fraction is the remainder: 7
- The denominator stays the same: 9
Therefore, 16/9 is equivalent to 1 7/9.
Final Answer
1 1/3 times 1 1/3 is equal to 16/9, or 1 7/9.