Multiplying Mixed Numbers: 1 1/2 times 1 1/2
This article explores how to multiply mixed numbers, focusing on the specific example of 1 1/2 times 1 1/2.
Understanding Mixed Numbers
A mixed number combines a whole number and a fraction. For example, 1 1/2 represents one whole plus one half.
Converting to Improper Fractions
Before multiplying, it's helpful to convert mixed numbers into improper fractions. Here's how:
- Multiply the whole number by the denominator of the fraction: 1 x 2 = 2
- Add the numerator: 2 + 1 = 3
- Keep the same denominator: 3/2
So, 1 1/2 is equivalent to 3/2.
Multiplying Fractions
Now that we have improper fractions, multiplication is straightforward:
- Multiply the numerators: 3 x 3 = 9
- Multiply the denominators: 2 x 2 = 4
This gives us 9/4.
Converting Back to Mixed Number
The result, 9/4, is an improper fraction. To express it as a mixed number:
- Divide the numerator (9) by the denominator (4): 9 ÷ 4 = 2 with a remainder of 1.
- The quotient (2) becomes the whole number part of the mixed number.
- The remainder (1) becomes the numerator of the fraction.
- The denominator remains the same (4).
Therefore, 9/4 is equivalent to 2 1/4.
Conclusion
Therefore, 1 1/2 times 1 1/2 is equal to 2 1/4. By converting mixed numbers to improper fractions and then following the rules of fraction multiplication, we can solve this and similar problems.