Multiplying Mixed Numbers: 1 1/2 x 1 1/2
This article will guide you through the process of multiplying mixed numbers, using the example of 1 1/2 x 1 1/2.
Understanding Mixed Numbers
A mixed number combines a whole number and a fraction. For example, 1 1/2 represents one whole and half of another.
Converting Mixed Numbers to Fractions
Before multiplying, we need to convert the mixed numbers into improper fractions:
- 1 1/2: Multiply the whole number (1) by the denominator of the fraction (2) and add the numerator (1): (1 * 2) + 1 = 3. Keep the denominator: 3/2.
- 1 1/2: Following the same process: (1 * 2) + 1 = 3. Keep the denominator: 3/2.
Multiplying Fractions
Now that we have improper fractions, we can multiply them:
- (3/2) x (3/2) = (3 x 3) / (2 x 2)
- = 9/4
Converting Back to a Mixed Number
The result, 9/4, is an improper fraction. To convert it back to 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, and the denominator stays the same (4).
Therefore, 9/4 is equivalent to 2 1/4.
Conclusion
We have successfully multiplied 1 1/2 by 1 1/2, finding that 1 1/2 x 1 1/2 = 2 1/4. By converting mixed numbers to improper fractions and following the rules of fraction multiplication, we can easily perform this calculation.