Multiplying Mixed Numbers: 1 1/2 x 3 1/2
This article will guide you through the process of multiplying mixed numbers, specifically focusing on 1 1/2 x 3 1/2.
Converting Mixed Numbers to Fractions
Before multiplying, we need to convert the mixed numbers into improper fractions. Here's how:
- 1 1/2: Multiply the whole number (1) by the denominator (2) and add the numerator (1). Keep the same denominator (2). This gives us 3/2.
- 3 1/2: Multiply the whole number (3) by the denominator (2) and add the numerator (1). Keep the same denominator (2). This gives us 7/2.
Multiplying Fractions
Now that we have improper fractions, we can multiply them:
(3/2) x (7/2)
To multiply fractions, simply multiply the numerators and the denominators:
(3 x 7) / (2 x 2)
This simplifies to 21/4.
Converting Back to a Mixed Number
The result, 21/4, is an improper fraction. Let's convert it back to a mixed number:
- Divide the numerator (21) by the denominator (4). This gives us 5 with a remainder of 1.
- The whole number part of the mixed number is 5.
- The remainder (1) becomes the numerator of the fractional part. The denominator stays the same (4).
Therefore, 21/4 is equivalent to 5 1/4.
Conclusion
We have successfully multiplied 1 1/2 by 3 1/2. The answer is 5 1/4. Remember to always convert mixed numbers to improper fractions before multiplying and then convert the result back to a mixed number if necessary.