Multiplying Mixed Numbers: 1 1/2 x 2 1/4
This article will guide you through the steps of multiplying the mixed numbers 1 1/2 and 2 1/4, resulting in a single fraction.
Converting Mixed Numbers to Fractions
Before multiplying mixed numbers, we need to convert them into improper fractions.
-
1 1/2: Multiply the whole number (1) by the denominator (2) and add the numerator (1). This gives us 3. Keep the same denominator (2). So, 1 1/2 becomes 3/2.
-
2 1/4: Multiply the whole number (2) by the denominator (4) and add the numerator (1). This gives us 9. Keep the same denominator (4). So, 2 1/4 becomes 9/4.
Multiplying Fractions
Now that we have our improper fractions, we can multiply them:
(3/2) * (9/4) = (3 * 9) / (2 * 4) = 27/8
Simplifying the Result
The fraction 27/8 is an improper fraction because the numerator is larger than the denominator. We can simplify it by converting it back to a mixed number:
- Divide the numerator (27) by the denominator (8): 27 / 8 = 3 with a remainder of 3.
- The quotient (3) becomes the whole number part of the mixed number.
- The remainder (3) becomes the numerator of the fraction.
- The denominator (8) stays the same.
Therefore, 27/8 is equivalent to 3 3/8.
Conclusion
The product of 1 1/2 and 2 1/4, expressed as a single fraction, is 3 3/8.