Calculating 1 3/4 times 2 1/4
This article will guide you through calculating the product of 1 3/4 and 2 1/4.
Understanding Mixed Numbers
Before we start, let's understand mixed numbers. A mixed number combines a whole number and a fraction, like 1 3/4. To work with mixed numbers in multiplication, we need to convert them into improper fractions.
Converting Mixed Numbers to Improper Fractions
- 1 3/4: Multiply the whole number (1) by the denominator of the fraction (4), then add the numerator (3). This gives you 7. Keep the same denominator (4). The improper fraction for 1 3/4 is 7/4.
- 2 1/4: Multiply the whole number (2) by the denominator (4) and add the numerator (1). This gives you 9. Keep the same denominator (4). The improper fraction for 2 1/4 is 9/4.
Multiplying Improper Fractions
Now that we have improper fractions, we can multiply them:
(7/4) * (9/4) = (7 * 9) / (4 * 4) = 63/16
Converting Back to Mixed Number
The result is an improper fraction, but we can convert it back to a mixed number:
- Divide the numerator (63) by the denominator (16): 63 / 16 = 3 with a remainder of 15.
- The whole number is 3, the remainder (15) becomes the numerator, and the denominator stays the same (16).
Therefore, 1 3/4 times 2 1/4 is equal to 3 15/16.