Multiplying Mixed Numbers: 1 1/4 x 2 3/4
This article will guide you through the process of multiplying mixed numbers, specifically focusing on the problem 1 1/4 x 2 3/4.
Understanding Mixed Numbers
Mixed numbers are a combination of a whole number and a fraction. For example, 1 1/4 represents one whole and one-quarter. To multiply mixed numbers, we need to convert them into improper fractions.
Converting to Improper Fractions
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1 1/4: Multiply the whole number (1) by the denominator (4) and add the numerator (1). This gives us 5. Keep the same denominator (4). So, 1 1/4 is equivalent to 5/4.
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2 3/4: Multiply the whole number (2) by the denominator (4) and add the numerator (3). This gives us 11. Keep the same denominator (4). So, 2 3/4 is equivalent to 11/4.
Multiplying the Improper Fractions
Now we have: (5/4) x (11/4)
To multiply fractions, we simply multiply the numerators and the denominators:
- (5 x 11) / (4 x 4) = 55/16
Converting Back to a Mixed Number
The result, 55/16, is an improper fraction. We need to convert it back to a mixed number.
- Divide the numerator (55) by the denominator (16): 55 ÷ 16 = 3 with a remainder of 7.
- The quotient (3) becomes the whole number part of the mixed number.
- The remainder (7) becomes the numerator of the fraction.
- The denominator (16) stays the same.
Therefore, 55/16 is equivalent to 3 7/16.
Conclusion
Therefore, 1 1/4 x 2 3/4 = 3 7/16.