Multiplying Mixed Numbers: 1 1/4 times 2 2/3
This article will guide you through the process of multiplying mixed numbers, using the example of 1 1/4 times 2 2/3.
Step 1: Convert Mixed Numbers to Improper Fractions
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1 1/4: Multiply the whole number (1) by the denominator (4), then add the numerator (1): (1 * 4) + 1 = 5. Keep the same denominator (4). This gives us 5/4.
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2 2/3: Multiply the whole number (2) by the denominator (3), then add the numerator (2): (2 * 3) + 2 = 8. Keep the same denominator (3). This gives us 8/3.
Step 2: Multiply the Fractions
Now we have: 5/4 * 8/3
To multiply fractions, we simply multiply the numerators and the denominators:
(5 * 8) / (4 * 3) = 40/12
Step 3: Simplify the Result
The fraction 40/12 can be simplified. Find the greatest common factor (GCF) of 40 and 12, which is 4. Divide both numerator and denominator by 4:
40/12 = (40/4) / (12/4) = 10/3
Step 4: Convert Back to a Mixed Number (Optional)
The answer 10/3 is an improper fraction (numerator is larger than the denominator). We can convert it back to a mixed number:
- Divide the numerator (10) by the denominator (3): 10 ÷ 3 = 3 with a remainder of 1.
- The quotient (3) becomes the whole number of the mixed number.
- The remainder (1) becomes the numerator of the fraction.
- The denominator stays the same (3).
Therefore, 10/3 as a mixed number is 3 1/3.
Conclusion
1 1/4 times 2 2/3 equals 10/3 or 3 1/3. By following these steps, you can confidently multiply any mixed numbers.