Multiplying Mixed Numbers: Finding 1 1/2 x 3 1/2
This article will guide you through the process of multiplying mixed numbers, using the example of 1 1/2 x 3 1/2.
Step 1: Convert Mixed Numbers to Improper Fractions
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1 1/2: Multiply the whole number (1) by the denominator (2) and add the numerator (1). This gives you 3. Keep the same denominator (2). So, 1 1/2 is equivalent to 3/2.
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3 1/2: Multiply the whole number (3) by the denominator (2) and add the numerator (1). This gives you 7. Keep the same denominator (2). So, 3 1/2 is equivalent to 7/2.
Step 2: Multiply the Fractions
Now we have: (3/2) x (7/2)
To multiply fractions, simply multiply the numerators and the denominators:
(3 x 7) / (2 x 2) = 21/4
Step 3: Convert the Improper Fraction to a Mixed Number (Optional)
The improper fraction 21/4 can be converted back to a mixed number:
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Divide the numerator (21) by the denominator (4): 21 / 4 = 5 with a remainder of 1.
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The quotient (5) becomes the whole number part of the mixed number.
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The remainder (1) becomes the numerator of the fraction.
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The denominator stays the same (4).
Therefore, 21/4 is equivalent to 5 1/4.
Conclusion
Therefore, 1 1/2 times 3 1/2 is equal to 21/4 or 5 1/4.