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How to Multiply a Mixed Number by a Mixed Number?

Published in Mixed Number Multiplication 2 mins read

To multiply mixed numbers, you must first convert them into improper fractions, then multiply the fractions, and finally simplify the result if needed.

Here's a detailed breakdown of the process:

Steps to Multiply Mixed Numbers

  1. Convert Mixed Numbers to Improper Fractions:

    • A mixed number has a whole number part and a fractional part (e.g., 2 1/2).
    • To convert it to an improper fraction:
      • Multiply the whole number by the denominator of the fraction.
      • Add the numerator to the result.
      • Keep the same denominator.
      • Example: 2 1/2 = ((2 * 2) + 1) / 2 = 5/2

  2. Multiply the Improper Fractions:

    • Multiply the numerators (the top numbers) together.
    • Multiply the denominators (the bottom numbers) together.
    • Example: If you have 5/2 7/3, multiply 5 7 = 35 (new numerator) and 2 * 3 = 6 (new denominator). The result is 35/6.

  3. Simplify the Result (if possible):

    • Convert back to a mixed number: If the numerator is larger than the denominator (improper fraction), convert it back to a mixed number.
      • Divide the numerator by the denominator. The quotient is the whole number part.
      • The remainder is the numerator of the fractional part.
      • Keep the same denominator.
      • Example: 35/6. 35 divided by 6 is 5 with a remainder of 5. Therefore, 35/6 = 5 5/6.
    • Simplify by Canceling Common Factors: According to the reference, it's often best to simplify before multiplying.
      • Look for common factors between any numerator and any denominator.
      • Divide both the numerator and denominator by their greatest common factor to simplify the fraction.
      • Example: If you have (7 * 3) / 3, you can cancel the 3s to get 7/1 or 7.

Example

Multiply 2 1/2 by 1 1/3.

  1. Convert to improper fractions:

    • 2 1/2 = 5/2
    • 1 1/3 = 4/3

  2. Multiply the improper fractions:

    • (5/2) (4/3) = (5 4) / (2 * 3) = 20/6

  3. Simplify the result:

    • 20/6 can be simplified. Both 20 and 6 are divisible by 2.
    • 20/6 = 10/3
    • Convert 10/3 to a mixed number: 10 divided by 3 is 3 with a remainder of 1. Therefore, 10/3 = 3 1/3.

Therefore, 2 1/2 multiplied by 1 1/3 equals 3 1/3.

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