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How to Multiply a Whole Number by a Mixed Number?

Published in Math Multiplication 2 mins read

There are two main methods to multiply a whole number by a mixed number: converting the mixed number to an improper fraction or using the distributive property.

Method 1: Converting to an Improper Fraction

This is often the easiest and most straightforward method.

  1. Convert the mixed number to an improper fraction. To do this, multiply the whole number part of the mixed number by the denominator of the fraction part, then add the numerator. Keep the same denominator.

    • Example: Convert 3 1/4 to an improper fraction.
      • 3 * 4 = 12
      • 12 + 1 = 13
      • So, 3 1/4 = 13/4

  2. Multiply the whole number by the improper fraction. Treat the whole number as a fraction with a denominator of 1. Multiply the numerators together and the denominators together.

    • Example: Multiply 5 by 13/4.
      • 5 can be written as 5/1
      • (5/1) (13/4) = (5 13) / (1 * 4) = 65/4

  3. Simplify the improper fraction (convert 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, and you keep the same denominator.

    • Example: Convert 65/4 to a mixed number.
      • 65 รท 4 = 16 with a remainder of 1.
      • So, 65/4 = 16 1/4

Example:

Multiply 5 * 3 1/4

  1. Convert 3 1/4 to 13/4 (as shown above)
  2. Multiply 5/1 * 13/4 = 65/4
  3. Convert 65/4 to 16 1/4

Therefore, 5 * 3 1/4 = 16 1/4

Method 2: Using the Distributive Property

This method involves breaking the mixed number into its whole number and fractional parts, and then distributing the multiplication.

  1. Separate the mixed number into its whole number and fractional parts.

    • Example: Separate 3 1/4 into 3 + 1/4

  2. Multiply the whole number by both the whole number part and the fractional part of the mixed number.

    • Example: Multiply 5 by (3 + 1/4).
      • 5 * 3 = 15
      • 5 * (1/4) = 5/4

  3. Add the two results together.

    • Example: Add 15 + 5/4.
      • You may need to convert 5/4 to a mixed number first: 5/4 = 1 1/4
      • 15 + 1 1/4 = 16 1/4

Example:

Multiply 5 * 3 1/4

  1. Separate 3 1/4 into 3 + 1/4
  2. Multiply: 5 3 = 15 and 5 1/4 = 5/4
  3. Add: 15 + 5/4 = 15 + 1 1/4 = 16 1/4

Therefore, 5 * 3 1/4 = 16 1/4

Both methods will result in the same answer. Choose the method that you find easier and more efficient.

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