How to Multiply a Whole Number by a Mixed Number?

To multiply a whole number by a mixed number, you'll need to first convert both numbers into fractions, then multiply and simplify.

Steps for Multiplying a Whole Number by a Mixed Number

Here’s a step-by-step guide on how to multiply a whole number by a mixed number, based on the method described in the reference video (How to Multiply a Mixed Number by a Whole Number | Math with Mr. J):

1. Convert the mixed number to an improper fraction: According to the reference video, you start at the bottom of the mixed number, multiply the denominator by the whole number part, then add the numerator. This result becomes the new numerator, and the denominator stays the same.

   • Example: If your mixed number is 2 1/4, multiply 4 (denominator) by 2 (whole number) to get 8 and add 1 (numerator) to get 9. Therefore, the improper fraction is 9/4.

2. Convert the whole number to a fraction: Any whole number can be written as a fraction by placing it over a denominator of 1.

   • Example: The whole number 3 becomes 3/1

3. Multiply the numerators: Multiply the top numbers (numerators) of the two fractions together.

   • Example: For 3/1 and 9/4 the numerators are 3 and 9, multiplying to get 27

4. Multiply the denominators: Multiply the bottom numbers (denominators) of the two fractions together.

   • Example: For 3/1 and 9/4, the denominators are 1 and 4, multiplying to get 4

5. Create the new fraction: The product of the numerators becomes the new numerator and the product of the denominators becomes the new denominator.

   • Example: Multiplying 3/1 and 9/4 results in 27/4

6. Simplify the fraction: If possible, simplify the fraction. If the numerator is greater than the denominator, it is often helpful to convert the improper fraction back to a mixed number.

   • Example: 27/4 can be converted back into the mixed number 6 3/4

Example

Let's calculate 3 * 2 1/4 using the steps above:

• Step 1: Convert 2 1/4 to an improper fraction: (4 * 2) + 1 = 9, therefore the improper fraction is 9/4.
• Step 2: Convert the whole number to a fraction: 3 becomes 3/1
• Step 3: Multiply numerators: 3 * 9 = 27
• Step 4: Multiply denominators: 1 * 4 = 4
• Step 5: Create the new fraction: 27/4
• Step 6: Simplify: 27/4 is equal to 6 3/4

Summary

By following these steps, you can successfully multiply a whole number by a mixed number.