To multiply an integer by a mixed fraction, you need to convert both numbers into fractional form and then multiply the numerators and the denominators. The reference video "How to Multiply a Mixed Number by a Whole Number | Math with Mr. J" explains the process.
Here's a breakdown of the steps:
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Convert the mixed fraction to an improper fraction: Multiply the whole number part of the mixed fraction by the denominator and add the numerator. Keep the same denominator.
- For example, to convert 2 1/4 to an improper fraction: (2 * 4) + 1 = 9. So, 2 1/4 = 9/4.
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Convert the integer to a fraction: Place the integer over 1. This doesn't change the value of the integer, but puts it in fractional form.
- For example, 5 becomes 5/1. According to the video reference at [1:24] - [4:58], this puts the whole number into fractional form, with a top and a bottom, making multiplication straight across possible.
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Multiply the fractions: Multiply the numerators (the top numbers) together to get the new numerator, and multiply the denominators (the bottom numbers) together to get the new denominator.
- For example, if you're multiplying 5 by 2 1/4, you would multiply 5/1 by 9/4. (5 9) / (1 4) = 45/4
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Simplify the result (if possible): Convert the resulting improper fraction back to a mixed number or simplify the fraction if possible.
- In our example, 45/4 can be converted back to a mixed number: 11 1/4
Example:
Let's multiply 3 by 1 1/2.
- Convert 1 1/2 to an improper fraction: (1 * 2) + 1 = 3. So, 1 1/2 = 3/2.
- Convert 3 to a fraction: 3 = 3/1.
- Multiply the fractions: (3/1) (3/2) = (3 3) / (1 * 2) = 9/2
- Simplify: 9/2 = 4 1/2
