How to Multiply a Mixed Number by a Whole Number
Multiplying a mixed number by a whole number can seem like a daunting task at first, but with the right approach, it can be broken down into simple steps. In this article, we will guide you through the process of multiplying a mixed number by a whole number, ensuring that you understand each step along the way.
Understanding Mixed Numbers
Before we dive into the multiplication process, it’s important to have a clear understanding of what a mixed number is. A mixed number consists of a whole number and a fraction. For example, 3 1/2 is a mixed number, where 3 is the whole number and 1/2 is the fraction.
Converting the Mixed Number to an Improper Fraction
To multiply a mixed number by a whole number, you first need to convert the mixed number into an improper fraction. An improper fraction is a fraction where the numerator (the top number) is greater than or equal to the denominator (the bottom number). To convert a mixed number to an improper fraction, follow these steps:
1. Multiply the whole number by the denominator of the fraction.
2. Add the numerator of the fraction to the result from step 1.
3. Write the sum from step 2 as the numerator of the improper fraction, keeping the same denominator.
For our example, 3 1/2, let’s convert it to an improper fraction:
1. 3 (whole number) 2 (denominator) = 6
2. 6 + 1 (numerator) = 7
3. The improper fraction is 7/2.
Multiplying the Improper Fraction by the Whole Number
Now that you have the mixed number as an improper fraction, you can multiply it by the whole number. To do this, simply multiply the numerator of the improper fraction by the whole number. Here’s how it works for our example:
1. 7 (numerator of the improper fraction) 2 (whole number) = 14
The result, 14, is the numerator of the product. The denominator remains the same as the denominator of the original fraction. In our case, the denominator is 2, so the product is 14/2.
Converting the Product Back to a Mixed Number
Finally, you may want to convert the product back to a mixed number. To do this, divide the numerator by the denominator and write the quotient as the whole number. The remainder becomes the numerator of the fraction, with the same denominator. For our example:
1. 14 (numerator) ÷ 2 (denominator) = 7 (whole number)
2. The remainder is 0, so the fraction part is 0/2, which simplifies to 0.
The product, 14/2, is equivalent to the mixed number 7 0/2, which can be simplified to 7.
Conclusion
Multiplying a mixed number by a whole number may seem complex at first, but by following these simple steps, you can easily convert the mixed number to an improper fraction, multiply it by the whole number, and then convert the product back to a mixed number if desired. With practice, you’ll find this process becomes second nature, allowing you to tackle more advanced multiplication problems with confidence.
