How to Multiply a Whole Number and a Mixed Number
Multiplying a whole number and a mixed number can seem like a daunting task at first, but with the right approach, it can be broken down into simple steps. Whether you’re a student or a teacher, understanding how to multiply these two types of numbers is essential for success in mathematics. In this article, we will guide you through the process of multiplying a whole number and a mixed number, ensuring that you can perform this operation with confidence.
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. Mixed numbers are often used to represent quantities that are not whole numbers, such as 3 and a half or 4 and three-quarters.
Converting Mixed Numbers to Improper Fractions
To multiply a whole number and a mixed number, the first step is 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 result to the numerator of the fraction.
3. Write the sum as the numerator of the improper fraction, keeping the same denominator.
For example, let’s convert the mixed number 3 1/2 to an improper fraction:
1. Multiply the whole number (3) by the denominator (2): 3 x 2 = 6.
2. Add the result to the numerator (1): 6 + 1 = 7.
3. Write the sum (7) as the numerator of the improper fraction, keeping the same denominator (2): 7/2.
Now we have the mixed number 3 1/2 as the improper fraction 7/2.
Multiplying the Whole Number and the Improper Fraction
Once you have converted the mixed number to 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. The result will be the numerator of the product, and the denominator will remain the same.
For our example, we have the whole number 3 and the improper fraction 7/2. Let’s multiply them:
1. Multiply the numerator (7) by the whole number (3): 7 x 3 = 21.
2. The denominator remains the same (2).
The product of 3 and 7/2 is 21/2, which can also be written as 10 1/2 as a mixed number.
Conclusion
Multiplying a whole number and a mixed number may seem complex at first, but by following these simple steps, you can easily perform this operation. First, convert the mixed number to an improper fraction, then multiply the whole number by the numerator of the improper fraction, and finally, write the result as a mixed number if necessary. With practice, you’ll be able to multiply whole numbers and mixed numbers with ease.
