Mastering Fraction Multiplication- A Step-by-Step Guide to Multiplying Fractions by Mixed Numbers

How do you multiply a fraction by a mixed number? Multiplying fractions by mixed numbers can seem daunting at first, but with a clear understanding of the process, it becomes a straightforward task. In this article, we will guide you through the steps to multiply a fraction by a mixed number, ensuring that you can confidently perform this operation in various mathematical contexts.

To begin, let’s define what a mixed number is. A mixed number consists of an integer part and a fractional part, separated by a plus sign. For example, 3 1/2 is a mixed number, where 3 is the integer part and 1/2 is the fractional part. When multiplying a fraction by a mixed number, you’ll need to follow these steps:

1. Convert the mixed number to an improper fraction.
2. Multiply the numerator of the fraction by the numerator of the improper fraction.
3. Multiply the denominator of the fraction by the denominator of the improper fraction.
4. Simplify the resulting fraction, if possible.

Let’s take an example to illustrate these steps. Suppose we want to multiply 2/3 by 3 1/2.

1. Convert the mixed number 3 1/2 to an improper fraction. To do this, multiply the integer part (3) by the denominator of the fractional part (2) and add the numerator of the fractional part (1). This gives us (3 2) + 1 = 7. Now, place this sum over the original denominator (2), resulting in the improper fraction 7/2.

2. Multiply the numerator of the fraction (2) by the numerator of the improper fraction (7), which gives us 2 7 = 14.

3. Multiply the denominator of the fraction (3) by the denominator of the improper fraction (2), which gives us 3 2 = 6.

4. The resulting fraction is 14/6. To simplify, divide both the numerator and the denominator by their greatest common divisor, which is 2. This gives us 7/3.

So, the product of 2/3 and 3 1/2 is 7/3. This method can be applied to any fraction multiplied by a mixed number. Remember to always convert the mixed number to an improper fraction before multiplying, and simplify the resulting fraction if possible.

By following these steps, you’ll be able to multiply fractions by mixed numbers with ease. This skill is essential for solving a variety of real-world problems, such as calculating discounts, measuring ingredients, and more. Practice these steps, and you’ll be well on your way to mastering this fundamental mathematical operation.