How to Divide Mixed Number by a Fraction
Dividing a mixed number by a fraction can be a challenging task for many students, but with the right approach, it can be broken down into manageable steps. In this article, we will discuss the process of dividing a mixed number by a fraction and provide you with a step-by-step guide to make the process easier to understand.
Understanding the Mixed Number and Fraction
Before diving into the division process, it is crucial to have a clear understanding of both the mixed number and the fraction. A mixed number consists of a whole number and a fraction, such as 3 1/2. On the other hand, a fraction represents a part of a whole, such as 1/2 or 3/4.
Step 1: Convert the Mixed Number to an Improper Fraction
The first step in dividing a mixed number by a fraction is to convert the mixed number into an improper fraction. To do this, multiply the whole number by the denominator of the fraction and add the numerator. Then, place the sum over the denominator.
For example, let’s convert the mixed number 3 1/2 to an improper fraction:
(3 2) + 1 = 7
So, 3 1/2 as an improper fraction is 7/2.
Step 2: Invert the Fraction
The next step is to invert the fraction you are dividing by. Invert means to switch the numerator and denominator. For instance, if you are dividing by 1/2, invert it to become 2/1.
Step 3: Multiply the Improper Fraction by the Inverted Fraction
Now that you have an improper fraction and an inverted fraction, multiply them together. To multiply fractions, simply multiply the numerators and the denominators.
Continuing with our example, we will multiply 7/2 by 2/1:
(7 2) / (2 1) = 14/2
Step 4: Simplify the Result
Finally, simplify the resulting fraction by dividing the numerator by the denominator. In our example, 14/2 simplifies to 7.
Conclusion
Dividing a mixed number by a fraction can be simplified by following these four steps: converting the mixed number to an improper fraction, inverting the fraction you are dividing by, multiplying the fractions, and simplifying the result. With practice, this process will become second nature, and you’ll be able to divide mixed numbers by fractions with ease.
