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How to divide fractions?

BingMag Explains how to divide fractions

To divide fractions, you need to follow these steps:

1. Flip the second fraction:

Take the reciprocal of the second fraction by swapping the numerator and denominator. For example, if you have the fraction 2/3, the reciprocal would be 3/2.

2. Multiply the first fraction by the reciprocal of the second fraction:

Multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator. For example, if you have the fraction 2/3 and the reciprocal 3/2, you would multiply 2/3 by 3/2 to get (2 * 3) / (3 * 2) = 6/6.

3. Simplify the fraction (if possible):

If the numerator and denominator have a common factor, divide both by that factor to simplify the fraction. In the example above, 6/6 can be simplified to 1/1.

So, when you divide 2/3 by 3/2, the result is 1/1 or simply 1.

Dividing fractions may seem daunting at first, but with a clear understanding of the concept and a step-by-step approach, it becomes a straightforward process. To divide fractions, you need to follow a few simple rules and perform a series of mathematical operations.

Before diving into the steps, let's review some key concepts. A fraction consists of two parts: a numerator and a denominator. The numerator represents the number of parts we have, while the denominator represents the total number of equal parts in a whole. For example, in the fraction 3/4, 3 is the numerator, and 4 is the denominator.

To divide one fraction by another, we use the following rule: "To divide fractions, multiply the first fraction by the reciprocal of the second fraction." The reciprocal of a fraction is obtained by swapping the numerator and the denominator. For instance, the reciprocal of 3/4 is 4/3.

Now, let's break down the steps to divide fractions:

Step 1: Identify the fractions you want to divide. Let's say we have the fraction 2/3 divided by 1/4.

Step 2: Write the first fraction as it is. In our example, we write 2/3.

Step 3: Change the division sign to multiplication. Instead of dividing, we will multiply the first fraction by the reciprocal of the second fraction. So, our expression becomes 2/3 multiplied by the reciprocal of 1/4.

Step 4: Find the reciprocal of the second fraction. The reciprocal of 1/4 is 4/1, which simplifies to just 4.

Step 5: Multiply the fractions. Multiply the numerators together and the denominators together. In our case, we have (2/3) multiplied by (4/1). Multiplying the numerators gives us 2 * 4 = 8, and multiplying the denominators gives us 3 * 1 = 3.

Step 6: Simplify the resulting fraction, if possible. In our example, the fraction 8/3 cannot be simplified further, so we leave it as is.

Step 7: Check if the fraction needs to be expressed as a mixed number or a decimal. In our case, 8/3 is an improper fraction, meaning the numerator is greater than the denominator. We can express it as a mixed number by dividing the numerator by the denominator. 8 divided by 3 equals 2 with a remainder of 2. Therefore, the fraction 8/3 can be written as 2 and 2/3 or as a decimal, approximately 2.67.

To summarize, dividing fractions involves multiplying the first fraction by the reciprocal of the second fraction. Remember to follow the steps: identify the fractions, change the division sign to multiplication, find the reciprocal, multiply the fractions, simplify if possible, and express the result as a mixed number or a decimal if needed.

With practice, dividing fractions becomes second nature, and you'll be able to tackle more complex problems effortlessly.

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