Dividing mixed fractions can be a challenging task for many individuals, especially those who are not well-versed in mathematics. However, with a step-by-step guide, the process becomes much more manageable. In this article, we will provide you with a comprehensive guide to dividing mixed fractions.

Step 1: Convert the mixed fractions to improper fractions
Before diving into the division process, it is essential to convert the mixed fractions into improper fractions. To do this, multiply the whole number by the denominator and then add the numerator. The result will become the new numerator, while the denominator remains the same. For example, if you have the mixed fraction 2 1/3, you would multiply 2 by 3 and add 1, resulting in 7 as the new numerator. The denominator will remain 3.

Step 2: Flip the second fraction and multiply
To divide mixed fractions, you need to flip the second fraction and turn it into its reciprocal. This means that the numerator becomes the denominator, and the denominator becomes the numerator. For instance, if you have the fraction 7/3 and want to divide it by 4/5, the reciprocal would be 5/4.

Step 3: Multiply the fractions
Now that both fractions are in proper form, multiply them together. To do this, multiply the numerators together and then multiply the denominators together. For example, if you have 7/3 divided by 4/5, you would multiply 7 by 5 and 3 by 4, resulting in 35/12.

Step 4: Simplify the fraction (if possible)
In some cases, the resulting fraction may not be in its simplest form. To simplify the fraction, find the greatest common divisor (GCD) between the numerator and the denominator. Then, divide both numbers by the GCD. For instance, if the fraction is 35/12, the GCD is 1, and the fraction cannot be simplified further.

Step 5: Convert the improper fraction back to a mixed fraction
If the resulting fraction is improper, meaning the numerator is equal to or greater than the denominator, you can convert it back to a mixed fraction. Divide the numerator by the denominator, and the quotient becomes the whole number. The remainder becomes the new numerator, while the denominator remains the same. For example, if the improper fraction is 35/12, you would divide 35 by 12, resulting in 2 with a remainder of 11. Therefore, the mixed fraction would be 2 11/12.

By following these step-by-step instructions, dividing mixed fractions becomes a more approachable task. Remember to convert the mixed fractions to improper fractions, flip the second fraction, multiply the fractions, simplify the fraction if required, and finally, convert the improper fraction back to a mixed fraction if necessary. Practice these steps frequently, and you will build confidence in dividing mixed fractions accurately.

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