How to Divide Mixed Fractions?

Dividing mixed fractions involves a few key steps to ensure accurate calculations. The process is outlined below:

Steps to Divide Mixed Fractions

The main idea behind dividing mixed fractions is to first convert them to improper fractions, then apply the concept of reciprocals and multiply, and finally, simplify the result.

Here's a step-by-step guide:

1. Convert Mixed Numbers to Improper Fractions:

   • A mixed number has a whole number part and a fractional part (e.g., 2 1/4).
   • To convert it into an improper fraction:
     • Multiply the whole number by the denominator of the fraction.
     • Add the result to the numerator.
     • Keep the same denominator.
     • Example: 2 1/4 becomes ((2 * 4) + 1) / 4 = 9/4

2. Take the Reciprocal of the Second Fraction:

   • When dividing fractions, we multiply by the reciprocal of the second fraction.
   • To find the reciprocal, simply swap the numerator and the denominator.
     • Example: The reciprocal of 3/5 is 5/3

3. Multiply the First Fraction by the Reciprocal:

   • Now that you have the reciprocal, multiply the first fraction (which was the first mixed number, but now an improper fraction) by the reciprocal of the second.
   • To multiply fractions, multiply the numerators together and the denominators together.
     • Example: (9/4) divided by (3/5) is (9/4) multiplied by (5/3), therefore: (9 5)/(4 3) = 45/12

4. Simplify the Resulting Fraction:

   • After multiplication, simplify the fraction by finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by it.
     • Example: 45/12 can be simplified by dividing by 3 (GCD), resulting in 15/4.

5. Convert Improper Fraction to Mixed Number (If Required):

   • If the result is an improper fraction (numerator is greater than the denominator), convert it to a mixed number.
     • Divide the numerator by the denominator.
     • The quotient becomes the whole number part.
     • The remainder becomes the numerator of the fractional part.
     • Keep the same denominator.
     • Example: 15/4 becomes 3 3/4 because 15 divided by 4 is 3 with a remainder of 3.

Example

Let's divide 2 1/4 by 1 1/2.

Step	Calculation	Result
1. Convert to Improper Fractions	2 1/4 = ((2 * 4) + 1) / 4 = 9/4 ; 1 1/2 = ((1 * 2) + 1)/2 = 3/2	9/4 and 3/2
2. Reciprocal of Second Fraction	Reciprocal of 3/2 is 2/3.	2/3
3. Multiply	9/4 * 2/3 = (9 * 2)/(4 * 3)	18/12
4. Simplify	18/12 simplified is 3/2	3/2
5. Convert to Mixed Fraction	3/2 = 1 1/2	1 1/2

Therefore, 2 1/4 divided by 1 1/2 equals 1 1/2.

Key Takeaways

• Convert: Always start by converting mixed numbers into improper fractions.
• Reciprocal: Remember to use the reciprocal of the second fraction.
• Simplify: Always simplify the fraction at the end, and convert to a mixed number if appropriate.
• Precision: Follow these steps to get accurate results when dividing mixed fractions.

By following these detailed steps, you can confidently divide mixed fractions and arrive at the correct answer.