Divide Fractions Worksheet With Answers

Mastering Fraction Division: A Comprehensive Worksheet with Answers and Explanations

Dividing fractions can seem daunting at first, but with a clear understanding of the process and consistent practice, it becomes second nature. This comprehensive guide provides a detailed explanation of fraction division, along with a worksheet containing various problems and their step-by-step solutions. Whether you're a student looking to solidify your understanding or a teacher seeking supplementary resources, this guide will equip you with the tools to conquer fraction division. This worksheet focuses on various complexities, including dividing proper and improper fractions, mixed numbers, and even word problems involving fraction division.

Understanding the Basics: Reciprocals and the "Keep, Change, Flip" Method

Before diving into the worksheet, let's refresh our understanding of the core concepts. The key to dividing fractions lies in understanding reciprocals. The reciprocal of a fraction is simply the fraction flipped upside down. For example, the reciprocal of 2/3 is 3/2. The reciprocal of 5 (which can be written as 5/1) is 1/5.

The most common and efficient method for dividing fractions is the "Keep, Change, Flip" method:

1. Keep the first fraction exactly as it is.
2. Change the division sign (÷) to a multiplication sign (×).
3. Flip the second fraction (find its reciprocal).
4. Multiply the numerators together.
5. Multiply the denominators together.
6. Simplify the resulting fraction to its lowest terms, if necessary.

Let's illustrate this with an example: 1/2 ÷ 1/4

1. Keep: 1/2
2. Change: ÷ becomes ×
3. Flip: 1/4 becomes 4/1
4. Multiply: (1 × 4) / (2 × 1) = 4/2
5. Simplify: 4/2 = 2

Therefore, 1/2 ÷ 1/4 = 2

Dividing Fractions: A Step-by-Step Approach

When working with more complex fractions, a systematic approach is crucial. Here’s a step-by-step breakdown:

Step 1: Convert Mixed Numbers to Improper Fractions

If you have mixed numbers (a whole number and a fraction, like 1 1/2), convert them to improper fractions before proceeding. To do this:

• Multiply the whole number by the denominator.
• Add the numerator to the result.
• Keep the same denominator.

For example, converting 1 1/2 to an improper fraction:

(1 × 2) + 1 = 3, so 1 1/2 becomes 3/2.

Step 2: Apply the "Keep, Change, Flip" Method

Once all mixed numbers are converted to improper fractions, apply the "Keep, Change, Flip" method as described earlier.

Step 3: Simplify the Result

After multiplying the fractions, simplify the resulting fraction to its lowest terms by finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by it.

Worksheet: Dividing Fractions

Now, let's put our knowledge into practice. Solve the following problems, showing your work step-by-step. The answers are provided below the worksheet.

Part 1: Proper and Improper Fractions

1. 2/5 ÷ 1/3 = ?
2. 3/4 ÷ 2/5 = ?
3. 5/6 ÷ 5/12 = ?
4. 7/8 ÷ 7/16 = ?
5. 1/9 ÷ 2/3 = ?
6. 4/7 ÷ 8/21 = ?
7. 10/11 ÷ 5/22 = ?
8. 9/10 ÷ 3/5 = ?

Part 2: Mixed Numbers

9. 1 1/2 ÷ 2/3 = ?
10. 2 1/4 ÷ 3/8 = ?
11. 3 2/5 ÷ 1 1/10 = ?
12. 4 3/7 ÷ 2 1/14 = ?
13. 1 5/8 ÷ 2 1/2 = ?
14. 5 1/3 ÷ 1 2/9 = ?
15. 2 3/4 ÷ 3/2 = ?
16. 6 1/5 ÷ 1 2/5 = ?

Part 3: Word Problems

17. A baker has 3/4 of a cup of sugar. Each batch of cookies requires 1/8 of a cup of sugar. How many batches of cookies can the baker make?

18. A painter has 2 1/2 gallons of paint. He uses 1/4 gallon of paint per room. How many rooms can he paint?

19. Sarah has 5/6 of a yard of ribbon. She wants to cut it into pieces that are 1/12 of a yard long. How many pieces can she cut?

Answers and Explanations

Part 1: Proper and Improper Fractions

1. 2/5 ÷ 1/3 = 2/5 × 3/1 = 6/5 or 1 1/5
2. 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 or 1 7/8
3. 5/6 ÷ 5/12 = 5/6 × 12/5 = 60/30 = 2
4. 7/8 ÷ 7/16 = 7/8 × 16/7 = 128/56 = 2
5. 1/9 ÷ 2/3 = 1/9 × 3/2 = 3/18 = 1/6
6. 4/7 ÷ 8/21 = 4/7 × 21/8 = 84/56 = 3/2 or 1 1/2
7. 10/11 ÷ 5/22 = 10/11 × 22/5 = 220/55 = 4
8. 9/10 ÷ 3/5 = 9/10 × 5/3 = 45/30 = 3/2 or 1 1/2

Part 2: Mixed Numbers

9. 1 1/2 ÷ 2/3 = 3/2 ÷ 2/3 = 3/2 × 3/2 = 9/4 or 2 1/4
10. 2 1/4 ÷ 3/8 = 9/4 ÷ 3/8 = 9/4 × 8/3 = 72/12 = 6
11. 3 2/5 ÷ 1 1/10 = 17/5 ÷ 11/10 = 17/5 × 10/11 = 170/55 = 34/11 or 3 1/11
12. 4 3/7 ÷ 2 1/14 = 31/7 ÷ 29/14 = 31/7 × 14/29 = 434/203 = 2
13. 1 5/8 ÷ 2 1/2 = 13/8 ÷ 5/2 = 13/8 × 2/5 = 26/40 = 13/20
14. 5 1/3 ÷ 1 2/9 = 16/3 ÷ 11/9 = 16/3 × 9/11 = 144/33 = 48/11 or 4 4/11
15. 2 3/4 ÷ 3/2 = 11/4 ÷ 3/2 = 11/4 × 2/3 = 22/12 = 11/6 or 1 5/6
16. 6 1/5 ÷ 1 2/5 = 31/5 ÷ 7/5 = 31/5 × 5/7 = 31/7 or 4 3/7

Part 3: Word Problems

17. 3/4 ÷ 1/8 = 3/4 × 8/1 = 24/4 = 6 batches of cookies.

18. 2 1/2 ÷ 1/4 = 5/2 ÷ 1/4 = 5/2 × 4/1 = 20/2 = 10 rooms.

19. 5/6 ÷ 1/12 = 5/6 × 12/1 = 60/6 = 10 pieces.

Further Practice and Resources

This worksheet provides a solid foundation in fraction division. To further enhance your understanding, consider working through additional practice problems with varying levels of difficulty. You can find numerous online resources and textbooks that offer further exercises and explanations. Remember, consistent practice is key to mastering any mathematical concept. Don't be afraid to seek help when needed – understanding the underlying concepts is far more important than simply memorizing procedures. Good luck, and happy calculating!