Multiplying and Dividing Fractions Made Easy
Multiplying and dividing fractions can seem intimidating at first, but with the right strategies and practice, it can become a breeze. In this worksheet, we will explore the rules and techniques for multiplying and dividing fractions, and provide you with exercises to help you master these essential math skills.
Multiplying Fractions
When multiplying fractions, you simply multiply the numerators (the numbers on top) and multiply the denominators (the numbers on the bottom), and then simplify the result.
The Formula:
a/b × c/d = (a × c) / (b × d)
Example:
1⁄2 × 3⁄4 = (1 × 3) / (2 × 4) = 3⁄8
Dividing Fractions
Dividing fractions is similar to multiplying fractions, but with a twist. To divide fractions, you invert the second fraction (i.e., flip the numerator and denominator) and then multiply.
The Formula:
a/b ÷ c/d = a/b × d/c = (a × d) / (b × c)
Example:
1⁄2 ÷ 3⁄4 = 1⁄2 × 4⁄3 = (1 × 4) / (2 × 3) = 4⁄6
Exercises
Now it’s your turn to practice multiplying and dividing fractions! Try to solve the following exercises on your own, and then check your answers with the solutions provided.
Multiplying Fractions Exercises:
- 1⁄3 × 2⁄5 =?
- 2⁄3 × 3⁄4 =?
- 3⁄4 × 1⁄2 =?
- 1⁄2 × 3⁄4 × 2⁄3 =?
- 2⁄5 × 3⁄4 × 1⁄3 =?
Dividing Fractions Exercises:
- 1⁄2 ÷ 3⁄4 =?
- 2⁄3 ÷ 1⁄2 =?
- 3⁄4 ÷ 2⁄3 =?
- 1⁄2 ÷ 2⁄3 ÷ 3⁄4 =?
- 3⁄4 ÷ 1⁄2 ÷ 2⁄3 =?
🤔 Note: Remember to simplify your answers by finding the greatest common divisor (GCD) of the numerator and denominator.
Solutions:
Multiplying Fractions Solutions:
- 1⁄3 × 2⁄5 = 2⁄15
- 2⁄3 × 3⁄4 = 6⁄12
- 3⁄4 × 1⁄2 = 3⁄8
- 1⁄2 × 3⁄4 × 2⁄3 = 6⁄24
- 2⁄5 × 3⁄4 × 1⁄3 = 6⁄60
Dividing Fractions Solutions:
- 1⁄2 ÷ 3⁄4 = 4⁄6
- 2⁄3 ÷ 1⁄2 = 4⁄3
- 3⁄4 ÷ 2⁄3 = 9⁄8
- 1⁄2 ÷ 2⁄3 ÷ 3⁄4 = 12⁄24
- 3⁄4 ÷ 1⁄2 ÷ 2⁄3 = 9⁄4
By following these rules and practicing with these exercises, you’ll become a pro at multiplying and dividing fractions in no time!
Now, let’s summarize what we’ve learned:
Multiplying and dividing fractions are essential math skills that can seem intimidating at first, but with practice and the right strategies, they can become easy. By following the formulas and practicing with exercises, you can master these skills and become more confident in your math abilities.
FAQ Section:
What is the rule for multiplying fractions?
+To multiply fractions, you multiply the numerators (the numbers on top) and multiply the denominators (the numbers on the bottom), and then simplify the result.
What is the rule for dividing fractions?
+To divide fractions, you invert the second fraction (i.e., flip the numerator and denominator) and then multiply.
How do I simplify fractions?
+To simplify fractions, you find the greatest common divisor (GCD) of the numerator and denominator and divide both numbers by the GCD.
