1. Dividing Fractions and Mixed Numerals Developed by: Kira Shank, M.Ed

2. What you will learn…. Definition of reciprocal How to divide fractions How to divide mixed numbers

3. Explanation Reciprocal: The reciprocal of a number is its opposite Examples: The reciprocal of 2/5 would be 5/2. The reciprocal of 1/8 would be 8. The reciprocal of 10 would be 1/10. What is the reciprocal of 3/11?

4. Explanation Steps to follow to divide fractions: 1.Change the second term to its reciprocal 2.Multiply numerators together 3. Multiply denominators together 4. Reduce the fraction, if needed, to simplest terms by finding the GCF

5. Worked Examples Example 1: Multiply the 1 st term by the reciprocal of the 2 nd term

6. Worked Examples Example 2: Reduce by GCF = 2 Final Answer:

7. Worked ExamplesPractice 1. 2.

8. Worked ExamplesSolutions 1. 2. GCF =2 Final Answer:

9. Explanation Steps to follow to divide mixed numbers: 1.Convert mixed numbers to improper fractions 2.Find the reciprocal of the second term 3.Multiply numerators together 2. Multiply denominators together 3.Reduce the fraction, if needed, to simplest terms by finding the GCF

10. Worked Examples Example 1: Convert Mixed numeral to fraction Final Answer:

11. Worked ExamplesPractice 1.

12. Worked ExamplesSolutions 1. Convert Final Answer:

13. Wrapping Up The reciprocal of a number is its opposite. To divide fractions, multiply the first fraction by the second fraction’s reciprocal. Reduce the fraction to lowest terms. To divide mixed numerals, convert the mixed numerals to fractions, then multiply the first fraction by the second fraction’s reciprocal. Finally, if needed, reduce the fraction to lowest terms.

14. Multiplying Fractions Developed by: Kira Shank, M.Ed

15. What you will learn…. How to multiply fractions How do multiply mixed numbers

16. Explanation Steps to follow to multiply fractions: 1.Multiply numerators together 2. Multiply denominators together 3.Reduce the fraction, if needed, to simplest terms by finding the GCF

17. Worked Examples Example 1: Multiply the numerators 6 * 3 = 18 Multiply the denominators 7 * 5 = 35 Final Answer:

18. Worked Examples Fraction needs to be simplified. Find the GCF of 12 and 32 = 4 Divide numerator by 4 = 3 Answer: Divide denominator by 4 = 8 Example 2: Multiply the numerators 4 * 3 = 12 Multiply the denominators 8 * 4 = 32 Final Answer:

19. Worked ExamplesPractice 1. 2.

20. Worked ExamplesSolutions 1. 2. Divide by GCF: 4 Final Answer:

21. Explanation Steps to follow to multiply mixed numbers: 1. Convert mixed numbers to improper fractions 2.Reduce any of the fractions if possible 3.Multiply numerators together 2. Multiply denominators together 3.Reduce the fraction, if needed, to simplest terms by finding the GCF

22. Worked Examples Example 1: Final Answer: Convert whole number to improper fraction Then multiply Reduce Fraction: GCF of 28 and 48 is 4

23. Worked ExamplesPractice 1.

24. Worked ExamplesSolutions 1. Reduce Fraction: GCF is 2 Final Answer: Convert mixed numeral to a fraction Multiply numerators and multiply denominators

25. Wrapping Up To multiply proper fractions, multiply the numerators together and the denominators together, then reduce if needed. To multiply mixed numerals, convert the mixed numeral to an improper fraction. Then multiply the numerators together and the denominators together. Finally, reduce if needed.