1. Lesson 4.3 Simplifying Fractions
Essential Question: How do you simplify fractions?

2. Before we start…
Do the following fractions represent the same quantity?
1 2 , , , 4 8

3. What is a fraction? 𝑎 𝑏 A ratio comparing two numbers
a is called the numerator
b is called the denominator

4. What is simplest form?
If the numerator and denominator have 1 as their greatest common factor
3 7

5. What are equivalent fractions?
Fractions representing the same number.
They have the same simplest form.
4 6 = 2 3

6. How do you simplify fractions?
Write the prime factorization of the numerator and denominator.
Divide out the common factor.
Simplify.

7. History One of the Czech Republic’s royal coronation jewels is the St
History One of the Czech Republic’s royal coronation jewels is the St. Wenceslas crown. It was made around 1345 and is decorated with 44 spinels, 30 emeralds, 22 pearls, 19 sapphires, and 1 ruby. Write in simplest form the fraction of jewels in the crown that are emeralds? Pearls? Sapphires? Spinels?

8. Students Twelve students in a group of 30 are boys
Students Twelve students in a group of 30 are boys. Write the fraction of boys in the group in simplest form.

9. Basketball Mr. Wilkens has attended 18 of his daughter’s 24 basketball games. What fraction of games has he missed?

10. Fundraiser Your class of 30 students votes on what type of fundraiser to have this year: a car wash, a fair, or a dance. Eight students choose a car wash and 12 students choose a fair. Find the fraction of students who choose to have a dance. Write your answer in simplest form.

11. Tell whether the fractions are equivalent.
3 8 and

12. Tell whether the fractions are equivalent.
3 7 and

13. Tell whether the fractions are equivalent.
and 4 6

14. Write two fractions that are equivalent to 4 10

15. Write two fractions that are equivalent to 8 16

16. Simplifying Variable Expressions
You can use prime factorization to simplify fractions that contain variable expressions.

17. How do you simplify variable expressions?
Factor the numerator and denominator.
Divide out common factors.
Simplify.

18. Simplify 14𝑥 7𝑥𝑦

19. Simplify 18𝑐𝑑 27𝑑

20. Simplify 3𝑥 𝑥 3

21. Simplify 4 𝑥 𝑥 3

22. Evaluate the expression −4 𝑥 3 2𝑥 when 𝑥=5

23. Evaluate the expression 3 𝑏 3 9 𝑏 2 when 𝑏=−4

24. Evaluate the expression 2 𝑥 3 𝑦 6𝑥 when 𝑥=−2 and 𝑦=3

25. How do you simplify fractions?

26. Ticket Out the Door
Simplify 32𝑥 8𝑥𝑦