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4. Example 2-4b Objective Express fractions in simplest form

5. Example 2-4b Vocabulary Equivalent fractions Fractions that have the same value

6. Example 2-4b Vocabulary Simplest form When the greatest common factor (GCF) of the numerator and denominator is 1

7. Lesson 2 Contents Example 1Write Equivalent Fractions Example 2Write Equivalent Fractions Example 3Write Fractions in Simplest Form Example 4Express Fractions in Simplest Form

8. Example 2-1a Replace the  with a number in so the fractions are equivalent. Write the proportion, placing a variable instead of a dot x 1/4 Cross multiply to solve for x Multiply the numerator of one ratio with the denominator of the other ratio Write it as a product (Remember: A number next to a variable means multiply 13x

9. Example 2-1a Replace the  with a number in so the fractions are equivalent. x 1/4 Multiply the numerator of the other numerator with the denominator of the other ratio Write it as a product using parenthesis 13x Bring down the = sign 13x =13x = 6(52) Bring down 13x = 13x = Multiply 6  52 13x = 312

10. Example 2-1a Replace the  with a number in so the fractions are equivalent. x 1/4 13x Ask: What is being done to the variable? 13x =13x = 6(52) 13x = 13x = 312 The variable is being multiplied by 13 Do the inverse on both sides of the equal sign The inverse of multiplying by 13 is dividing by 13

11. Example 2-1a Replace the  with a number in so the fractions are equivalent. x 1/4 13x Using a fraction bar, divide both sides by 13 13x =13x = 6(52) 13x = 13x = 312 13 Combine “like” terms Divide 13 by 13 1 Bring down  x = 1  x = Combine “like” terms 1  x = 24 Use the Identity Property to multiply 1  x x Bring down = 24 x = 24 Write fraction replacing the  with 24 Answer:

12. Example 2-1b Answer: Replace the  with a number in so the fractions are equivalent. 1/4

13. Example 2-2a Replace the  with a number in so the fractions are equivalent. x 2/4 Write the proportion, placing a variable instead of a dot Cross multiply to solve for x Multiply the numerator of one ratio with the denominator of the other ratio Write it as a product (Remember: A number next to a variable means multiply 24x

14. Example 2-2a Replace the  with a number in so the fractions are equivalent. x 2/4 24x Bring down the = sign 24x = Multiply the numerator of the other numerator with the denominator of the other ratio Write it as a product using parenthesis 24x = 40(3) Bring down 24x = 24x = Multiply 40  3 24x = 120

15. Example 2-2a Replace the  with a number in so the fractions are equivalent. x 2/4 24x24x =24x = 40(3) 24x =24x = 120 Ask: What is being done to the variable? The variable is being multiplied by 24 Do the inverse on both sides of the equal sign The inverse of multiplying by 24 is dividing by 24

16. Example 2-2a Replace the  with a number in so the fractions are equivalent. x 2/4 24x24x =24x = 40(3) 24x =24x = 120 Using a fraction bar, divide both sides by 24 24 Combine “like” terms 1 1  x = Divide 24 by 24 Bring down  x = Combine “like” terms 1  x = 5 Use the Identity Property to multiply 1  x Bring down = 5 x = x = 5 Write fraction replacing the  with 24 Answer:

17. Example 2-2b Replace the  with a number in so the fractions are equivalent. 2/4 Answer:

18. Example 2-3a Write in simplest form. 1442 2 7 2 21 3 7 2  7 14 3/4 Prime factor both the numerator and denominator Circle factors that are common in each number and write as factors Multiply common factors Identify as GCF GCF =14

19. Example 2-3a Write in simplest form. 14 is the GCF 1 3 Answer: 3/4 Divide the numerator by the GCF of 14  14 Divide the denominator by the GCF of 14  14

20. Example 2-3c Write in simplest form. Answer: 3/4

21. Example 2-4a GYMNASTICS Lin practices gymnastics 16 hours each week. There are 168 hours in a week. Express the fraction in simplest form. 161682 8 2 4 2 2 2 842 42 2 21 4/4 Prime factor both the numerator and denominator 3 7

22. Example 2-4a 16 168 2 8 2 4 2 2 2 84 2 42 2  2 21 2 2  8 4/4 3 7 Circle factors that are common in each number and write as factors Multiply common factors Identify as GCF GCF = 8

23. Example 2-4a 8 is the GCF 2 21 4/4 GYMNASTICS Lin practices gymnastics 16 hours each week. There are 168 hours in a week. Express the fraction in simplest form. Divide the numerator by the GCF of 8  8 Divide the denominator by the GCF of 8  8 Add dimensional analysis hours Answer:

24. Example 2-4b TRANSPORTATION There are 244 students at Longfellow Elementary School. Of those students, 168 ride a school bus to get to school. Express the fraction in simplest form. Answer: * 4/4 students

25. End of Lesson 2 Assignment Lesson 5:2Simplifying Fractions9 - 30 All