This document provides instruction on simplifying fractions. It discusses finding the greatest common factor (GCF) to simplify fractions by dividing the numerator and denominator by the GCF. Examples are provided of simplifying fractions with numbers and variables, including evaluating expressions by substituting values for variables. Students are guided in practicing these skills and assigned homework problems applying the concepts.

1. Lesson 4.1, For use with pages 175-180 2. 75 ÷ 5 1. 52 ÷ 13 Please do not use a calculator to solve these.

2. Lesson 4.1, For use with pages 175-180 2. 75 ÷ 5 1. 52 ÷ 13 Please do not use a calculator to solve these. ANSWER 4 ANSWER 15

3. Essential Questions What is the value of studying fractions? What is the relationship between good number sense and working with fractions?

4. Simplifying Fractions Section 4.3 P. 187 - 191

5. Simplest Form When the only common factor of the numerator and denominator is 1, the fraction is in simplest form. 3 4 3 4 ÷ 1 1 =

6. In this section you will be REVIEWING the concept of simplifying fractions to lowest terms You will use the GCF skills to simplify fractions. You will also use the GCF skills to simplify algebraic fractions.

7. The GCF is the largest number of two or more numbers that is a common factor. For example – if we look at the factors for: = 1, 2, 3, 4, 6, 12 20 = 1, 2, 4, 5, 10, 20 Common factors are 1,2,4. The GCF is 4.

8. A method to find GCF is using the “box” or “division box” method. Divide out until the numbers at the top are “ relatively prime ”. Relatively prime means “no common factors besides the number one.” (critical vocabulary word) GCF: 12 Find the GCF for 120 and 84

9. We can use GCF to simplify fractions. Using the division box, we found the GCF of 120 and 84 is 12. Think of 120 and 84 as the fraction 120/84. Use the division box and divide out common factors until the top two numbers are relatively prime. That is your fraction in simplest form. So 120/ 84 simplifies to 10/7 or 1 3/7. 10 7

10. You have also simplified fractions like this before: Either method is fine to use. Tip: Use your divisibility rules to determine what numbers you can divide by. 120 84 = 10 7 120 ÷ 12 84 ÷ 12 = = 1 3 7

11. Simplify the fraction 27/96 Hint: What number are both 27 and 96 divisibly by? 3 because the sum of 2 +7 and 9 + 6 are both divisible by 3. 27 96 =

12. Simplify this fraction 12 18 2 3 ÷ 6 6 =

13. Simplify this fraction 9 21 3 7 ÷ 3 3 =

14. Simplify this fraction -12 20 -3 5 ÷ 4 4 =

15. Simplify this fraction 12 16 3 4 ÷ 4 4 =

16. Simplify this fraction -10 16 -5 8 ÷ 2 2 =

17. Vocabulary Monomial: a number, a variable, or a product of a number and one or more variables. Factor a Monomial : write it as a product of prime numbers and variables with exponents of one .

18. EXAMPLE 4 Factoring a Monomial Factor the monomial 12 x 2 y . Factor 12 . 12 x 2 y = Write x 2 as x x . = 2 2 3 x x y 2 2 3 x 2 y

19. GUIDED PRACTICE for Example 4 10. 3 mn Factor the monomial. 3 mn = 11. 18 t 2 Factor 18 . 18 t 2 = 3 m n 2 3 3 t 2 = 2 3 3 t t Write t 2 as t t .

20. GUIDED PRACTICE for Example 4 13. 54 w 3 z 4 Factor the monomial. 54 w 3 z 4 = Factor 54 . 2 3 3 3 w 3 z 4 = 2 3 3 3 w w w z z z z Write z 4 as z z z z Write w 3 as w w w = 2 3 3 3 w w w z 4

21. Simplifying fractions with monomials Factor the numerator and denominator Divide out common factors

22. EXAMPLE 4 use the GCF skills to simplify algebraic fractions 14 x 7 xy Factor numerator and denominator. Divide out common factor. Simplify. = 2 · 7 · x 7 · x · y = 2 y 2 · 7 · x 7 · x · y = 1 1 1 1

23. EXAMPLE 5 use the GCF skills to simplify algebraic fractions Evaluate powers and simplify. Factor numerator and denominator. Simplify. Divide out common factor. Substitute 5 for x . Simplify and then evaluate the expression when x = 5 . – 4 x 3 2 x – 4 x 3 2 x = – 2 x 2 = – 2( 5 ) 2 = – 50 – 1 · 2 · 2 · x · x · x 2 · x = 1 1 1 1 = – 1 · 2 · 2 · x · x · x 2 · x

24. GUIDED PRACTICE use the GCF skills to simplify algebraic fractions Simplify the variable expression. Then evaluate for x = – 2 and y = 3. Simplify. Simplify. Divide out common factor. Substitute 3 for y . Factor numerator and denominator. 12. 4 xy 6 x = 2 = 2 · 2 · x · y 2 · 3 · x = 2 y 3 = 2(3) 3 = – 1 · 2 · 2 · x · y 2 · 3 · x 1 1 1

25. GUIDED PRACTICE use the GCF skills to simplify algebraic fractions Simplify the variable expression. Then evaluate for x = – 2 and y = 3. Simplify. Divide out common factor. Substitute 3 for y . Factor numerator and denominator. 13. 32 x 8 xy = 4 y = 2 · 2 · 2 · 2 · 2 · x 2 · 2 · 2 · x · y 1 1 1 1 1 1 1 1 = 4 3 = 2 · 2 · 2 · 2 · 2 · x 2 · 2 · 2 · x · y

26. GUIDED PRACTICE use the GCF skills to simplify algebraic fractions Simplify the variable expression. Then evaluate for x = – 2 and y = 3. Simplify. Divide out common factor. Substitute –2 for x . Factor numerator and denominator. Simplify. 15. 5 x 2 y 10xy = x 2 = – 2 2 = 5 · x · x · y 2 · 5 · x · y = – 1 = 5 · x · x · y 2 · 5 · x · y 1 1 1 1 1 1

27. Assignment: P. 189 #3-12, 26-29 Put some work/steps on your paper – NOT JUST THE ANSWER!!! Make sure you follow directions.