1. 3-5 to 3-6 What You’ll Learn To write equivalent fractions To write equivalent fractions To simplify fractions To simplify fractions To compare and order fractions To compare and order fractions

2. What is a Fraction?? A fraction is comprised of two parts: A fraction is comprised of two parts: a numerator (the top number) a numerator (the top number) denominator (the bottom number). denominator (the bottom number). For example, in the fraction 2/3 the "2" is the numerator and the "3" is the denominator. For example, in the fraction 2/3 the "2" is the numerator and the "3" is the denominator.

3. Equivalent Fraction Equivalent fractions of numbers name the same numbers or amounts Equivalent fractions of numbers name the same numbers or amounts Fractions can be written in equivalent forms by multiplying both the numerator and denominator by a common multiple Fractions can be written in equivalent forms by multiplying both the numerator and denominator by a common multiple x2x3x4 7142128 8162432

4. Equivalent Fraction Fractions can be written in equivalent forms by dividing both the numerator and denominator by a common factor Fractions can be written in equivalent forms by dividing both the numerator and denominator by a common factor /2/3/6 241284 3015105

5. Equivalent Fraction Write 3 equivalent fractions for the following Write 3 equivalent fractions for the following 1/3 1/3 ¼ 7/8 7/8

6. Reducing Fractions or Simplest Form A fraction is in lowest terms when the numerator and the denominator do not have a common factor greater than one A fraction is in lowest terms when the numerator and the denominator do not have a common factor greater than one

7. Example 1: Reduce the fraction to lowest terms Step 1: Divide the numerator and the denominator by a common factor (2). Step 2: The fraction (15/36) is still not in lowest terms. Divide the numerator and the denominator by a common factor (3). Answer: 30/72 can be reduced to 5/12.

8. Is this the only way?? Another method for reducing fractions is dividing by the greatest common factor. The greatest common factor is the largest number that is a factor of both the numerator and the denominator. Another method for reducing fractions is dividing by the greatest common factor. The greatest common factor is the largest number that is a factor of both the numerator and the denominator.

9. Example 2: Reduce the fraction to lowest terms. Step 1: Determine the greatest common factor of the numerator and denominator by listing the factors of each number. The greatest common factor is the largest factor of both the numerator and denominator. The greatest common factor of 12 and 36 is 12. Step 1: Determine the greatest common factor of the numerator and denominator by listing the factors of each number. The greatest common factor is the largest factor of both the numerator and denominator. The greatest common factor of 12 and 36 is 12. Step 2: Divide the numerator (12) by and the denominator (36) by 12 to reduce the fraction. Step 2: Divide the numerator (12) by and the denominator (36) by 12 to reduce the fraction. Answer: 12/36 can be reduced to 1/3. Answer: 12/36 can be reduced to 1/3.

10. Reduce the following Fractions 32/98 32/98 45/100 45/100 66/122 66/122 54/330 54/330

11. Comparing Fractions The following list provides the definitions for the commonly used ordering symbols. The following list provides the definitions for the commonly used ordering symbols.

12. Example 3: Compare ½ and ¾ ½ ¾ ½ ¾ 4x1=4 4x1=4 2x3=6 2x3=6 4 < 6 4 < 6 ½ < ¾ ½ < ¾ Cross multiple Cross multiple Compare products Compare products Insert symbol Insert symbol

13. Example 4: Compare ¾ and 9/10 3/4 and 9/10 3/4 and 9/10 4:4,8,12,16,20… 4:4,8,12,16,20… 10:20… 10:20… 3/4 x 5/5 = 15/20 3/4 x 5/5 = 15/20 9/10 x 2/2 = 18/20 9/10 x 2/2 = 18/20 15/20 < 18/20 15/20 < 18/20 Find LCM Find LCM LCM of 4 and 10 is 20 Make Equivalent Fractions Make Equivalent Fractions 3/4=?/20 9/10=?/20 Compare Numerators Compare Numerators Insert symbol Insert symbol