6th Grade Math Textbook, Fundamentals

Multiplying or dividing both

terms of a fraction by the

same number is the same

as multiplying or dividing

the fraction by 1.

Method 3 Use Division

Lesson 5-2 for exercise sets. &KDSWHU 

3UDFWLFH   $FWLYLWLHV

Find the greatest common factor. List the factors or use prime factorization.

1.20 and 45 2.10 and 24 3.6, 14, 28 4.8, 16, 36

Write each fraction in simplest form. Use the GCF or prime factorization.

5. 
   
   
   
   6. 
      
      
      
      7. 
         
         
         
         8. 
            
         
         
         
         
      
      
      
      
   
   
   
   

9.Find two fractions equivalent to.

10.Discuss and Write Can the greatest common factor of 24 and 36

be greater than 24? Explain.

25

85

16

44

22

55

12

30

49

56

Two numbers are if their only common factor is 1.

The numbers 3 and 4 are relatively prime.

You can use the GCF to express fractions in simplest form.

Write in simplest form.

Method 1 Divide by the GCF

• Find the GCF of the numerator and the denominator.
  Factors of 45: 1, 3, 5, 9, 15, 45
  Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
  The GCF of 45 and 60 is 15.


• Divide the numerator and denominator by the GCF.  


• Check by multiplying the numerator and denominator
  of by the GCF you used in simplifying the original expression.^3434  3 •154 •15^4560

45  15

60  15

3

4

45

60

45

60

relatively prime

Remember:A fraction is in simplest

form, or lowest terms, when its

numerator and denominator have no

common factor other than 1.

Method 2 Use Prime Factorization



 Simplify.



So^4560 ^34 in simplest form.

3

4

33 5

223 5

11

11

••

•• •

3 • 3 • 5

2 • 2 • 3 • 5

45

60

prime factorization of 45

prime factorization of 60

Two fractions that have the same value are called.

To find equivalent fractions, you can multiply or divide the numerator

and denominator of a fraction by the same nonzero number.

Find two fractions equivalent to.

Multiply:  Divide: 

So^3054 and are equivalent to.^591527

5

9

15  3

27  3

30

54

15 •2

27 •2

15

27

equivalent fractions

54560

3912

34

prime factors for

both 45 and 60