Lesson 4-2

Example 1 Write Equivalent Fractions
Replace the ■ with a number so the fractions are equivalent.
 = 

×7

 = 	Since 9  7 = 63, multiply the numerator and denominator by 7.

×7

Example 2 Write Equivalent Fractions
Replace the ■ with a number so the fractions are equivalent.
 = 

÷3

 = 	Since 21  3 = 7, divide the numerator and denominator by 3.

÷3

Example 3 Write Fractions in Simplest Form
Write  in simplest form.

METHOD 1 Divide by common factors.

÷3

÷2

A common factor of 24 and 30 is 2. 
A common factor of 12 and 15 is 3.

  =    =  	 

÷3

÷2

METHOD 2 Divide by the GCF.

factors of 24:  1, 2, 3, 4, 6, 8, 12, 24
factors of 30:  1, 2, 3, 5, 6, 10, 15, 30
The GCF of 24 and 30 is 6.

÷6

	
 =  	Divide the numerator and denominator by the GCF, 6.

÷6

Since the GCF of 4 and 5 is 1, the fraction  is in simplest form.

Example 4 Express Fractions in Simplest Form
STUDENTS   In a class of 42 students, 28 of them participate in after-school sports activities. Express the fraction  in simplest form.   
The GCF of 28 and 42 is 14.

2

3

 = 	Mentally divide both the numerator and denominator by 14.
	
So,  or 2 out of every 3 students participate in after-school sports activities.