F2 Comparing and Ordering Fractions

COMPARE FRACTIONS WITH THE SAME NUMERATORS

For the GREATEST/BIGGEST Value

Example

Which fraction has the greatest value?

                        2        2         2  

                        3        7         5       

By Drawing:

            

We can see that:

(1) The fraction (2/3) with the SMALLEST DENOMINATOR (3) is the GREATEST.

(2) The fraction (2/7) with the BIGGEST DENOMINATOR (7) is the SMALLEST.

            Answer: 2/3

However, we cannot be drawing for all ordering fractions.

Ordering Method

Step1: Check for Same numerators/denominators. 

Step2: Same Numerators – YES. Arranged from Smallest is Greatest

Step3: Underline the smallest denominator (3)

Answer: 2/3

Example: Which fraction has the greatest value?  

4   ,    4  ,   4    ,    4     ,     4

9        7      5        11         12

Step1: Check for Same numerators/denominators. 

Step2: Same Numerators? – YES.

Step3: (Smallest is Greatest). Underline the smallest denominator (5)

4 /5 has the greatest value

Order from greatest to smallest

Arrange the fraction from the greatest to the smallest value.

4   ,    4  ,   4    ,    4     ,     4

9        7      5        11         12

Step1: Check for Same Numerators/Denominators. 

Step2: Same Numerators? – YES. => Smallest is Greatest

Step3: Arrange the fraction from the smallest to largest denominator 

4   ,    4  ,   4    ,    4     ,     4

5        7      9        11         12

For the SMALLEST Value

Example:  

Which fraction has the smallest value?  

4   ,    4  ,   4    ,    4     ,     4

9        7      5        11         12

Step1: Check for Same Numerators/Denominators. 

Step2: Same Numerators? – YES => Smallest is Greatest

Step3: Underline the Largest denominator

4 /12 has the smallest value

Order from Smallest to Greatest 

Arrange the fraction from the smallest to the greatest value.

4   ,    4  ,   4    ,    4     ,     4

9        7      5        11         12

Step1: Check for Same Numerators. Yes => Smallest is greatest

Step3: Arrange the fraction from the largest to the smallest denominator 

4   ,    4  ,   4    ,    4     ,     4

         12       11     9         7           5 

For the SMALLEST Value

Example:  

Which fraction has the smallest value?  

            4   ,    4  ,   4    ,    4     ,     4

            9        7      5        11         12

Method

Step1: Checkfor SameNumerators(top)/Denominators(bottom). 

Step2: Same Numerators? – YES. Use: STSG

Step3: (SG: Smallest is Greatest). Circlethe Largest denominator(12)

             4 /12 has the smallest value

Order from SMALLEST to GREATEST 

Arrange the fraction from the smallest to the greatest value.

            4   ,    4  ,   4    ,    4     ,     4

            9        7      5        11         12

Method

Step1:Checkfor SameNumerators/Denominators. 

Step2:Same Numerators? – YES. Use: STSG

Step3: Arrangethe fraction from the largest to the smallestdenominator 
            4   ,    4  ,   4    ,    4     ,     4

            12     11     9         7           5 

COMPARE FRACTIONS WITH THE SAME DENOMINATORS

FOR the GREATEST Value

Example

Which fraction has the greatest value?

                        2        5         3  

                        7        7         7       

By Drawing:

              

(1) The fraction (5/7) with the BIGGEST NUMERATOR (5) is the BIGGEST/GREATEST.

(2) The fraction (2/7) with the SMALLEST NUMERATOR (7) is the SMALLEST.

                        Answer: 5/7

However, we cannot be drawing for all ordering fractions.

Method

Step1: Check for Same Numerators/Denominators. 

Step2: Same Denominators? – YES.

Step3: -> greatest is greatest, Circle the LARGEST numerator (5)

Example:  

(a) Which fraction has the greatest value?  

2  ,   4    ,    3    ,    6

7      7         7         7

Step1: Check for Same Numerators/Denominators. 

Step2: Same Denominators? – YES  --> Greatest is greatest.

Step3: Circle the greatest denominator (5)

6/7 has the greatest value.

Order from Greatest to Smallest

(b) Arrange the fraction from the greatest to the smallest value.

Step1: Check for Same numerators/denominators. 

Step2: Same Denominators? – YES --> Smallest value is Smallest

Step3:  Arrange the fraction from the largest to smallest denominator 

6  ,   4    ,    3    ,    2

7      7         7         7

For the Smallest Value

(c) Which fraction has the smallest value?  

Step1: Check for Same Numerators/Denominators. 

Step2: Same Denominators? – YES --> Smallest value is Smallest

Step3: Circle the Smallest denominator (12)

2/7 has the smallest value

ORDER from SMALLEST to GREATEST 

(d) Arrange the fraction from the smallest to the greatest value.

2  ,   4    ,    3    ,    6

7      7         7         7

Step1: Check for Same Numerators/Denominators. 

Step2: Same Denominators? – YES--> SS: Smallest is Smallest

Step3: Arrange the fraction from the smallest to the largest denominator 

2  ,   3    ,    4    ,    6

7      7         7         7

COMPARE OTHER FRACTIONS

Example

Which fraction has the greatest value?

            2         1        3

            3         2        4

Method

Step1 Convert all to LIKE fractions

                       2x4 = 8    ,   1x6 = 6     ,   3x3 =  ⑨

                       3x4   12       2x6   12        4x3 = 12

Step2 Circle the numerator with the biggest value

  9/12 has the greatest value
   ~~~~ END ~~~~ :)