Monday, 1 October 2018

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 MethodSTSB (Same Top - Small is/to Great)
  Step1:  Checkfor SameNumerators(TOP) /Denominators(BOTTOM). 
  Step2:  Same Numerators– YES. Use STSG
  Step3(SG: Smallest is Greatest)Circlethe smallest denominator (3)
            Answer: 2/3
Example: 
(a) Which fraction has the greatest 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 smallest denominator (5)
                         4 /5 has the greatest value

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

            4   ,    4  ,   4    ,    4     ,     4
            9        7      5        11         12


Step1:Checkfor SameNumerators/Denominators. 
Step2:Same Numerators? – YES. Use: STSG
Step3(SG: Smallest is Greatest).Arrangethe 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


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
Step3Arrangethe 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
                    Remember:  SBSS
Step1:Checkfor SameNumerators(top)/Denominators(bottom). 
Step2:Same Denominators(Bottom) ? – YES. Use: SBSS
Step3(SS: Smallest isSmallest)-> greatest is greatest
            Circlethe LARGEST numerator (5)
            Answer: 5/7

Example:  
(a) Which fraction has the greatest value?  
            2  ,      ,       ,    6
            7      7         7         7

Method
Step1:Checkfor SameNumerators(top)/Denominators(bottom). 
Step2:Same Denominators? – YES. Use: SBSS
              -> Greatest is greatest.
Step3Circlethe 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.
Method
Step1:Checkfor SameNumerators/Denominators. 
Step2:Same Denominators? – YES. Use: SBSS
Step3(SS: Smallest isSmallest)->  
Arranget he fraction from the largest to smallest denominator 
            6  ,      ,       ,    2
            7      7         7         7

For the SMALLEST Value
(c) Which fraction has the smallest value?  

            2  ,   4    ,    3    ,    6
            7      7         7         7

Method
Step1:Checkfor SameNumerators/Denominators. 
Step2:Same Denominators(bottom)? – YES. Use: SBSS
Step3(SS: Smallest isSmallest)Circle the Smallestdenominator(12)
             2/7 has the smallest value

ORDER from SMALLEST to GREATEST 
(d) Arrange the fraction from the smallest to the greatest value.
            2  ,      ,       ,    6
            7      7         7         7

Method
Step1:Checkfor SameNumerators/Denominators. 
Step2:Same Denominators? – YES. Use: SBSS
Step3(SS: Smallest isSmallest)Arrange the fraction from the smallest to the largest denominator 
            2  ,   3    ,    4    ,    6
            7      7         7         7

SUMMARY
         

COMPARE OTHER FRACTIONS
Example
Which fraction has the greatest value?
                    1        3
            3         2        4

Method
Step1 Convert all to LIKE fractions

                       2x4 = 8    ,   1x6 = 6     ,   3x3 =  
                       3x4   12       2x6   12        4x3 = 12


Step2 Circle the numerator with the biggest value
  9/12 has the greatest value
   ~~~~ END ~~~~ :)