F7 Fractions : Equal or Same Fractions

‘EQUAL/SAME’FRACTIONS

(a) Sentence Construction

Words Problems with ‘equaling fractions’ are usually constructed as 

              

Words such as SAME or EQUAL are good clues.

(b)  Relationship between the numbers in the sentence.

There are two main objects(actors) each associated with a fraction. The Units of the respective fractions are equal. 

(c)  Drawing Model for EQUAL/SAME

Example: 

¾ of Ali’s money is the same as 9/11 of Mary’s money

   ->¾ of Ali’s money (assume it is $x) is the same as 9/11 of Mary‘s money(also $x).

Using Model,

                      

-> 3/4 of Ali’s money(assume it is $x)  is the same as 9/11 of Mary‘s money(also $x).

Model Method for ‘EQUAL/SAME’ Fractions Word Problems

Step 1:  Circle/Underline keywords. Write Objects / Who

Step2a: Draw for each object: ‘Equal portion’ of  numerator, and denominators as total units

Step2b: Equal numerator’s to same portion of U <Fraction values are unchanged)

Step 3:  Solve

Example:  

 1/4 of the boys is equal to 2/5 of the girls. There are 10 girls. How many boys are there?

Step 1:  Circle/Underline keywords. Write Objects / Who

            Boys     

Girls

Step2a: Draw for each object: ‘Equal portion’ of  numerator, and denominators as total units

              

Step2b: Equal numerator’s to same portion of U <Fraction values are unchanged)    

numerators: Boy = 1, and girl = 2.  Equate numerator-> Boy = 1x2 / 4x2 = 2/8  

            Girls -> 2/5, Boys -> 2/8

             

Step 3:  Solve

              

          There are 10 girls. 

               5U = 10, u = 2

         Boys -> 8u = 8 x 2 = 16

    There are 16 boys

Example: 

¾ of Ali’s money is the same as 9/11 of Mary’s money. There have $46 altogether. How much does each of them have?

<< Read the sentence carefully and spot the word patterns>>

Step 1:  Circle/Underline keywords. Write Objects / Who

            Ali     

            Mary

Step2a: Draw for each object: ‘Equal portion’ of  numerator, and denominators as total units

            

Step2b: Equal numerator’s to same portion of U <Fraction values are unchanged)   

Ali = 3, and Mary = 9.  Ali = 3x3 / 3x4 = 9/12

 

Step 3:  Solve

             

 They have $46 

      11U + 12U = 23U

      23U = 46

      U = 2

            Ali has 12x2 = $24. 

            Mary has 11x2 = $22.

Example:

3/5 of John’s marbles is the equal to 2/7 of Harry’s. John has 30 marbles. How many does Harry have?

Step 1:  Circle/Underline keywords. Write Objects / Who

            John

            Harry

Step2a: Draw for each object: ‘Equal portion’ of  numerator, and denominators as total units

           

Step2b: Equal numerator’s to same portion of U <Fraction values are unchanged)

John = 3, Harry = 2. John’s fraction = 3x2/5x2 =6/10, Harry’s = 2x3/7x3= 6/21

   

Step 3:  Solve

            

            John has 30 marbles

            10U = 30

               U = 3 

            Harry has 3 x 21 = 63 marbles.

Example

Linda bought some white sugar and some brown sugar for baking a cake. She used an equal amount of white and brown sugar. She had ¾ of the white sugar and 3/8 of brown sugar left. What fraction of the sugar which Linda bought was used for baking?

Step 1:  Circle/Underline keywords. Write Objects / Who

            White   

Brown

Step2a: Draw for each object: ‘Equal portion’ of  numerator, and denominators as total units. 

For this question, the used portion is the ‘equal’ portion -> ¼ for white sugar and 5/8 for brown sugar

          

Step2b: Equal numerator’s to same portion of U <Fraction values are unchanged)

numerators: White = 1, and brown = 5.  Equate numerator-> white = 1 x 5 

            White -> 5/20, Brown -> 5/8

           

Step 3:  Solve

Total portion = 20 + 8 = 28

Used portion = 5 + 5

Fraction used = 10/28 = 5/14

      ~~~~ END ~~~~ :)