Arithmetic Grade Four

Lesson Sixty-five: Equivalent Fractions

Equivalent Fractions
Here's a list of fractions which are equivalent to two-fifths.


  2	4   	 6	  8	  10	  12	  14	  16
 ---   ----     ----     ----    ----    ----    ----    ----
  5     10       15       20      25      30      35      40
You should notice a pattern between the numerators and the denominators.

In the next activity you will fill in the missing fraction. Let's say that you are given this sequence: 


     2/3, 4/6, ___, 8/12.
What is the missing fraction in this sequence? You should notice that a pattern exists between the numerators and the denominators: 

      1		2	   3	     4

      2		4	   ?         8
     ---       ---        ---       ----
      3         6          ?         12
To find the missing fraction we multiply the numerator and the denominator of the first fraction by 3. 

        2       3     6
       ---  x  --- = ---
        3       3     9
Here's another example: 

      1		2	   3	     4

      3		6	   ?         12
     ---       ---        ---       ----
      4         8          ?         16
To find the missing fraction we multiply the numerator and the denominator of the first fraction by 3. 

        3       3     9
       ---  x  --- = ---
        4       3     12
Here's one more example: 

      1		2	   3	     4

      2		?	   6         8
     ---       ---        ---       ----
      7         ?          21        28
To find the missing fraction we multiply the numerator and the denominator of the first fraction by 2. 

        2       2     4
       ---  x  --- = ---
        7       2     14
You get to try some of these on the next page.

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