Math Tutor Bob

This is likely one of the things you just need to accept right now, but there are times when you need to express a fraction as an "equivalent fraction" ... that is to say a fraction that has the same value as compared to another fraction, but has a different numerator and denominator.

And like many things in math the "trick" to determining an "equivalent fraction" is to multiply the original fraction by one (1). And remember anything multiplied by 1 is itself. To explain

    5*1=5
	   
    42*1=42

    155*1=155

    and so on ... and also
       
    1⁄2 *1 = 1⁄2
    2⁄3 *1 = 2⁄3
       
    But how does this help? Well, actually it doesn't help, 
    but consider that (2/2)=1   Now, consider this
		   
         1⁄2 * 2⁄2 = 2⁄4 
				
    therefore, 1⁄2 and 2⁄4 are "equivalent fractions".
      
    And other fractions which are equivalent to 1/2 are as follows:
      
         1⁄2 * 2⁄2 = 2⁄4
         1⁄2 * 3⁄3 = 3⁄6
         1⁄2 * 4⁄4 = 4⁄8
         1⁄2 * 5⁄5 = 5⁄10
            
   and so on. So, 1⁄2,
                  2⁄4,                                                    
                  3⁄6, 
                  4⁄8, and 
                  5⁄10 are all "equivalent fractions".
                     
      
   OK, so find the equivalent fractions of 3⁄4               

    3⁄4 * 2⁄2 = 6⁄8                   

    3⁄4 * 3⁄3 = 9⁄12                   

    3⁄4 * 4⁄4 = 12⁄16                   

    3⁄4 * 5⁄5 = 15⁄20                   
                 and just to be different

      3⁄4 * 100⁄100 = 300⁄400                   

    And if someone ask you if you would like three-fourths 
    of a dollar or three hundred-four hundredths of a dollar, 
    just tell them you don't care. 
	   
         For goodness sakes they are equivalent.      
  	

One thing that might be obvious (or maybe not), is that "creating" equivalent fractions is the opposite of simplifying a fraction. That is to say, if you got 5/10 as an answer, and turned it in to a math teacher then you would likely be hit with a minus 5 (-5), or maybe more, because ⁵⁄₁₀ can be simplified to ¹⁄₂.

⁵⁄₁₀ and ¹⁄₂ are equivalent fractions, but ¹⁄₂ is the fraction which is in the "simpliest form".

So, that is what equivalent fractions are. And why would one need to know about equivalent fractions? Well, to add and subtract fractions one needs to be very familiar with the concept of and use of equivalent fractions to create fractions with the same denominator - that is to say a "common denominator".

References for equivalent fractions:

MathIsFun

VideoMathTutor This is a 31 minute youTube video which is worth watching.

Kahn Academy And this is about a 6 minute youTube video worth watching.

More rap from 6th graders with your equivalent fractions.

With an English accent. 11 minutes long.