How to Remember Where Zero Can Go in a Fraction

It is important that a student knows where 0 is allowed in a fraction.  Can it be the numerator, the denominator, or both?  The answer is that it can ONLY be the NUMERATOR!  You can NOT divide by Zero.


A Trick to Remembering Where Zero Can Go in A Fraction

An easy trick I learned (if I remember correctly) from a student when I taught at a community college is that it is O/K for 0 to be the numerator, but it’s a N/O for 0 to be the denominator.

So it CAN be the numerator/top of the fraction as that’s OK.  However, 0 can NOT be the denominator/bottom as it’s a NO NO!

gaps in kids mathHow to Evaluate a Fraction Where Zero is the Numerator or the Denominator

What’s the difference in how we evaluate a fraction if 0 is the numerator versus when it is the denominator?  When 0 is the numerator and NOT the denominator, the fraction is equal to ZERO.  If however, 0 is the denominator, mathematicians call that fraction UNDEFINED (it’s not a number).

So for example,    0/2= 0,    0/-10 = 10,    0/100 = 0,     0/1 = 0.

However,    2/0  is undefined.  -10/0 is undefined.   100/0  is undefined.    1/0 is undefined.

What is Zero Divided by Zero Equal to?

0/0 is also called undefined by mathematicians.  Anytime that 0 is the denominator of a fraction, the fraction is called undefined.


How will this be important in Algebra?

Remembering that 0 can not be the denominator  will be important in Algebra.  For example, when asked to graph the reciprocal function y = 1/x, we must remember that x can not be zero because we can NOT DIVIDE by zero.  So as you will learn in Algebra, the domain (the  domain is the input values of the function that produce a real number output….don’t worry you can learn this later in Algebra)….so the domain here is all the real numbers except for 0.

If given a variation of the reciprocal function ( a transformation) such as y = 1/(x-2), again, we have to remember, that the denominator x-2 can NOT be zero.  The only real number that will make x-2 zero is 2.  So here the domain is all real numbers except for 2.

Use the easy trick OK and NO to remember that zero can be the numerator but NOT the denominator of a fraction.

Was this trick helpful for you? Comment below if it was or if you have any other helpful math tricks. Stick around for more helpful math tips!

Encourage Your Child to be a STEM Problem Solver with STEM books

Do you want to encourage your kids to be little inventors?  Check out the first book in a kids’ fictional STEM series that I wrote called Anna, Kid Engineer. Encourage your child to be creative, inventive, and to not give up!

You can purchase the pdf ebook on my website, or you can purchase the physical book on Amazon.

STEM book for kids

Andre, Kid Aviator is the 2nd book in the STEM series for kids.  In Andre, Kid Aviator, the STEM Club Andre is a part of is presented with a problem.  Check out this book to see if the club is able to solve the problem.  Encourage your kids to be problem solvers!  You can purchase the ebook of Andre, Kid Aviator here.

The physical book of Andre, Kid Aviator is also available on Amazon.


20 Possible Holes in Your Child’s Math Education

Is your child in 6th grade or higher, and he is struggling with math?  Do you need help identifying possible holes in your child’s math education?  Check out the ebook 20 Possible Holes in Your Child’s Math Education. Here is another sample page.

help kids with math20 Possible Math Holes in Your Child's Math Education

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