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.
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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!
How 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!
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