Explain why multiplying the numerator and denominator of a fraction by the same number results in an equivalent fraction

To understand why multiplying or dividing the numerator and denominator of a fraction by the same number will always result in an equivalent fraction, take a look at the following example.

When we multiply both the numerator and denominator of 1/2 by 3, we can see equivalent fraction 3/6. Notice that we're really multiplying 1/2 by the fraction 3/3 which is the same as one whole and remember that when we multiply any number by one whole the value of the number doesn't change. Therefore we know that our resulting fraction 3/6 must be equivalent to the original fraction 1/2.

So in summary, multiplying or dividing the numerator and denominator of a fraction by the same number will always result in an equivalent fraction because we're really just multiplying or dividing the original fraction by one whole.