Equivalent Fractions
Two fractions which represent the same numerical values are
said to be equivalent fractions.
For example,
are all fractions equal to the decimal value 0.75. Even though
each fraction in this list has a different numerator and
denominator combination than the others, still each of these
fractions represents the same numerical value – hence they
are equivalent fractions.
Two fractions are equivalent when you can convert the one with
the smaller (or simpler) numerator and denominator into the other
fraction by multiplying both its numerator and denominator by the
same number. Thus

is equivalent to 

because if we multiply both the numerator and denominator of 3
/ 4 by 5, we get 15 / 20:
The importance of recognizing two fractions are equivalent is
that you can replace a fraction by another equivalent fraction if
it is convenient or useful to do so, and you will not have
changed the numerical value of the expression with which you are
working. This provides a powerful tool for doing mathematics with
fractions.
Two fractions are also equivalent if we can convert the
fraction with the larger numerator and denominator into the other
fraction by dividing both numerator and denominator by the same
number. Thus

is equivalent to 

because
That is, when we divide both the numerator and the denominator
of 15 / 20 by 5, we end up with 3 / 4.
