WHAT IS EQUIVALENT
Equivalent fractions are fractions that have
different denominators, but the same overall
value. By the quot;same overall value,quot; I mean that
the result is the same if the numerator is
divided by the denominator. For instance, the
fraction ¾ has a value of .75, because 3
divided by 4 equals 0.75. 3/4 and 6/8 are also
The best way to think about equivalent fractions is that they are
fractions that have the same overall value. Equivalent fractions
represent the same part of a whole. For example, if we cut a pie
exactly down the middle, into two equally sized pieces, one piece is
the same as one half of the pie. And if another pie (the same size) is
cut into 4 equal pieces, then two pieces of that pie represent the
same amount of pie that 1/2 did. So we can say that 1/2 is equivalent
(or equal) to 2/4.
DON’T BE CONFUSED!
(Take a look at the four circles above. Can you see that the one
quot;1/2quot;, the two quot;1/4quot; and the four quot;1/8quot; take up the same amount
of area colored in red for their circle? Well that means that each
area colored in red is an equivalent fraction or equal amount.
Therefore, we can say that 1/2 is equal to 2/4, and 1/2 is also
equal to 4/8
And yes, 2/4 is an equivalent fraction for 4/8 too.
As you already know, rules are important to math. So, let's look
at the Rule to check to see if two fractions are equivalent or
equal. The rule for equivalent fractions can be a little tough to
explain, but hang in there, I will clear things up in just a bit.
HERE’S THE RULE...
What this Rule says is that two fractions are equivalent (equal) only if the product of
the numerator (a) of the ﬁrst fraction and the denominator (d) of the other fraction
is equal to the product of the denominator (b) of the ﬁrst fraction and the numerator
(c) of the other fraction. A product simply means you multiply.
That sounds like a mouthful right?, so let's try it with numbers...
Now let's plug the numbers into th Rule for equivalent fractions to be sure you have it down.
3/4 is equivalent (equal) to 9/12 only if the product of the numerator (3) of the ﬁrst fraction and the denominator
(12) of the other fraction is equal to the product of the denominator (4) of the ﬁrst fraction and the numerator
(9) of the other fraction. So we know that 3/4 is equivalent to 9/12, because 3x12=36 and 4x9=36.
A simple way to look at how to check for equivalent fractions is to do what is called quot;cross-multiplyquot;, which means
multiple the numerator of one fraction by the denominator of the other fraction. Then do the same thing in
reverse. Now compare the two answers to see if they are equal. If they are equal, then the two fractions are
equivalent fractions. The graphic below shows you...
Okay, let's do one with numbers where the fractions are not equivalent...
So you can see by this example, 1/2 is not an equivalent fraction of 2/3. If you remember to use the
cross-multiply method, you should not have any problems verifying equivalent fractions.
OTHER IMPORTANT FACT
ON EQUIVALENT FRACTIONS
The table below lists some common fractions and their equivalents. Just
read the table from left-to-right. What it shows you are values multiplied
by different variations of fractions equal to quot;1quot;. You do remember that any
number divided by itself is equal to quot;1quot; right? For example...
Fractions equivalent to 1/2 are 2/4, 3/6, 4/8, 5/10, 6/12, ...
Fractions equivalent to 1/5 are 2/10, 3/15, 4/20, 5/25, ...
Equivalent Fractions Table