Let’s talk about simplifying
fractions. To do that, we’re gonna talk about
three parts. One, what does it mean to simplify
a fraction? Two, why we would do it? And three, how would we simplify a
Number one, what does simplifying
fractions mean? To simplify a fraction is to make
it as simple as possible. You might also hear people use the
word reduce. Reducing fractions and simplifying
fractions are the same thing. Onto question two, why would we
simplify a fraction? We simplify a fraction for two main
reasons; it clarifies communication and it helps us avoid misunderstandings.
You might be wondering, what in the
world does she mean, clarify communication? Isn’t this math? And yes, I am talking about
communication in math because good mathematicians communicate clearly. Good mathematicians explain and
present their data in simplified terms. Here’s an example in clarity. Sara and Sam both took a math test
and their teacher gave them the grades you see on the screen. She gave Sara a 130 out of 182 and
Sam got 90 out of 126.
Whose score is higher? Did they do okay? Is this a good score for a math
test? It’s not really clear. The simplified form of both of
these fractions is five-sevenths. Sam and Sara actually got the same
score. But it wasn’t clear because they
were using very complex fractions, instead of simplifying them. Taking the time to simplify
fractions makes your communication more clear and avoids misunderstandings between
you and the people you’re communicating your math to.
There is a third and more practical
reason, and that would be easier computations. For example, 130 over 182𝑥 equals
five doesn’t seem like that simple of a problem to solve. But five-sevenths 𝑥 equals five is
a much easier problem to solve. Before we get to our third
how-to-simplify-fractions portion, there’s one more thing we need to note.
Simplifying does not change the
value of a fraction. It does not change how much we’re
talking about. Here is an illustration of the fact
that the value doesn’t change. The first pizza is
four-eighths. The second pizza is two-fourths of
a pizza. The third pizza is one-half. Here, the only thing changing is
the number of slices but not the amount of pizza that you ate. One-half is four-eighths in a
simplified form. And one-half is also the simplified
form of two-fourths.
Now, on to how we simplify
fractions. Let’s take the example four-eighths
from the pizza problem I just showed you and try and simplify it. To do that, I’m going to consider a
number that’s a factor of both the numerator and the denominator. In other words, I’m looking for a
number that the top and the bottom are both divisible by. So, in this problem, I recognize
that both the numerator and the denominator are divisible by four.
Now, I just divide the numerator by
four and the denominator by four, one-half. This was a very simple example and
probably one you can recognize immediately. You might even memorize that
four-eighths equals one-half. Not all fractions are that easy to
simplify. Here’s a slightly harder one.
Let’s simplify 12 over 28.
Again, we need to consider a number
that both 12 and 28 are divisible by. I’m going to start with four. The simplified form of 12 over 28
Here’s another example to simplify,
30 over 72.
Our process is still the same. We need to come up with a number
that 30 and 72 are both divisible by. I recognize that 30 and 72 are both
even numbers, so I’m going to start there and divide them both by two. This gives me 15 over 36. 15 over 36, however, is not the
simplest form of this fraction. If you look closely, there’s a
number that 15 and 36 are both divisible by, and that number is three. When I divide the top and bottom by
three, I get five twelfths. And I know that five twelfths is
the simplest form of this fraction because five and 12 do not share any common
Here’s our final example.
Adults need eight hours of sleep
per day. What fraction of the day is
this? Give your answer in simplest
We can identify that in our
problem, we have these two pieces of information, eight hours of sleep is what they
need per day. We also know that that means 24
hours. So, we can start with our fraction
of eight twenty-fourths. We then need to reduce the fraction
just like all the others we’ve practiced. Eight and 24 share a common factor
of eight, so we’re gonna divide the numerator and the denominator by eight here. When you divide the numerator and
the denominator by eight, you get the simplified fraction one-third. Based on the information given,
that would mean that adults need to sleep one-third of the day.
Simplifying fractions is a simple
process that helps us communicate effectively. And now, you have the tools to
simplify fractions and communicate more clearly to the people around you.