Simplifying Common Fractions Grades 3 and 4
This lesson is on simplifying or reducing common fractions.
This is a 3rd and 4th grade level exercise.
To
simplify a fraction you need to figure out the greatest number that can be
divided into both the numerator and the denominator equally.
Many children have trouble understanding that a
simplified fraction represents the same amount as the original fraction. To
illustrate this, it is often helpful to see the fraction as shaded parts.
Let’s look at an example…
This fraction shows that 4/8 of a circle is shaded.
Have your student count the number of parts shown in the circle. The total
number of parts including both the shaded and blank areas is the denominator of
the fraction. Then have your student count the number of shaded parts. The
shaded area is the numerator.
Now let’s look at simplifying the fraction. If we
divide both the numerator and the denominator by the number 2, we get the
fraction 2/4. This is shown below.
4/2=2 and 8/2=4
If we look
at the fraction for 2/4 we can see that the same amount of the circle is
shaded.
This fraction can be simplified further by dividing
both the numerator and the denominator by 2.
This gives
us the fraction 1/2. Again show your student that the same amount of the
fraction is shaded.
Simplifying using the
greatest common factor:
Factors are the numbers that multiply to get
another number. For example the natural factors of 6 are...1, 2, 3 and 6.
To
simplify a fraction we want to find the greatest common factor. This
will be the largest number that is a factor of both the numerator and the
denominator. So for the fraction 6/12, the greatest common factor is 6.
Therefore
6/12 can be simplified as 1/2.
Factoring numbers:
Sometimes
it is necessary to “factor” the numbers to find the greatest common factor. To
factor a number, write down all of the factors that can be used to make that
number. Sometimes it is necessary to take one factor at a time and break them
down into smaller parts.
For
example, to factor the number 42 we can begin by writing down 1 and 42 because
all numbers have themselves and 1 as factors. Then because 42 is an even number
we can divide by 2, which will give us the factors 2 and 21.
Now look
at the newfound factors and determine if they can be factored. The number 2 is
as small as it can get but 21 can be factored into 3, 7.
This means
that the numbers 3 and 7 are also factors of 42.
Now check
to see if these numbers can be broken down any further. 14 can be divided by 7,
which is already in the factor list and 6 can be factored to 2 and 3 which are
also in the list. So if written in numerical order, the factors of 42 are 1, 2,
3, 6, 7, 14, 21 and 42.
So if you
are trying to simplify a fraction like 12/42, you would factor 12 the same way
and then look for the greatest common factor between the two numbers. The
natural factors of 12 are 1, 2, 3, 4, 6 and 12. The greatest common factor for
both 12 and 42 is the number 6.
So to
simply 12/42 you would divide both the numerator and the denominator by 6. You
then get the simplified fraction 2/7.
Discuss
with your student the idea behind simplifying. Basically we want them to
understand that simplifying means to find the simplest or easiest answer. This
helps people to understand what portion a fraction truly represents. After all
1/2 is easier to understand than 16/32. You can even show that a large fraction
such as 16/32 can be reduced by dividing by the highest number. In this case
the highest number is 16.
Reducing larger numbers as an example can show
students why simplifying fractions is necessary and commonly asked for. You can
take this lesson further by discussing the reasoning of simplification and
having your students’ share their thoughts. Many students benefit from hand on
lessons such as making fractions out of construction paper or by using
commercial math manipulatives.
For your convenience here is a practice worksheet on
simplifying fractions. Remember the Home School Cyber School Alliance offers
free and low cost tutoring.
For more information visit
www.homeschoolcyberschoolalliance.org