Hello and welcome to Tutoring Hour!
In this video, we'll learn how to simplify fractions.
Let’s take this pizza, for instance.
We'll slice that into six equal parts.
If you gobble three slices,
what fraction of the pizza will be left over?
We’ll have three over six.
Now to make this fraction simpler,
we can put the leftover pieces together.
You can see that one-half of the pizza is left.
So three-sixths when reduced or simplified is nothing but half.
The pizza-eating fun aside, let’s see how this can be done mathematically.
One simple, but very effective, way is to write the numerator and denominator as the product of their prime factors.
So 3 can be written as 1 times 3 or just 3,
and 6 can be written as 2 times 3.
The 3 in the numerator and the 3 in the denominator cancel each other out,
and we are left with 1 over 2.
Now we cannot reduce this any further as the only common factor between the numerator and denominator is 1.
From this we can conclude that a fraction is said to be in its simplest form
if 1 is the only common factor of its numerator and denominator.
As simple as ABC, isn’t it?
Let’s gallop through by reducing or simplifying one more fraction.
12 over 15
Now 12 can be written as 2 times 2 times 3,
and 15 can be written as 3 times 5.
The 3 in the numerator and the 3 in the denominator cancel out each other,
and multiplying what’s left, we have 4 over 5.
So 12 over 15 is reduced to 4 over 5.
Great job!
Now we’ll take a look at how to simplify fractions using the GCF.
The fraction is 10 over 35.
Before we leap in, let’s list out the factors of the numerator 10.
And they are 2, 5, and 10.
The factors of 35 are 5, 7, and 35.
The factor 5 is common to the numerator and the denominator.
Hence 5 is our GCF.
Now we'll divide the numerator and denominator by 5.
First, let’s divide 10 by 5 and we have a 2, and 35 divided by 5 is 7.
And our reduced fraction is 2 over 7.
2 and 7 have no common factors except 1.
Hence we can conclude that the fraction has been reduced to its lowest terms.
We’ve cracked one more!
Let’s forge ahead by simplifying one more fraction using the GCF method.
This time we have 18 over 24.
First, we'll list out the factors of 18.
The factors are 2, 3, 6, 9, and 18.
Let’s also write down the factors of 24.
And they are 2, 3, 4, 6, 8, 12, and 24.
The factors 2, 3, and 6 are common to both lists.
However, the greatest common factor is 6.
Hence we will divide both the numerator and the denominator by 6.
So 18 divided by 6 is 3,
and 24 divided by 6 is 4.
So our reduced fraction is 3 over 4.
Now that’s what we call simplifying!
Looks like we have totally nailed it and in a jiffy!
It’s time to start putting it into practice
by solving some of these worksheets @Tutoringhour.com.
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