Let's compare two fractions?
Which fraction is bigger? 3 divided by 2 or 5 divided by 3?
We see that they are fractions with different denominators.
So, we will have to make the denominators equal to make the comparison.
Since the denominators are similar, we can compare the numerators and identify the bigger fraction.
So, to make the denominators equal, we need to know the NEUTRAL ELEMENT OF MULTIPLICATION.
Let's see:
One divided by one equals one.
Two divided by two equals one.
Three divided by three equals one.
Four divided by four equals one.
Five divided by five equals one.
Ten divided by ten equals one.
One hundred and twenty divided by one hundred and twenty equals one.
A thousand divided by a thousand equals one.
So, we see that the number 1 can be any fraction of a number divided by itself.
Example: 15 divided by 15 is equal to one.
The neutral element can become any number I need, being the same number over the other.
The neutral number allows me to put the missing number in the fraction, making the denominators equal.
The neutral element has other functions, but we will restrict ourselves to this function of making denominators equal.
Example:
I have two fractions
1 divided by 2 and 4 divided by 3
In the first fraction we have the denominator 2 but we do not have the denominator of the other fraction, which is the number 3, only the number 2.
So, I will include the 3 (denominator of the second fraction) in the first fraction, using the neutral element.
1 divided by 2 times 1 which is the neutral element.
The neutral element can be equal to 3 divided by 3. Because 3 divided by 3 is equal to 1.
And since 3 is the denominator of the second fraction, we must use the number 3.
So, 1 divided by 2 times 3 divided by 3.
So, 1 over 2 times 3 over 3 is equal to 3 over 6.
Now, taking the second fraction, we will do it the same way.
The second fraction is 4 divided by 3.
Using the neutral element, we can do...
4 divided by 3 times 1 which is the neutral element.
The neutral element can be equal to 2 divided by 2. Because 2 divided by 2 is equal to 1.
And since 2 is the denominator of the first fraction, we must use the number 2.
Therefore, 4 divided by 3 times 2 divided by 2.
Therefore, 4 over 3 times 2 over 2 equals 8 over 6
So, let's compare the two fractions:
3 over 6 and 8 over 6
We saw that the denominators were equal.
This is the importance, to equalize the denominators, using the neutral element.
So, we analyze the numerators and identify the largest among them.
Therefore, between 3 over 6 and 8 over 6, we conclude that the largest fraction is the second one, 8 over 6.
Now, let's go back to the first question:
Which fraction is larger: 3 over 2 or 5 over 3?
So, let's use the neutral element to equalize the denominators and find out which fraction is larger.
3 divided by 2 or 5 divided by 3.
So, let's take the first fraction and multiply it by the neutral element.
3 divided by 2 times 1
Now, can I replace the neutral element with 3 divided by 3
Let's see, 3 divided by 2 times 3 divided by 3?
It becomes 3 divided by 2, times 3, divided by 3 equals 9/6
So, the result of the first fraction 9/6
So, let's take the second fraction and multiply it by the neutral element.
5 divided by 3 times 1 (which is the neutral element)
Now, can I replace the neutral element with 2 divided by 2
Let's see, 5 divided by 3 times 2 divided by 2?
It is 5 divided by 3, times 2, divided by 2 is equal to 10 over 6
So, the result of the second fraction 10 over 6
Now, we can make the denominators of the fractions equal, see:
9 over 6 and 10 over 6
We can reach a conclusion about which fraction is the largest.
9 over 6 or 10 over 6?
The largest fraction is the one that has the largest numerator when its denominators are similar.
Therefore, the largest fraction is 10 over 6
Well, another video is over, but there are more videos to come...see you next time.
See you later, guys!
