Welcome to lesson on ratios the goals for this video to determine ratios and simplify ratios.
A ratio is a comparison of two quantities in the form of a quotient.
The ratio between A and B can be written three different ways.
A to B, A colon B or A divided by B written in traction form.
And ratios can also be simplified just like fractions can.
So let's take a look at some examples of how we can create ratios.
A class has 15 female students and 12 male students. What is the ratio of males to females?
One of the most important things about a ratio, is its order.
So here we want the ratio of males to females.
Since there are 12 male students and 15 female students.
The ratio would be 12 to 15 and I'm gonna go ahead and write this in fraction form
So it will be 12 to 15.
Now as mentioned before, most of the time ratios are in simplest form. So we can simplify this just like we would simplify the faction twelve fifteenths
So since 12 is three times four.
And 15 is three times 5.
We can see they have a common factor of three.
So the simplified ratio would be four to five.
If we want the ratio from females to males.
There would be 15 to 12.
Which would simplify to 5 to 4.
And then lastly if want the ratio of females to the total number of students.
Well there are 15 female students.
The total number of students would be 15 plus 12 or 27, so the ratio would be fifteen to twenty seven.
And again this can be simplified.
15 would be three times 5, 27 is three times nine's so they have a common factor three.
So the ratio of female students to total students would be five to nine.
Let's go and take a look at another example.
The team played a total of 24 games last season.
They won 18 games and lost six games.
What is the ratio of wins to losses?
Well if they won 18 games and lost six games the ratio would be 18 to 6
Now we can simplify this.
18 is the same as three times 6.
And we can write six as one time six. So the greatest common factor
between 18 and six is six. Therefore the ratio is 3 to 1.
Now it is important that we leave this as a ratio of 3:1 and not just right 3.
Because three by itself would not be a ratio comparing wins and losses.
So even though this quotient is equal to three.
A ratio must compare two numbers.
Next what is the ratio wins to total games?
Well there's 18 wins and the total games would be 18 plus 6 or 24.
And again this simplifies.
The greatest common factor of 18 and 24 would be 6
So eighteen to six times three and 24 six times four.
So the simplified ratio would be three to four.
And then lastly the ratio of losses to total games. Well there were six losses and there were 24 total games or six to 24.
Since 24 is equal to six times four.
Six would simplify out and the ratio would be one to four.
And hopefully that should make sense.
Because the ratio of wins to total games was three to four.
Then the ratio of losses to total games should be 1 to 4 accounting for all of the games played
Okay, I hope you found this video helpful.
Thank you for watching!