In this video we discuss what are ratios and proportions. We go through examples of ratios and proportions and cover how they are related. We also discuss using the method of cross products in proportion problems.
Transcript/notes
A ratio is a comparison of 2 quantities. It compares 1 number to another number, such as hours to pay, miles to gallons and even one brand of shampoo to another brand of shampoo.
It is typically written as a fraction, such as a over b, but can be written as a colon b or a to b. And all of these are pronounced the same “a to b”.
As an example, if a company sold 2 types of index cards, thin ruled and wide ruled. Sales of thin ruled were 250, and sales of wide ruled were 100. What is the ratio of sales of thin ruled to wide ruled?
When we write a ratio, we take the first number mentioned, in this case thin ruled, and put that on top, so 250 in the numerator, and the second number, wide ruled, which is 100, on the bottom in the denominator. So, we have the fraction 250 over 100, which is pronounced “250 to 100”.
And ratios can be reduced. In this case, since both 250 and 100 are divisible by 50, we can reduce this to 5 to 2.
Now for proportions.
A proportion is made up of 2 ratios that are equal. For instance, 4 to 7 equals 8 to 14. To determine if a proportion is true, you check to see if their cross products are equal.
The cross products are found by multiplying the numerator of the 1st fraction or ratio by the denominator of the 2nd fraction and multiplying the denominator of the first fraction by the numerator of the second fraction, and if these values are equal, the proportion is true. This is often written as a over b equals c over d if a times d equals b times c, and this is called the method of cross products.
In our example of 4 over 7 equals 8 over 14, using the method of cross products, we have 4 times 14, the numerator of the 1st fraction times the denominator of the 2nd fraction, and this equals 56. Next, we have 7 times 8, the denominator of the first fraction times the numerator of the second fraction, and this equals 56. 56 equals 56, so this proportion is true.
Many times in proportion problems, you are required to find an unknown value, such as in the proportion y over 9 equals 25 over 45. In this case we will use the method of cross products to set up an equation to find the value of y.
We have y times 45 equals 9 times 25. And, 9 times 25 equals 225, giving us 45y equals 225. To get the y alone, we can divide both sides by 45, so y equals 225 over 45. 225 divided by 45 equals 5, so we get y equals 5.
Timestamps
0:00 What is a ratio?
0:20 Example of a ratio
1:05 What is a proportion?
1:17 Method of cross products
2:08 Finding an unknown value using the method of cross products
0 Comments