What Is A Proportion? - How To Solve For Proportions Using Cross Products - Is A Proportion True?

In this video we discuss what are proportions? We also cover how to solve for an unknown value in a proportion, what makes a proportion true and we go through a few examples of proportions.

Transcript/notes
What is a proportion?
A proportion is made up of 2 ratios that are equal. And, if you recall, a ratio is a comparison of 1 number to another number, such as hours to pay or miles to gallons.

Ratios are typically written as fractions, such as a over b, which is pronounced “a to b”. An example of a ratio could be slices of cheese pizza to slices of pepperoni pizza. If a pizza joint sold 40 slices of cheese pizza and 15 slices of pepperoni pizza, then the ratio of cheese to pepperoni would be 40 to 15. And this fraction can be reduced as both numbers are divisible by 5, which results in 8 to 3 as the ratio.

Again, a proportion is made up of 2 ratios that are equal. 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.

For example, the proportion 4 to 3 equals 16 to 12. Is this proportion true? Checking the cross products we have 4 times 12, the numerator of the 1st fraction times the denominator of the 2nd fraction, and this equals 48. Next, we have 3 times 16, the denominator of the first fraction times the numerator of the second fraction, and this equals 48. 48 equals 48, 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.
Here are a couple of more examples on the screen for you of solving a proportion for unknown values.

Timestamps
0:00 What is a proportion and ratio?
0:22 Example of a ratio
0:42 How to determine if a proportion is true
1:10 Example of checking cross products
1:37 Unknown values and proportions
2:17 More examples

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