In this sub-module, we’re going to work through some application problems involving percents, decimals, fractions, and ratios. I've included the solutions to the worked examples in text format because I thought it would be best for you to attempt the problems on your own and refer to the solutions for help if you are stuck or want to check your work; I don't think watching me solve problems will be overly helpful on its own, because everyone has their own problem-solving style.

If you've done the sub-modules on percent, decimals, fractions, and ratios you have all the necessary tools and this sub-module is all about learning to apply them.

The problems solved in this module and the problems for Check Your Understanding are pulled from the following resources:

Enslow Publishers

Online Math4All

Solution to Problem 1:

The ratio of phone calls to text messages is 21 : 3. But we can simplify this ratio.

Simplifying ratios is exactly the same as simplifying fractions. You can use any method, but I used the GCF method.

First, I found the factors of 3 and the factors of 21.

Factors of 3:

1 and 3 (because 1 x 3 = 3)

Factors of 21:

1, 3, 7, and 21 (because 1 x 21 = 21, 3 x 7 = 21)

Therefore the Greatest Common Factor of 3 and 21 is 3.

Therefore, I divided the 3 text messages by 3 to get 1, and the 21 phone calls by 3 to get 7.

The ratio 21 : 3 in lowest terms is therefore 7 : 1.

Solution to Problem 2:

We can write the ratio of 9th to 10th graders as is:

62 : 104

Because both numbers are even, we can simplify the ratio by dividing both numbers by 2, similar to how we would divide the numerator and denominator by the same number to simplify a fraction:

31 : 52

This ratio is the ratio of 9th to 10th graders.

To find the percent of Mr. Foley’s students that are ninth-graders, we need to first find the total number of students that Mr. Foley has:

62 ninth-graders + 104 tent- graders = 166 students in total

To find the percent of his students that are ninth-graders, we compute the following:

Therefore, 37% of Mr. Foley’s students are ninth-graders.

Solution to Problem 3:

When we get a score on a test, we can perform calculations similar to the following to find the equivalent percentage score:

So here, we can work backwards with the same method to find out how many Michael got right if he received an 80%. To do this, we perform the following calculations:

Therefore, Michael got 32/40 on his test. We can check to make sure that a score of 32/40 results in 80%:

If Michael got 32/40 on his test, he got 8 answers incorrect.

Solutions to Problem 4:

We are looking for the number of girls in the school and we are told that ⅔ of the total school are boys, so therefore ⅓ of the school are girls.

Now, we want to find ⅓ of 450.

Whenever we are looking for a fraction or percent “of” something, we are going to need to multiply.

Therefore, there are 150 girls in the school.

Solutions to Problem 5:

Alternatively, you could note that with a discount of 20% and a 13% tax rate, you could calculate a discount of 7% to account for both.