Best Number: How to Choose F,D, or P

What is the best number to use when completing application problems with fractions, decimals, and percent?

#1 – What Usually Happens

How often do you see student answers that do not reflect the best number for application problems with fractions, decimals, and percent?

For example, “To paint a room, Mr. Wilks will need two gallons of paint. He opens gallon-sized paint cans to determine if he will have enough. The amount of paint in each can is as follows:

# 1 is 1/3 full
#2 is 3/4 full
#3 is 1/2 full

How many gallons of paint does he have altogether?

How many times do students answer the question with an improper fraction, such as 19/12 vs 1 7/12? When students give me this kind of answer, I respond with the following questions.

For example:

1. “Does this form of the fraction tell me how many literal gallons he has?”
2. Would this form of the fraction make sense? Why or why not
3. “How can you change the number 19/12 to make sense?”
4. “Ok, if 19/12 is 1 7/12, how many gallons does this represent?” (2 gallons)

Likewise, students must also understand when the best answer should be in a fraction, decimal, or percent form.

#2 – Fractions: Best Numbers

First, let’s consider when it is best to represent a number as a fraction.

When there are non-terminating decimal numbers, such as o.333…, written instead as 1/3.
If measurements used for a recipe which uses U.S. Customary Measurements: 1/4 cup, 1/2 a teaspoon
For equalizing portions: 1 cake, divided into eight equal pieces, on serving = 1/8 of the cake
Use of ratios: 1 part cornstarch to 3 parts water, 1:3 ratio, 1/3

Best Number: measuring cup pouring out flour

#3 – Decimals

Second, decimals are best used when the aim is precision. Below are examples.

1. Basic Math Operations: adding, subtracting, multiplying, and dividing numbers with decimals
2. Representation of money: $2.19
3. Consumer Math Calculations: discounts, interest, 1.2
4. Precise Measurement: science, medical, and engineering fields measures, such as 3.8 mm
5. Statistics: when comparing decimals such as 1,236, 1,237, 1.238, and 1.239.
6. Measurements used for a recipe written in metric measures: 1 gram of flour, 5 ml vanilla extract
7. Medications: 5 ml of couph syrup

Best number: tablets, medicine, supplement, vitamin, pharmaceutical, cure, medical treatment, remedy, pill, prescription, medicine, medicine, medicine, medicine, medicine

Close-up of a healthcare professional with arms crossed wearing medical scrubs and stethoscope.

#4 – Percent

Third, percentages are most often used in the following ways:

1. Sales and Discounts: 60% markdown, 20 % markup
2. Statistics representing part of a whole: 90% percent of a given shampoo is water.
3. Poles and Surveys: A survey is taken in a classroom to determine the percentage of students who prefer chocolate candy with nuts, chocolate candy without nuts, and those who do not like chocolate or nuts. The results: 30 % prefer without nuts, 60% prefer with nuts, and 10% do not like nuts or chocolate.
4. Test Scores: Test scores given in percent provide a number that is easy to visualize and understand, particularly if letter grades are associated with scores: 70 -80 % = C, 80-90% = B, and 90-100% = A.

Best NumberLaptop displaying charts and graphs with tablet calendar for data analysis and planning.

Conclusion

In conclusion, when students understand the best number to use when describing solutions to application problems, they will provide a much clearer understanding to others. These concepts are also important when students begin writing research papers.