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Real World Math: Fractions

1. Criminal Justice

There are many important formulas that are used in the field of criminal justice. For example, the Widmark formula is used to calculate the blood alcohol concentration (BAC) at a particular time for an individual. Widmark's research found that the average man's body can hold alcohol in even distribution in 73% of its weight. In other words, 73% of a 150-pound man's body holds all the alcohol he consumes, in even distribution. 73% of 150 pounds = 0.73 - 150 = 109.5 pounds. Widmark found that the average for a woman's body to hold alcohol in even distribution is 66%.

Change 66% to a reduced fraction (proper fraction) and to a decimal (rounding your answer to the nearest thousandth).
Give an example of a particular weight for a woman, and find the average portion of the body that holds the alcohol.

2. Business

Many interest rates, such as those on car loans, credit cards, and home loans, are given in as a percent. However, if you need to make any calculations with the percent interest rate, you must convert it to a decimal.

Research and find the interest rate, as a percent, for a particular credit card.
Change the interest rate percent to a decimal and then to a fraction.
If you wanted to compare your researched rate to 12 1/5%, how could you change this percent to a decimal? Compare the 12 1/5% to your researched interest rate, and explain which interest rate is better.

3. Medical

It is important that physicians know how long a medicine will stay in a person's body to keep a sufficient amount so the person does not overdose. For example, a patient takes a pill that has a dosage of 50 mg. (milligrams) and wakes up the next day with a particular percentage of the medication washed out.

Demonstrate your knowledge of conversions by first choosing a percentage of the medicine that is washed out the next day, and then convert this percentage to a decimal and then a fraction.
How much medication remains in the body after the percentage amount of your choosing is washed out?

4. Landscaping

When buying mulch for your lawn, you find that it is ordered in square yards. However, you have the area measurements of your lawn in square feet, found by multiplying the length of the yard times the width.

Demonstrate with an example by first giving the size of the yard in square feet (length and width), and then convert how much in square yards is needed to cover the area in mulch. (Hint: Research to find how many square feet equals 1 square yard).
Because lawns may not come out with exact whole-number measurements, give an example that ended in a fractional value. How would this change your conversion to square yards? Show with a fractional amount example.

Solution Preview

1.
>Change 66% to a reduced fraction (proper fraction)

33/50

> and to a decimal (rounding your answer to the nearest thousandth).

0.660

> Give an example of a particular weight for a woman,

120 pounds

> and find the average portion of the body that holds the alcohol.

120 pounds * 0.660 = 79.2 pounds

2.
> Research and find the interest rate, as a percent, for a particular credit card.

Fusion Platinum Mastercard: 9.9%

> Change the interest rate percent ...

Solution Summary

Solutions to 4 real-world problems involving fractions and percentages:

1. Blood-alcohol concentration
2. Credit card interest rates
3. Medication
4. Lawn size

$2.19