By the end of this lesson, you should be able to
When given quantitative information, it is sometimes difficult to figure out what to do first, or if there are different ways to simplify an expression. For the following two situations, read the information carefully on your own. Before starting the problem on your own or in your small group, we will discuss rules of order of operations, when multiplication and division occur.
A. A total of $12,840 bonus money is to be divided among the three directors. You calculate what your bonus will be. Several days later, the vice president receives an email that there was a mistake, and the actual amount to be given as a bonus is twice as much as she announced. Write an expression that represents the above scenario of your actual bonus. Determine the amount of your actual bonus.
B. What if the vice president had told you all of the information right away? How could you have correctly calculated your bonus in a different way? Hint: What would the expression now be to represent the order the information was given?
2. At a financial planning course, 35 people have a total of $245,000 in savings, but they have four times that amount in credit card debt. If each person has about the save amount in savings and debt, about how much credit card debt does each person have?
A. Write an expression that represents the amount each person has in credit card debt given this scenario.
B. Determine the amount each person has in credit card debt.
When performing arithmetic operations, there can be only one correct answer. We need a set of rules in order to avoid confusion of which answer is correct. Mathematicians have devised a standard order of operations for calculations involving more than one arithmetic operation.
Why do we have these rules? Let’s do a problem to demonstrate.
Our expression from Question 1 was \(12840\div 3\times 2\), which produces 8,560 when we perform the operations from left to right, according to the rules above.
First, we divided 12,840 by 3, and then we multiplied by 2 to give us 8,560.
Now, let's see what happens if we perform the operations from right to left: we'd start by multiplying 2 by 3, which gives us 6. Then we'd have \(12840\div 6\), which produces 2,140. Wait a minute. This is a much smaller bonus! What happened?! Working from right to left does not always lead to the same answer.
For the following practice problems, you will be working to simplify expressions that contain addition, subtraction, multiplication, and division.
3. \(10\div 5\times 3\times 3\)
4. \(10 - 8\div 2 - 7\)
5. \(4\times 8 - 22\div 11\)
6. \(35\div 7\times 3 - 3\times 2\)
Opioids are a class of drugs that include the illegal drug heroin, synthetic opioids such as fentanyl, and pain relievers available legally by prescription, such as oxycodone (OxyContin ® ), hydrocodone (Vicodin ® ), codeine, morphine, and many others. 6 Patients prescribed higher opioid dosages are at higher risk of overdose death. In a national sample of Veterans Health Administration (VHA) patients with chronic pain receiving opioids from 2004–2009, patients who died of opioid overdose were prescribed an average of 98 MME/day, while other patients were prescribed an average of 48 MME/day. Calculating the total daily dose of opioids helps identify patients who may benefit from closer monitoring, reduction or tapering of opioids, or other measures to reduce risk of overdose. (Note: MME = Morphine Milligram Equivalent. 7 )
HOW SHOULD THE TOTAL DAILY DOSE OF OPIOIDS BE CALCULATED?
Step 1: DETERMINE the total daily amount of each opioid the patient takes.
Step 2: Using the table below, CONVERT each to MMEs—by multiplying the dose for each opioid (mg per day) by the conversion factor.
Step 3: ADD them together.
Opioid (doses in mg/day)
Conversion Factor
7. John suffers from chronic back pain. On days when he is feeling a low amount of pain, he takes 4 tablets of Hydrocodone at 5 mg each. On days that he has a high amount of pain, he takes 8 tablets of the Hydrocodone at 5 mg each and 2 tablets of Oxycodone at 20 mg each.
A. Calculate his daily dose of opioids for days with a low amount of pain.
B. Calculate his daily dose of opioids for days with a high amount of pain.
8 The infographic below 8 states that each day 78 Americans die from an Opioid overdose.
A. Assuming there are 365 days in a year, about how many Americans die each year from an Opioid overdose?
B. About how many Americans die each month? Round to the nearest person.
9. From 2007 – 2015 (which is nine years in total), there were 4,036 Virginia deaths related to prescription Opioid overdose. On average, how many deaths were there for each year? Round to the nearest person.
Simplify the following:
6. Maria is planning a party. She figures out that food will cost $20 for each pizza and $5 for each snack that she buys. Maria creates the following expressions for different party scenarios. Simplify them to help Maria determine the potential cost of each party scenario.
\(20\times 3 + 5\times 3\)
\(20\times 10 + 5\times 10\)
\(20\times 2 + 5\times 4\)
7. At each marketing event, Marylou puts 40 brochures from her business on each of the 12 tables in the event room. The brochures come in boxes of 120. Which expression below correctly determines how many boxes of brochures are needed to complete this task?
(iii) 40 × 12 ÷ 120
8. During 2016, there were more than 63,600 overdose deaths in the United States. For every 100 drug overdose deaths, 66 involved an opioid.
Determine the number of drug overdose deaths that involved an opioid in 2016.
If there are 365 days in a year, about how many overdose deaths were there each day in 2016?
How many drug overdose deaths that involved an opioid were there each day in 2016?
