In common parlance, Order of Operation is the sequence of activities to complete a task. It is similar to Math operations too. Maths is a complex subject involving various operations we use to arrive at a solution.
In mathematics order of operations are the rules that tell us the sequence in which the various operations of an expression have to be solved. The order is usually remembered for convenience by the letters PEMDAS. Each letter denotes a mathematical operation. P – parentheses, E- exponent, D- division, M- multiplication,A- addition, and S- Subtraction
The math problem must therefore be solved by solving anything in the parenthesis first, going on to the exponent, the multiplication or the division, and then addition or subtraction. We use this order in many activities of daily life too.
In this article, let us look at some real-life situations where the order of operation is used.
Applications of the order of operations in our day to day lives
1. Shopping- bills
When we are out shopping, the order of operations is always used. During billing, the price of multiple pieces of an object is obtained by multiplication. The sum of various items is added. Subtraction of the discount amount, if any is also done. Then the total amount to be paid is arrived at. It makes the calculation error-free and systematic.
2. Combined bills
A clothing store is organizing a sale with a price reduction on certain garments. If two people decide to buy clothes together on one bill, the order of operation can be used to calculate how much each one has to contribute. The cost of the garments is added and the total amount is paid. The discount amount is subtracted from the bill and the contribution of each is calculated by division.
3. Calculating savings
A person saves their salary for a year and puts together a particular amount. The savings per month are added up to generate a larger amount. A part of it is given to charity, and a part of it is spent on a holiday. These two expenditures are added together and subtracted from the annual savings. The order of operations is thus used to calculate the final savings of the person.
4. Admission for courses
A dance school offers courses at three different price packages. There are a particular number of admissions every day. The total money earned in the day is calculated by multiplying the price by a number of candidates and the total across all price packages in a week can be calculated again by using the PEMDAS rule.
In the travel industry, the PEMDAS rule can be applied to calculate the available seats on a flight and the booking status, the fares, and organizing schedules as the entire procedure involves a lot of mathematical operations. For travelers, the PEMDAS can be used to calculate foreign exchange rates, convert kilometers to miles, or calculate how much time one needs to get to the railway station or airport according to the distance.
6. Online shopping
When we order a pizza online with friends, the total cost and the tip, delivery charges, or service charges are added to the bill. This is equally shared among the total number of friends. There is addition and division that are carried out. This is a real-life example of where PEMDAS is put to use.
Manufacturing units also require many calculations to be made simultaneously. In the product design and manufacturing fields, order of operations is crucial to ensure you have the right amount of raw material and stock. The wrong order of operations can lead to over-purchasing or even a shortage of material needed to complete production.
The order of operations is also greatly used in dosage calculations in medicine. The dosage based on quantity per kg is known and is calculated according to the weight of the patient. Similarly, the per day dose is also calculated by dividing the permitted daily quantities by the number of times the medicine has to be administered. Any previous doses given are considered and the dose is again titrated accordingly. Multiplication, division, and addition are put to use here, demonstrating the use of the order of operations.
While cooking, the PEMDAS is extensively used without us even realizing it. For example, the recipe for a cake, mentions four people. But the required preparation is for ten people, and the order of operations is used to calculate the quantities of various ingredients. Firstly the division is done to calculate the per person quantity and then multiplication into the number of people is done to obtain the total quantity.
Some programming languages also work on the same principles of PEMDAS. Various online applications like Microsoft Excel, Google Sheets, Quip, WPS spreadsheets, etc. follow the order of operations to determine the order in which calculations are to be performed.
Interesting ways to learn and practice order of operations
Basic math operations are taught to students during the elementary stage. As they progress they have to learn a combination of operations to be in a specified order. This is where the worksheets are handy. Regular practice will lead to perfection and help in putting the technique to use wherever required.
2. Games and activities
Games and activities help in making the most difficult tasks enjoyable. Fun-filled experiences always help to retain the associated subject in memory and help in better comprehension. Here are some games and activities that will make learning the order of operations less difficult.
3. Using it in daily life
When the child learns a new concept, it is also important that he or she learns to apply it in daily life situations. Order of operations is something a child would be using quite often. Regular practice and reinforcement will make the child think and work accordingly. For example, when the child goes out with friends to have ice cream, the order of operations as discussed earlier can be put to use. The price of all the icecreams is added and a bill is created. The cost is then equally split by all through means of division. Such real-life situations will improve the critical reasoning of the child.
4. Math mnemonics
The child may find it difficult initially to remember the right sequence in the order of operations. It is a good idea to use mnemonics for this purpose. A fun way for children to remember this is by the sentence “ Please Excuse My Aunt Sally”, where each word begins with the letter of the order of operations. P – parenthesis E- exponent M- multiplication D- division A- addition S- subtraction.
Order always helps things to be done in a systematic manner. Similarly, the order of operations gives us a consistent sequence to solve problems in math. Without the order of operations, we might all come up with different answers to the same problem.
To sum up, PEMDAS refers to different situations where everything goes through multiple steps in a predetermined sequence. Order of operations keeps math consistent. If we consider a normal desk calculator, it works as per the operations we feed in. If the PEMDAS rule is not followed, even the calculator will display an incorrect result.
Now that we know how important remembering the order of operations is, the above methods and activities might be of help.