We all have learned addition in maths and are quite confident to do it even today despite learning it in the early years of school. Did you ever wonder what makes you so confident? It is a process of addition using standard algorithms. The algorithm is a set of procedures that, when followed correctly, will always give you the right answer. We have learned this process so well that even today we will be able to do addition whenever anyone tells us to do. What is algorithm in maths and how do we solve a standard algorithm? We will cover them all.
1. What is an Algorithm in Maths?
Before understanding how to solve addition using standard algorithm, let us see what is algorithm in maths. An algorithm in maths is a set of rules and instructions made to solve a problem. It is a procedure that tells about how to solve a mathematical problem or computation. It is the most used thing in maths as every topic and its problem has a certain algorithm that has to be followed to get the right output. Every algorithm that exists today is arranged sequentially, so avoid missing any steps as it will cause a hindrance in finding the solution. (See What is a Mathematical Sentence Example?)
2. How do You write an Algorithm?
An algorithm is written after analyzing any problem. Algorithms are the steps or procedures that have to be followed to achieve a certain solution. These procedures take into consideration every step that is important to get the problem solved. Following are some of the steps you need to follow to write an algorithm:
- Getting an idea and details of the problem
- Analyzing the problem
- Develop a high-level and simple algorithm
- Refining the draft with more details
- Review the final algorithm
3. What is an Example of Algorithm in Maths?
An algorithm in maths is any set of processes that has to be followed to solve a certain problem. There are different algorithms for different problems in maths. We can take the example of- What is 78 divided by 3? It could be achieved by following this algorithm.
- How many times does 3 go into 7? The answer is 2, since, 3 × 2 = 6.
- How much is left now? 1 is left here as the remainder (7 − 6 = 1).
- From 78, we have the number 8 left to get solved. It will be placed after 1, the remainder, which makes it 18. So we calculate the number of times 3 goes into 18. The answer is 6.
- The quotient in this algorithm is 2 and 6 together, which is 26. 26 is the final answer.
This is an example of how algorithms are in maths. (See How can You Find the Sum of the First 100 Natural Numbers?)
4. What is Standard Algorithm in Maths?
A standard algorithm in maths is a set of procedures that are followed to solve a certain type of question. It is conventionally taught as a method to solve mathematical computations. These algorithms are the same for a specific category and will have to be followed by anyone who is solving that particular type of mathematical problem. (See What are the Types of Functions?)
5. What is an Example of Standard Algorithm?
The standard algorithm is a set of processes that have to be followed to achieve a final result for certain types of problems. In maths, there are different algorithms for addition, multiplication, division, and subtraction. The algorithm for each of these four different forms of calculations remains the same and does not change. Whatever the value is, it can be solved by applying and following the correct algorithm. So, before we discuss what a standard algorithm for addition is, let us understand the standard algorithm in terms of subtraction:
What do you get when you subtract 253 from 486?
The algorithm to solve this problem goes like this:
- You start by arranging these numbers. 486 will come above 253 for solving this problem. They will be arranged sequentially in Ones, Tens, and Hundreds- forms of tables. The solving will start from the right digits and go to the left.
- 3 from 253 will be subtracted from 6 which will leave the remainder of 3.
- 5 will be subtracted from 8 and the remainder will be 3 again.
- 2 from 253 will be subtracted from 4 which will leave the remainder of 2.
- All the final digits together will be counted as the answer to this question. These digits will be acknowledged from left to right.
- So, the answer to the question is 233.
This is an example of a standard mathematical algorithm for subtraction. Check out Why is Mathematical Concept Important?
6. What is a Standard Algorithm for Addition?
The standard algorithm for addition is a very simple and basic set of rules or instructions that have to be followed to add any two numbers. The rules of addition using standard algorithm has some basic steps that have to be followed. These are:
- First of all, the numbers should be arranged according to their place values. The digits belonging to the tens place have to come together for the proper calculation.
- The second rule is to add all the numbers together that fall in the same place value. The addition will start from the ones digit place, ie., from right to left. The extra digits will be carried forward to the next digit that falls under the subsequent place value and will be added there.
7. How to do Addition using Standard Algorithm?
The addition using standard algorithm is an easy and simple additive process that will help you achieve the answer to any mathematical problem. It follows some pre-defined rules to reach the solution. Here you will look at an example to see how addition using standard algorithm works.
What do you get when you add 168 and 53?
- As you can see in this question, both the numbers here do not have the same place values, the number 168 is having a place value till the hundreds because it has three digits whereas the number 53 has a place value till the tens because of the two digits. This difference in place values needs to be taken care of while solving this problem.
- So according to addition using standard algorithm, any number can come above the other. In this case, you can take 168 above 53 for addition.
- The digits will be written according to the place value. For instance, 3 from 53 will come under 8 from 168 because they both have the same place value of ones. 5 will come under 6 as they both share the tens place value. The digit 1 will be written alone because there isn’t any other digit that has the place value of hundreds that 1 has.
- When you add 8 and 3, we get the answer 11. So the 1 that is at the right will be carried forward to 6 and will be added along with 6 and 5.
- The sum of 6, 5, and 1 is 12. Here, again, the 1 will be carried forward to 1 at hundreds’ place and will be added with it.
- So, at hundreds’ places, you will get the sum 2 which is 1 + 1.
- Looking at the remainder from left to right, you get the answer 221.
8. How do You solve a Standard Algorithm?
You have just read how to solve addition using standard algorithm, and it is quite easy because of the pre-defined set of rules. To solve a standard algorithm, you need to follow these rules step by step and the conclusion will be easy to reach. In maths, there are different standard algorithms, different for each of the mathematical operations, i.e., addition, multiplication, division, and subtraction. The algorithms remain the same throughout even when the values for mathematical operation change. These sets of rules are universally accepted and followed. (See What are Some Examples of Categorical Variables?)
9. What does it Mean to Solve using the Standard Algorithm?
When you solve using the standard algorithm, you are using a method that is universally accepted and followed to solve problems. There are few chances of making mistakes and not reaching the conclusion because these rules are systematic which reduces the chance of arriving at the wrong conclusion. These rules are different for different types of problem categories but remain the same for every problem under that category. (See What is the Very Last Number in the World?)
10. Why do You use Standard Algorithm?
You use a standard algorithm for solving any problem with ease. The steps are sequentially prepared which when followed correctly, will reduce the chances of mistakes. You will get the same answer every time you solve using these algorithms which also makes them reliable. The step-by-step process makes them easier to understand and they avoid confusion by offering a single solution to any problem. These are basic and clear rules that make solving easy for all.
Now you know how important an algorithm is for any activity to get performed correctly. Through this article, you got a quick recap of standard algorithms for addition in maths. I think this might have made you nostalgic too! So now, share this article with your friends with whom you used to do addition using standard algorithm in school and relive those good old days. (See What is a Circle Degree Chart?)