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What is a Standard Algorithm in Math? – Definition & Examples

standard algorithm

Can you recall what the term ‘standard’ means? Or perhaps, the meaning of the word ‘algorithm’? The standard algorithm comprises ‘Standard’ and ‘Algorithm’. Standard means the generalized way or the way most people do things, for example, brushing their teeth, bathing, or eating. Algorithms are nothing but the step-by-step process of carrying out a task. Thus a standard algorithm in mathematics is the stepwise method of completing a problem. In this article, you will learn and get familiar with what is a standard algorithm and the standard algorithms for addition, subtraction, multiplication, and division. 

What is the Standard Algorithm?

Before learning the standard algorithm in Math, let us understand the concept of the standard algorithm. Everything we do in our daily life is linked to the standard algorithm. From waking up in the morning to sleeping at night, we have been following an algorithm like everyone else on this planet. For instance, if we need to bake a fluffy and delicious cake, we must follow certain steps, or the result will be garbage. There are step-by-step procedures to bake a cake and get a perfect cake out of the oven as follows:

Step 1: Find the recipe for the cake you want to bake.

Step 2: Look for all the ingredients, and if you can’t find them go to the store to buy them.

Step 3: Mix all the ingredients in the proper order by taking the correct measure of each ingredient as instructed in the recipe.

Step 4: Put the mixture in a pan and bake for a set time.

Step 5: When baked, take it out of the oven and refrigerate it for frosting.

Step 6: Take it out of the refrigerator and decorate it according to your desire.

That’s it; you have now learned how to make a delicious cake all by yourself. If you keep using these steps in the future, you won’t have to look at the recipe. You will become a master of tasty baking cakes. Although baking a cake is not an algorithm, this was necessary to understand why a step-by-step approach is essential. 

Think what would have happened if you didn’t follow the steps and mixed all the ingredients without measuring them or baked all the ingredients before mixing them. The ingredients would become too hot to handle, and you would have to throw everything away. Therefore remember to follow a standard algorithm everywhere. Similarly, in Math, if you don’t follow the standard algorithm, you will have wrong answers. 

 Next, this article will look at the standard algorithms for all the basic arithmetic operations like addition, subtraction, multiplication, and division. We will learn all the algorithms by taking examples in each case.

Standard Algorithm Addition

The standard algorithm for addition is the easiest of all. This is also the first algorithm taught to the students. The steps for standard algorithm addition are as follows:

  • Write the numbers horizontally. If the numbers are given as 346 + 294, then write them as:

            346 + 294 = 640

  • Add the one’s place first followed by tens place, hundreds place, thousands place, and so on. 
  • If the sum of digits is less than 10, write them below the digits. 
  • If the sum of the digits at any place is greater or equal to 10, write the one’s place of the result in the answer and send the tens place of the result to the preceding addition. 
  • If there is no preceding addition, write the answer’s result.  

For example, Add 532 with 859

Write the numbers horizontally.

532 and 859

Add the digits from one’s place onwards and see whether numbers are getting carried or not.

532 + 859 = 1391

Here the one’s addition is 9 + 2 = 11. Thus 1 at one’s place is written below the digit, and one at the tens place is sent to the preceding digits. Addition at tens place becomes 5 + 3 + 1 = 9. Last the addition at hundreds place is 8 + 5 = 13. Since we cannot carry the one ahead, the addition is written in the answer given to us as 1391.

Standard Algorithm Subtraction

The standard algorithm for subtraction is rather tough than that of addition. Let us look at the steps for standard algorithm subtraction below:

  • Write the numbers horizontally as discussed above.
  • Subtract the one’s place first followed by tens place, hundreds place, thousands place, and so on. 
  • If the digit written on the number at the top is greater than the number at the bottom, subtract directly. 
  • If the number on the top is less than the digit on the bottom number, you need to borrow one from the preceding digit. The number borrowed from one is subtracted by one, and the number borrowed becomes ten more.

For example, subtract 519 from 723

  • Write the numbers horizontally. 

  723 – 519 = 204

  • Subtract the digits from one’s place onwards.
  • Here we can see that three is less than nine. Therefore, we must carry one from the preceding digit and add 10 to 3. Thus two becomes 1, and 3 becomes 13. Now 13 – 9 = 4 at one’s place. At tens place 1 – 1 = 0, and at hundreds place 7 – 5 = 2. Thus the result is 204.

Standard Algorithm Multiplication

The standard algorithm is somewhat complex as it involves multiplication and addition in its step. Let us look at the steps with the help of an example.

Example 1: Multiply 273 by 18

Step 1: Write the numbers horizontally.

 273 x 18 = 4914

Step 2: Take the first digit of the bottom number and multiply it with the one’s digit, the tens digit, and the hundreds digit of the number above. 

  • If the number after multiplication turns out to be more than or equal to 10, then write the one digit of the number in the result and carry the tens digits to the preceding number. If eight is multiplied by 3, the answer is 24. Thus four is written in the result two is carried to the next digit, which is 7. 
  • Now eight is multiplied by 7, which gives 56, and the carried digit (2 in this case) is added to 56 giving us 58. Now eight is written in the answer, and five is carried to the next digit, 2 in 273. 
  • Multiplying 8 by 2 we get 16. Now add 5 to the answer we get (16 + 5) = 21. 

Thus the first line of the result of the multiplication is 2184.

 273

x 18

________

 2184

Step 3: Now, we multiply the second digit of the bottom number 1 with the number at the top, which is 273. Follow the same steps as step 2 but write the answer below the first result and skip the 1’s place. See below:

 273

x 18

—————

  2184

+273x

—————

   4914

Here x means that we have skipped the one’s place. If there remains one more digit to multiply, you will skip 2 places (one’s place and tens place) while writing the answer and similarly move forward.

Step 4: Add the answers 2184 and 273x together using the standard algorithm addition. Remember ‘x’ = 0. So the answer is 4914. 

Standard Algorithm Division

The latest algorithm is the standard algorithm for division. It is the most complex of all because it involves many steps and subtraction. Let us look at these steps using an example:

Example: Divide 245 by 5.

Step 1: Write the number to be divided (245 in this case) and the divisor as:

Step 2: Take one digit at a time, starting from the digit in the hundreds place in our case. We see 2 is not divisible by 5, so we take it with the next number (4 in our case); therefore, 24 is not completely divisible by 5 but is close to 5 x 4 = 20. So we subtract 24 by 20. We get the remainder as 4. 

Step 3: Now, we take the digit in one’s place (5 in 245) and combine it with the remainder. We have 45, which is divisible 9 times by 5. Therefore 45 – 45 is 0. Hence we have divided the number with a quotient of 49 and a remainder of 0. See the figure below to understand this. 

While dividing a number sometimes, we may be left with a remainder, and it is completely fine. Remainder signifies that the dividend is not completely divisible by the divisor. Now, you are ready to calculate mathematical expressions by using the standard algorithm mentioned above. 

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