How to do standard algorithm?

Introduction

The standard algorithm is a widely used method for performing arithmetic operations, particularly addition, subtraction, multiplication, and division. It provides a systematic approach to solving mathematical problems step by step. In this article, we will explore how to do the standard algorithm and understand its application in various scenarios.

Addition

Step 1: Start by aligning the numbers vertically, ensuring that the digits are in their respective place values.

Step 2: Begin adding the digits from right to left, starting with the ones place. If the sum of the digits exceeds 9, carry over the tens place to the next column.

Step 3: Repeat the process for each subsequent column, carrying over as necessary.

Step 4: Once all the columns have been added, the final sum is obtained.

For example, let’s consider the addition problem: 345 + 267.

“`
345
+ 267
——
“`

Starting from the rightmost column, we add 5 and 7, which equals 12. We write down 2 in the sum column and carry over 1 to the next column. Moving to the next column, we add 4, 6, and the carried-over 1, resulting in 11. We write down 1 and carry over 1 again. Finally, in the leftmost column, we add 3, 2, and the carried-over 1, resulting in 6. The final sum is 612.

Subtraction

Step 1: Align the numbers vertically, with the number being subtracted below the number it is subtracted from. Ensure that the digits are in their respective place values.

Step 2: Begin subtracting the digits from right to left, starting with the ones place. If the digit being subtracted is larger than the corresponding digit above it, borrow from the next column.

Step 3: Repeat the borrowing process as necessary and subtract the digits.

Step 4: Once all the columns have been subtracted, the final difference is obtained.

Let’s consider the subtraction problem: 583 – 267.

“`
583
– 267
——
“`

Starting from the rightmost column, we subtract 7 from 3. Since 7 is larger than 3, we borrow 1 from the next column. The calculation becomes 13 – 7, resulting in 6. Moving to the next column, we subtract 6 from 8, resulting in 2. Finally, in the leftmost column, we subtract 2 from 5, resulting in 3. The final difference is 316.

Multiplication

Step 1: Align the numbers vertically, with the multiplier above the multiplicand. Ensure that the digits are in their respective place values.

Step 2: Begin multiplying the digits from right to left, starting with the ones place. Write down the partial products below each digit.

Step 3: Add up the partial products to obtain the final product.

Let’s consider the multiplication problem: 34 x 12.

“`
34
x 12
—–
“`

Starting from the rightmost column, we multiply 4 by 2, resulting in 8. We write down 8 in the rightmost column. Moving to the next column, we multiply 4 by 1, resulting in 4. We write down 4 in the leftmost column. Finally, we add up the partial products, which gives us a final product of 408.

Division

Step 1: Align the divisor outside the division bracket and the dividend inside the bracket. Ensure that the digits are in their respective place values.

Step 2: Begin dividing the digits from left to right, starting with the leftmost digit. Write down the quotient above the dividend.

Step 3: Multiply the quotient by the divisor and subtract the result from the dividend to obtain the remainder.

Step 4: Bring down the next digit from the dividend and repeat the division process until there are no more digits.

Let’s consider the division problem: 256 ÷ 8.

“`
32
—–
8 | 256
24
—
16
16
—
0
“`

We divide 2 by 8, which results in 0. We bring down the next digit, 5, and divide 25 by 8, resulting in 3. We bring down the last digit, 6, and divide 16 by 8, resulting in 2. Since there are no more digits to bring down, the division process ends. The quotient is 32, and the remainder is 0.

Conclusion

The standard algorithm provides a systematic approach to perform arithmetic operations such as addition, subtraction, multiplication, and division. By following the step-by-step process, we can accurately solve mathematical problems. Understanding and practicing the standard algorithm can greatly enhance our mathematical skills.

References

1. mathsisfun.com
2. khanacademy.org
3. mathantics.com