Date Subtraction Made Easy: A Step-by-Step Guide

My eldest son, Aakhyaan, will turn 10 years old in February 2024 and is currently in the 4th grade. Like many Indian children, his favorite subject is Mathematics. In addition to his regular school classes, he also takes online Math classes through CueMaths, as well as other learning platforms such as Khan Academy and YouTube. Sometimes, I discuss Math problems and problem-solving approaches with him.

Aakhyaan has been taking CueMaths classes for the past four years, and I am very satisfied with the platform and his online teacher. However, one evening, he was unable to solve a Math problem involving date differences. He was trying a new approach that I had discussed with him in the past, which was different from the teacher’s approach. Unfortunately, in his haste, he did not follow the proper steps and did not get the correct answer.

As his answer was incorrect, the teacher asked about his approach. Since he had followed a new approach that was not taught by the teacher, he was scolded. Although his answer was incorrect, I later realized that the teacher was not aware of his approach, which caused confusion. This incident inspired me to write this blog to share our observations of the number system and explore whether we can use the number system concept in date calculations. If you have any specific scenarios or insights to share, I welcome further discussion on the topic.

How does normal subtraction work?

1. Put the bigger number on top of the smaller number.
2. Stack the numbers so the digits are in columns according to their place value.
3. Subtract starting with the column on the right and go left.

What if the top digit is smaller than the bottom digit?

1. Put the bigger number on top of the smaller number.
2. Stack the numbers so the digits are in columns according to their place value.
3. Subtract starting with the column on the right and go left.
4. If the top digit is smaller than the bottom digit, borrow from the next column to the left.

That’s easy, isn’t it? When it comes to the decimal number system, our mind accepts this approach very easily.

Now, to find the difference between 3 feet 9 inches and 2 feet 11 inches

Please try using pen and paper.

One possible approach using below steps :

1. Convert the feet and inches into inches. For example, 3 feet 9 inches is equal to (3 x 12) + 9 = 45 inches, and 2 feet 11 inches is equal to (2 x 12) + 11 = 35 inches.
2. Subtract the smaller number from the larger number. In this case, 45–35 = 10 inches.
3. Convert the answer back into feet and inches if necessary. Since 10 inches is less than 12 inches, the answer is 10 inches or 0 feet 10 inches.

Suppose you want to use the traditional decimal number system approach. However, this method does not provide the correct answer.

Initially, we borrowed 10 from the left column to perform the subtraction. However, since 1 foot has 12 inches, what if we borrow 12 instead of 10 and add in 9 inches? This approach yields the correct answer of 0 feet 10 inches.

Perhaps this task was not difficult because once we understand the concept of borrowing and its weightage (1 foot = 12 inches), the entire calculation becomes easy.

Is it possible to use the same approach for date calculations?

Of course, it’s possible to use the same approach for date calculations. However, it’s important to remember that months do not have the same number of days, and February has a leap year too. It’s possible to use this approach if you understand the core rules.

Example 1: When the month and day do not require borrowing.

Example 2: When the only month requires borrowing.

Example 3.1: When the only day requires borrowing.

When we need to borrow a month, we must look at the previous completed month and the number of days in that month. For example, if we have a date of July 15th, 2023, and we need to borrow a month, we would look at the previous completed month, which is June, and it has 30 days. Therefore, we would borrow June, which is equivalent to 30 days, and the new day becomes 45.

Example 3.2: When the only day requires borrowing.

If we have a date of February 16th, 2023, and we need to borrow a month, we would look at the previous completed month, which is January, and it has 31 days. Therefore, we would borrow January, which is equivalent to 31 days, and the new day becomes 47.

Example 4: When we need to borrow both a month and a day.

To calculate the difference between two dates when both the month and day require borrowing, follow these steps: Suppose we have a date of March 16th, 2024. Since March is not yet completed, we borrowed the previous month, which is February with 29 days due to the leap year. Therefore, the new day is 16+29=45. Since the top month is smaller than the bottom month, we need to borrow a year too. We have landed one month and borrowed 1 year (12 months), hence the new month is 03–01+12=14.

Example 5: The LAST Example

If we have a date of January 16th, 2023, and we need to borrow a month, we would look at the previous completed month, which is December, and it has 31 days. Therefore, we would borrow December, which is equivalent to 31 days, and the new day becomes 47. We would also need to borrow a year, similar to the previous example.

Finally, I would say that the above is not a conventional approach, and someone must practice enough, which my son did not do. However, I would still say to my son to never hesitate to take risks and learn from his mistakes.

Try and fail, but never fail to try!

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