Subtraction with making tens hundreds and thousands strategy

Subtraction is a fundamental mathematical operation that plays a crucial role in our daily lives. Whether we’re balancing a checkbook, measuring ingredients for a recipe, or solving complex mathematical problems, subtraction is an essential skill. To make subtraction easier and more efficient, mathematicians and educators have developed various strategies. One such strategy is the “Making Tens, Hundreds, and Thousands” method, which is especially helpful when dealing with large numbers. In this comprehensive guide, we will explore this strategy in depth, providing a step-by-step breakdown and practical examples to help you master subtraction like never before.

Understanding the Basics of Subtraction

Before delving into the “Making Tens, Hundreds, and Thousands” strategy, it’s essential to understand the basic principles of subtraction. Subtraction is the process of finding the difference between two numbers. It involves taking away one quantity from another. The numbers involved in a subtraction operation are typically referred to as the minuend (the number we start with), the subtrahend (the number we subtract), and the difference (the result of the subtraction).

The “Making Tens, Hundreds, and Thousands” Strategy: Overview

The “Making Tens, Hundreds, and Thousands” strategy is a powerful technique for simplifying subtraction, particularly when dealing with multi-digit numbers. This strategy involves regrouping or borrowing numbers from higher place values to facilitate the subtraction process. It can be summarized in the following steps:

Align the Numbers: Begin by aligning the minuend and subtrahend, ensuring that the digits in each place value column (ones, tens, hundreds, etc.) are properly aligned.
Start from the Right: Begin the subtraction process from the rightmost column (the ones place). Subtract the digit in the subtrahend from the digit in the minuend at that place value.
Check for Borrowing: If the digit in the minuend is smaller than the digit in the subtrahend, you’ll need to borrow from the next higher place value.
Regroup and Subtract: Borrow the necessary amount from the next higher place value and subtract it from that place value in the minuend. Then, subtract the digits in the current place value column as usual.
Repeat the Process: Continue this process, moving from right to left through each place value column until you’ve subtracted all the digits.
Write Down the Result: Once you’ve subtracted all the digits, write down the difference, starting from the rightmost column and moving to the left.

Illustrating the Strategy with Examples

Let’s walk through a few examples to illustrate how the “Making Tens, Hundreds, and Thousands” strategy works:

Example 1: 437 – 268

Align the numbers:

diff

437 - 268
Start from the right: Subtract 8 from 7 in the ones place. Since 7 is smaller than 8, we need to borrow from the tens place.
Borrowing: Borrow 1 from the tens place, making it 3 in the tens place. Add the borrowed 1 to 7 in the ones place, making it 17.
Subtract: Now, subtract 8 from 17 in the ones place, which gives us 9.
Move to the tens place: Subtract 6 from 3 in the tens place. Again, we need to borrow, this time from the hundreds place.
Borrowing: Borrow 1 from the hundreds place, making it 3 in the hundreds place. Add the borrowed 1 to 3 in the tens place, making it 13.
Subtract: Now, subtract 6 from 13 in the tens place, which gives us 7.
Finally, move to the hundreds place: Subtract 2 from 3 in the hundreds place, giving us 1.
Write down the result: The difference is 169.

Example 2: 5,648 – 3,721

Align the numbers:

diff

5,648 - 3,721
Start from the right: Subtract 1 from 8 in the ones place.
No need to borrow this time, so subtract directly: 8 – 1 = 7.
Move to the tens place: Subtract 2 from 4 in the tens place.
Again, no need to borrow: 4 – 2 = 2.
Move to the hundreds place: Subtract 7 from 6 in the hundreds place. Here, we need to borrow from the thousands place.
Borrowing: Borrow 1 from the thousands place, making it 4 in the thousands place. Add the borrowed 1 to 6 in the hundreds place, making it 16.
Subtract: Now, subtract 7 from 16 in the hundreds place, which gives us 9.
Finally, move to the thousands place: Subtract 3 from 4 in the thousands place.
No need to borrow: 4 – 3 = 1.
Write down the result: The difference is 1,927.

Example 3: 12,543 – 8,927

Align the numbers:

diff

12,543 - 8,927
Start from the right: Subtract 7 from 3 in the ones place. We need to borrow from the tens place.
Borrowing: Borrow 1 from the tens place, making it 4 in the tens place. Add the borrowed 1 to 3 in the ones place, making it 13.
Subtract: Now, subtract 7 from 13 in the ones place, which gives us 6.
Move to the tens place: Subtract 2 from 4 in the tens place. Again, we need to borrow from the hundreds place.
Borrowing: Borrow 1 from the hundreds place, making it 5 in the hundreds place. Add the borrowed 1 to 4 in the tens place, making it 14.
Subtract: Now, subtract 2 from 14 in the tens place, which gives us 12.
Move to the hundreds place: Subtract 9 from 5 in the hundreds place. This time, we need to borrow from the thousands place.
Borrowing: Borrow 1 from the thousands place, making it 11 in the thousands place. Add the borrowed 1 to 5 in the hundreds place, making it 15.
Subtract: Now, subtract 9 from 15 in the hundreds place, which gives us 6.
Finally, move to the thousands place: Subtract 8 from 11 in the thousands place. No need to borrow.
Subtract: 11 – 8 = 3.
Write down the result: The difference is 3,616.

Conclusion

The “Making Tens, Hundreds, and Thousands” strategy for subtraction is a valuable tool for simplifying complex subtraction problems, especially when dealing with multi-digit numbers. By following the step-by-step process outlined in this guide and practicing with various examples,