Give and Take - Subtraction of 3-Digit Numbers

Subtraction is the process of taking away a smaller number (Subtrahend) from a larger number (Minuend) to find the 'Difference'. It can be visualized as removing objects from a set or moving backward on a number line.

Place Value Alignment: When subtracting 3-digit numbers, digits must be arranged vertically in columns according to their place value: Hundreds (H), Tens (T), and Ones (O). Visualize this as a grid where each digit sits in its own box, ensuring the Ones are under the Ones, Tens under Tens, and Hundreds under Hundreds.

Subtraction without Regrouping: If every digit in the top number is greater than or equal to the digit below it, we subtract column by column starting from the right (Ones place). For example, in $567 - 234$, we subtract $7 - 4$ in the Ones, $6 - 3$ in the Tens, and $5 - 2$ in the Hundreds.

Subtraction with Regrouping (Borrowing): If a digit in the top row is smaller than the digit in the bottom row, we must borrow from the next higher place value. For instance, if you cannot subtract 8 from 5 in the Ones column, you 'take' 1 Ten from the Tens column and 'give' it to the Ones column, making it 15. Visually, imagine exchanging 1 ten-rod for 10 small unit cubes.

Borrowing Across Zeros: If you need to borrow from the Tens place but it contains a $0$, you must go further to the Hundreds place. You borrow 1 Hundred to make 10 Tens, then borrow 1 Ten from that to make 10 Ones. This looks like a chain reaction across the columns in your vertical calculation.

Checking Subtraction with Addition: To ensure the answer is correct, you can add the Difference to the Subtrahend. If the sum equals the Minuend, the subtraction is correct. This is known as the inverse relationship between addition and subtraction.

Mental Math - The Give and Take Strategy: This involves making numbers easier to subtract by adding or subtracting a small value from both numbers. For example, to solve $345 - 198$, you can add $2$ to both numbers to get $347 - 200 = 147$. This keeps the difference the same while making the calculation simpler.