Subtraction - Properties of Subtraction

Subtraction is the process of taking one number or amount away from another. The larger number from which another number is subtracted is called the Minuend, the number that is subtracted is called the Subtrahend, and the result is called the Difference. Imagine a row of 10 toy cars; if you remove 4 cars, the remaining 6 cars represent the Difference.

Zero Property of Subtraction: When zero is subtracted from any number, the difference is the number itself. For example, if $45 - 0 = 45$, it means that taking away nothing from a group leaves the group unchanged. Visually, if a plate has 8 cookies and you take away 0, the plate still shows 8 cookies.

Subtracting a Number from Itself: When a number is subtracted from itself, the difference is always zero ($0$). For example, $256 - 256 = 0$. Visually, if you have a box of 12 crayons and you give away all 12 crayons, the box becomes empty, representing zero.

Order Property: In subtraction, the order of numbers is very important. We cannot change the order of numbers as we do in addition. For example, $15 - 10$ is possible and equals $5$, but $10 - 15$ is not possible for whole numbers. On a number line, you can easily jump backward from a larger number, but jumping backward from a smaller number to a larger extent goes past zero.

Subtraction of 1: When $1$ is subtracted from any number, the difference is the 'Predecessor' (the number just before) of the given number. For example, $99 - 1 = 98$. Visually, if you are standing on step 10 of a staircase and move down 1 step, you land on step 9.

Relationship with Addition: Subtraction is the inverse (opposite) of addition. Every addition fact has two corresponding subtraction facts. For example, if $12 + 8 = 20$, then $20 - 8 = 12$ and $20 - 12 = 8$. This can be visualized as a part-part-whole diagram where two parts (8 and 12) combine to make the whole (20).

Checking Subtraction: You can check if your subtraction is correct by adding the Difference to the Subtrahend. If the sum equals the Minuend, your answer is correct. This forms the equation: $\text{Difference} + \text{Subtrahend} = \text{Minuend}$.