Subtraction

Definitions

Have you ever given away some of your toys or candies to a friend? When you do that, you're subtracting! Let’s see: if you have 1 237 cubes, and you give 1 114 cubes to your friend, how many cubes do you have left?

$-$

$=$

Answer

Counting each cube individually would be quite cumbersome, especially with larger numbers. In such cases, column subtraction is a more efficient method.

Now you have 123 cubes left!$$1\,237-1\,114=123$$

$-$

$=$

Definition Subtraction

Subtraction means taking something away. When we subtract, we find out how many are left.

The $-$ symbol means "subtract."
The $=$ symbol shows that the two sides are the same.

We can represent subtraction as:

Numbers: $$1\,237 - 1\,114 = 123$$
Cubes: $-$ $=$
Words:one thousand two hundred thirty-seven minus one thousand one hundred fourteen equals one hundred twenty-three
Subtraction Using Columns :

Subtraction Using Columns

Discover

You have learned how to perform column subtraction using the borrowing method. This involves "borrowing" a ten from the neighboring column when the digit on top is smaller than the digit below. But today, we will discover another method: the compensation method.
The compensation method is based on the following principle: if the same number is added to or subtracted from both terms of a subtraction, the difference remains unchanged. This property allows us to simplify the calculation by transforming the numbers to make the subtraction easier.

Method Subtraction in Columns with Compensation

To calculate:$32 - 14$

Step 1: Set up the subtraction
Step 2: Compensate 1 Ten $$2 \text{ ones} - 4 \text{ ones}$$There are not enough ones. You regroup $10$ ones to make it $12$. You compensate by adding 1 ten to $14$, which makes it $2$ tens.
Step 3: Subtract the ones $$12 \text{ ones} - 4 \text{ ones} = 8 \text{ ones}$$
Step 4: Subtract the tens $$3 \text{ tens (from 32)} - 1 \text{ ten (from 14)} - 1 \text{ ten (compensation)} = 1 \text{ ten}$$
Result: There is 1 ten and 8 ones. So, $$32 - 14 = 18$$