Crossing out also helps to calculate

Seven marbles with three crossed out and four remaining.
Count the remaining balls. Then draw your own account: 9 − 2.
An empty box next to a box with five marbles.
If we remove the five marbles, the box is empty: 5 − 5 = 0.
Check out the discovery

6 − 6 = 0 and 6 − 4 = 2. Zero records the quantity when there are no caps left.

Subtraction of natural numbers is the operation that removes one natural number from another. The method we are going to introduce is the abacus method which is the Japanese method.

Predecessor of a natural number

The predecessor of a natural number is the natural number that is the result of subtracting the number by unity. More specifically, the predecessor of a natural number \(a\) is the natural number whose successor is \(a\). We define the predecessor as \(a-1\).

$$ \begin{aligned} \underbrace{1+1+\dots+1}_{\text{a unidades} } - 1 &= \underbrace{1+1+\dots+1-1}_{\text{a - 1 unidades} } = a-1 \end{aligned} $$

Example: the predecessor of 3 is 2.

Numeral Predecessor
2 1
3 2
4 3
5 4

In this way, the result of subtracting natural numbers \(a\) from \(b\) indicated by \(a-b\) is called a difference.

Children, as well as Egyptian adults or people of antiquity, carried out sums with the concept of predecessors. For example, given \(a=7\) and \(b=6\) the difference obtained by predecessor is given by:

$$ \begin{aligned} 7 - 1 &= 6\\ 6 - 1 &= 5\\ 5 - 1 &= 4 \\ 4 - 1 &= 3 \\ 3 - 1 &= 2 \\ 2 - 1 &= 1 \\ \end{aligned} $$

Therefore, \(7-6=1\) in the Arabic decimal system.

Subtracting is going backwards on the straight line: the frog jumps back a little for each unit taken.

Subtraction using the abacus method

The subtraction of 56 and 35 is given below:

Abacus School method
Western writing. Oriental writing.

Now let’s look at the calculation of 52-35:

Abacus School method
Western writing. Oriental writing.

Definition

The next step is to present some definitions:

Subtraction Definition
7 Minuend
-5 Subtrahend
2 Difference or Remainder
  • Impa Portal: Time to Subtract

How to avoid borrowing

One method to bypass the loan method is to use the scale method.

Balance.

What is the scale method like? To balance the scales, everything you do on one side, you do on the other in the same proportion. For example, to subtract 43 and 28 we would have to use the loan method. To avoid borrowing, we will add in the minuend 2 and the subtrahend 2 also to balance the scale.

Balance. Balance.
  • Impa Portal: Subtraction
  • Impa Portal: Subtraction
  • Portal Impa: Shall we subtract?
  • Impa Portal: The difference

Training

Time to practice! Answer and see how many stars you get.

Subtractions to train. Change the difficulty on the buttons.