abacus formula

Abacus Formula: Big Friend & Small Friend Explained [Pdf]

Abacus is considered one of the important tools to promote mental math abilities in early learners. For those unaware, Abacus  is  a manual aid to calculating that consists of beads or disks that can be moved up and down on a series of sticks or strings within a usually wooden frame. It is consider one of the best way to develop number sense.

Numbers are physically constructed and manipulated in Abacus. We already discussed different types of Abacus and their uses. Although not included in regular math curriculum, but kids must try their hands on practicing various math operations with it once in a while.

If you just started learning the abacus, you must first learn the basics of abacus. After getting your hands on abacus and playing with it for a little while, its time to practice the basic operations (Addition & Substraction) on it. In general practice, we take the help of abacus formula to do addition and substraction, specially when there are not enough beads in a column to add on Abacus. It involves using the concept of small friends and big friends for solving the basic operations.

Look at the abacus formula sheet given below. You can also view/download pdf version by clicking this link.

Abacus Formula Small Friend Addition
Abacus Formula Small Friend Addition
Abacus Formula Small Friend Substraction
Abacus Formula Small Friend Substraction

In the case of Small friend, we take the bead of value 5 as the reference. To obtain the number from the addition and substraction on abacus, we operate the reference 5 with the small friend. Here, we will explain it the examples of both.

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Let’s add 3+4,

abacus formula small friend  addition model
  1. Place 3 (3 lower bead of value 1) on abacus
  2. Now, we have to add 4 but there are not enough beads left, so we will take the help of small friend as per the formula ‘add 5 less 1’.
  3. We will add 5(1 upper bead on the same column) on abacus and remove 1 (1 lower bead on the same column )
  4. We are left with (1 upper bead of 5, 2 lower bead of value 1). The solution is 5 + 2 = 7

Similarly, Let’s subtract 7 -4,

abacus formula small friend  subtraction model
  1. To make 7: Slide 2 lower bead of unit place and 1 upper bead of unit place (value 5).
  2. To subtract 4, we have to take the help of big friend as there are not enough beads on the unit place. Use the formula ‘Less 5 add 1’.
  3. Now remove 5 (slide down the upper bead of value 5) and add 1 (slide up the 1 lower bead of unit place)
  4. We are left with (0 upper bead and 3 lower bead of unit’s place). The solution is 0 + 3 = 3, which is our answer.

Abacus Formula Big Friend Addition
Abacus Formula Big Friend Addition
Abacus Formula Big Friend Subtraction
Abacus Formula Big Friend Subtraction

In the case of Big friend, we take the bead of value 10 as the reference. To obtain the number from the addition and substraction on abacus, we operate the reference 10 with the small friend. Here, we will explain it the examples of both.

Let’s add 8+9,

abacus formula big friend  addition model
  1. Place 8 (3 lower bead of value 1 and 1 upper bead of value 5) on abacus
  2. Now, we have to add 9 but there are not enough beads left, so we will take the help of big friend as per the formula ‘add 10 less 1’.
  3. We will add 10(1 lower bead on the adjacent left column) on abacus and remove 1 (1 lower bead on the same column )
  4. We are left with (1 lower bead of value 10, 1 upper bead of 5, 2 lower bead of value 1). The solution is 10 + 5 + 2 = 17
READ :   Different types of Abacus and their uses

Similarly, Let’s subtract 15 -7,

abacus formula big friend subtraction model
  1. To make 15: Slide 1 lower bead of value 10 and 1 upper bead of unit place (value 5).
  2. To subtract 7, we have to take the help of big friend as there are not enough beads on the unit place. Use the formula ‘Less 10 add 3’.
  3. Now add 3 (slide up the 3 lower beads of unit place) and remove 10 (slide down the lower bead of value 10 column).
  4. We are left with (1 upper bead and 3 lower bead of unit’s place). The solution is 5 + 3 = 8, which is our answer.

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