Abacus Lesson 2

Welcome to Abacus Lesson 2!

In the previous lesson, we introduced you to the abacus, covering its essential elements such as components, proper hand positioning, correct posture, and how to reset it.

In this lesson, we’ll delve into how numbers are represented on the abacus. Unlike digital calculators or computers that display numerical symbols, the abacus relies on a unique method of representation. While the beads may all look the same, they carry distinct positional values.

Despite the absence of numerical signs like those on a digital calculator or computer, once you understand the principles of number representation, you’ll soon become proficient at reading an abacus.

By the end of this lesson, you’ll be capable of reading numbers, including large ones, on the abacus. 

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Understanding The Place Value Column

choosing the ones column

When using the abacus, always be on the lookout for the ones place column—it’s the one with the black dot, making it easy to spot. While there are a few dots on the abacus, using the one closest to the center is recommended. It just makes calculating with the beads and jotting down answers on paper a bit easier.

Once you’ve set your ones column, keep in mind that the place value of numbers increases as you move to the left of the ones place column and decreases as you move to the right. (You’ll explore decimals as you progress.

Ones Place Column

Ones Place Column

The image on the left shows the ones place column, recognizable by the dot on the horizontal bar.

Each bead on the lower column has a value of “1” and the upper bead has a value of “5”. Therefore, it can have value up to “9”. 

Similarly, the tens, hundreds, thousands,etc. every column can have up to “9”. However, the value of each column is different. Each column has its own place value. 

For instance, the ones column represents the single digit (1-9), and the tens column represents the 2-digit numbers (10-90). The hundreds column represents the 3-digit numbers (100-900).

Tens Place Column

The tens place column is positioned to the left of the ones place column. As you can see in the image on the right, the tens place column can be found once you find the ones place column. 

Each lower bead in the tens column carries a value of “10”, while the upper bead represents “50”. Consequently, the column can reach a maximum value of “90”. 

Tens Place Column

Hundreds Place Column

hundreds place column

The hundreds place column is positioned to the left of the tens place column, or the second position to the left of the ones place column.

Each lower bead in the hundreds column is worth “100”, while the upper bead holds the big value of “500”. So, when we fill up all the lower beads and add in the upper one, the column can show numbers up to “900”. That’s the highest value it can display.

See how the values increase by ten times as you move one column to the left? So, when you move to the next place value, like from ones to tens or tens to hundreds, the numbers get ten times bigger.

How are numbers represented on abacus?

On the Japanese abacus, when you slide the beads towards the bar, they represent numbers.

Take a look at the picture on the right. 

When the abacus is reset, both the upper and lower beads are away from the bar (none of them are touching it), which means the number is “0”.

But when you move three lower beads on the tens column and the upper bead on the ones column towards the bar, it shows “35”.

how to read the abacus

[ Example ]

representing 333 on abacus

Take a look at the example on the left.

In the picture, you’ll see the number “333” shown on the abacus. You’ll notice that three lower beads in the hundreds, tens, and ones columns are moved towards the bar. (Just count the beads that have been shifted towards the bar). When you read the abacus, always start from the highest digit.

Now, let’s try some more examples below.

What number is represented in each square?

Inside each box, there’s an abacus displaying a number. Let’s take a look at each one and see how it represents the number.

The image shows "0" on the abacus.
The image shows "3" on the abacus.
The image shows "4" on the abacus.
The image shows "5" on the abacus.
The image shows "6" on the abacus.
The image shows "8" on the abacus.
The image shows "9" on the abacus.
The image shows "10" on the abacus.
The image shows "24" on the abacus.
The image shows "35" on the abacus.
The image shows "41" on the abacus.
The image shows "56" on the abacus.
The image shows "630" on the abacus.
The image shows "1735" on the abacus.
The image shows "5616" on the abacus.
The image shows "6407" on the abacus.
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Video Tutorial

Be sure to check out the video lesson below for more detailed guidance. Once you’ve watched the video, give the practice questions a try! They’re available in both printable and video formats.

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Let's practice!

We’ve just uncovered how numbers come alive on the abacus!

Each upper bead represents “5”, while every lower bead counts as “1”.

When they slide towards the bar, they transform into a “numeric number”.

To read the number displayed, simply tally up the beads attached to the bar in each column, starting from the largest place value.

Understanding this representation method will guide you in placing the beads on the abacus with confidence. Let’s dive into some practice questions below to solidify your grasp. Then, we’ll move on to the next lesson to master bead placement on the abacus.

Practice Questions

We offer two types of practice questions for your child’s abacus learning journey:
printable and video formats.

For now, focus on understanding how numbers are represented on the abacus and becoming adept at reading the numeric values.

Don’t stress about placing beads just yet – it’s all about building a solid foundation!

Click the button below to print out the practice questions

Click the button below to try the practice questions in video.
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I can read numbers on the abacus!

In this lesson, we’ve mastered reading numbers on the abacus. We discovered that the abacus follows the place value system, where each column holds a specific value. Now, we can interpret numbers on the abacus, even though they’re not displayed as digital numbers.

Don’t stress about reading larger numbers, like those with 5 or 6 digits, just yet. And don’t worry about placing the numbers either. We’ll dive into finger techniques in our next lesson.