The abacus as an ancient calculator

Quick answer

The abacus is an ancient calculator that uses beads to represent numbers and help with addition, subtraction, multiplication, and division. It helps you see how numbers work and makes big calculations easier to understand.

Learning outcome

By the end of this page, you will understand how the abacus works and use it to solve simple calculations. You will be able to:

• Recognise how beads show place value (ones, tens, hundreds)
• Use the abacus to add and subtract small numbers
• See how numbers can be broken into groups
• Understand how ancient people did maths before calculators

Why this matters

Learning about the abacus helps you understand how numbers work. It shows how place value works, which is important for all your maths. The abacus was used for thousands of years and helped people do business, trade, and keep records. Even today, some people still use it to learn maths or calculate quickly.

Understanding how ancient people did maths can help you see that maths is a human invention that grows and changes. It also helps you appreciate how much we’ve learned and how clever we can be with numbers.

How it works

The abacus is a frame with beads that you move to show numbers. It has different rows for different place values:

• The bottom row shows ones (1, 2, 3, 4, 5, 6, 7, 8, 9)
• The next row up shows tens (10, 20, 30, 40, 50, 60, 70, 80, 90)
• The row above that shows hundreds (100, 200, 300, 400, 500, 600, 700, 800, 900)

Each bead usually represents 1. You move beads towards a bar to show how many you have. To make a number like 34, you move 3 beads in the tens row and 4 beads in the ones row.

Examples you can see

Let’s look at how to show numbers on the abacus:

Here’s how to add 12 + 7:

1. Set 12 on the abacus (1 bead in tens row, 2 beads in ones row)
2. Add 7 more beads to the ones row
3. Count how many beads you have in the ones row (9 beads)
4. Count the tens row (still 1 bead)
5. The answer is 19

Here’s how to subtract 19 - 5:

1. Set 19 on the abacus (1 bead in tens row, 9 beads in ones row)
2. Take away 5 beads from the ones row
3. Count the ones row (4 beads)
4. Count the tens row (still 1 bead)
5. The answer is 14

Try it as a mini adventure

Adventure: The Market Trader’s Challenge

You are a trader in ancient times, and you have to count your goods. You have 32 apples and 15 oranges. How many fruits do you have in total?

1. Set 32 on your abacus (3 beads in tens row, 2 beads in ones row)
2. Add 15 more (1 bead in tens row, 5 beads in ones row)
3. Count the beads in the ones row (2 + 5 = 7)
4. Count the beads in the tens row (3 + 1 = 4)
5. You have 47 fruits in total

Now try this: You had 47 fruits, but you sold 23. How many do you have left?

1. Set 47 on your abacus (4 beads in tens row, 7 beads in ones row)
2. Take away 23 (2 beads in tens row, 3 beads in ones row)
3. Count the ones row (7 - 3 = 4)
4. Count the tens row (4 - 2 = 2)
5. You have 24 fruits left

Common mistakes

• Mistake: Mixing up the rows when setting numbers
  Why it happens: Confusing which row shows tens and which shows ones
  Fix: Always check that beads in the bottom row show ones, and the row above shows tens
• Mistake: Adding too many beads in one row
  Why it happens: Not knowing that each row only goes up to 9
  Fix: When you have 10 beads in a row, move 1 bead to the next row up
• Mistake: Forgetting to move beads back when subtracting
  Why it happens: Thinking you can just take beads without moving them
  Fix: Always move beads away from the bar when subtracting

Parent and carer guide

Help your child by:

• Using real abacus beads or drawing an abacus on paper to practice
• Starting with simple numbers like 5, 12, 23
• Letting them explain how they set a number on the abacus
• Encouraging them to check their answer with another method
• Practising place value by asking them to show 100, 200, 300

Ask questions like:

• How many beads are in the tens row?
• What number do you have now?
• Can you show me 45 using the abacus?

Don’t worry if they make mistakes. They’re learning how numbers work. The abacus helps them see what’s happening with numbers, so it’s a great tool for understanding.

Practice questions

1. Set 23 on the abacus. What does each row show?
2. Add 14 to 23. What is the answer?
3. Subtract 9 from 15. What is the answer?
4. Set 47 on the abacus. How many beads are in the tens row?
5. How many beads are in the ones row when you show 68?

Answers:

1. Tens row shows 2 beads, ones row shows 3 beads
2. 37
3. 6
4. 4 beads
5. 8 beads

FAQ

What is an abacus?

An abacus is an ancient calculating tool with beads that you move to show numbers and do maths.

Why did people use abacuses?

People used abacuses because they helped them count, add, and subtract without writing numbers down. It was useful for trade and business.

How many beads does an abacus have?

Most abacuses have 10 beads per row, but some have 5 beads. The number of rows depends on how many numbers you want to show.

Can I still use an abacus today?

Yes! Some people still use abacuses for learning maths or calculating quickly. You can even find abacuses in schools or online.

Is the abacus better than a calculator?

They are different tools. The abacus helps you understand how numbers work. A calculator is faster for big numbers, but the abacus helps you think about place value and how numbers are built.