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Maths History

Russian peasant multiplication

Explore doubling and halving as a historic multiplication method.

Quick answer

Russian peasant multiplication is a historic method of multiplying numbers using doubling and halving. You can multiply any two numbers by repeatedly halving one and doubling the other, then adding up the doubled numbers that match up with odd halves.

Learning outcome

By the end of this page, you will be able to multiply any two numbers using the Russian peasant method by halving one number and doubling the other, then adding the doubled numbers that match odd halves. Success signs:
  • You can halve numbers and double numbers correctly
  • You can identify which doubled numbers to add together
  • You can use this method to solve multiplication problems
  • You can explain why this method works

Why this matters

This method was used by ancient peoples and is still a useful way to multiply numbers without a calculator. It helps you understand how multiplication works and shows that there are many ways to solve a problem. You might even use this method when playing games or building with blocks where you need to count large groups quickly.

How it works

Let's learn how Russian peasant multiplication works step by step:
  1. Write down the two numbers you want to multiply
  2. Halve the first number (divide by 2) and double the second number
  3. Keep halving the first number and doubling the second number until the first number becomes 1
  4. Circle the doubled numbers that match with odd numbers in the halved column
  5. Add up all the circled doubled numbers

Examples you can see

Let's try multiplying 18 by 25 using Russian peasant multiplication.
Halving Double
18 25
9 50
4 100
2 200
1 400
Now we look for the odd numbers in the halving column: 18 (even), 9 (odd), 4 (even), 2 (even), 1 (odd). We circle the doubled numbers that match with odd halved numbers: 50 and 400. Add them together: 50 + 400 = 450. So 18 × 25 = 450. Let's try another example with 13 × 17:
Halving Double
13 17
6 34
3 68
1 136
Odd numbers in halving column: 13 (odd), 6 (even), 3 (odd), 1 (odd). Circled doubled numbers: 17, 68, 136. Add them together: 17 + 68 + 136 = 221. So 13 × 17 = 221.

Try it as a mini adventure

Imagine you're a medieval merchant in Russia who needs to count how many apples you have. You have 24 baskets, and each basket has 32 apples. You need to find the total number of apples using Russian peasant multiplication!
  1. Write down 24 and 32
  2. Halve 24 and double 32
  3. Continue until 24 becomes 1
  4. Circle the doubled numbers that match odd halved numbers
  5. Add them up to find the total
Halving Double
24 32
12 64
6 128
3 256
1 512
Odd numbers in halving column: 24 (even), 12 (even), 6 (even), 3 (odd), 1 (odd). Circled doubled numbers: 256 and 512. Add them together: 256 + 512 = 768. So you have 768 apples!

Common mistakes

  • Mistake: Forgetting to double the second number each time. Why it happens: Kids might get confused about which number to double. Fix: Always double the second number and keep track of it in a column.
  • Mistake: Halving odd numbers and getting decimals. Why it happens: Kids might not know that 5 ÷ 2 = 2.5, so they round down to 2. Fix: When halving odd numbers, always round down to the nearest whole number (5 ÷ 2 = 2, not 2.5).
  • Mistake: Not circling the right doubled numbers. Why it happens: Kids might get confused about which doubled numbers to add. Fix: Only circle the doubled numbers that match with odd numbers in the halving column.
  • Mistake: Adding all doubled numbers together. Why it happens: Kids might not understand that only odd halved numbers matter. Fix: Focus only on the doubled numbers that match odd halved numbers.

Parent and carer guide

To help your child with Russian peasant multiplication:
  • Start by explaining that this is an old way to multiply numbers
  • Use physical objects like counters or blocks to show halving and doubling
  • Practice with simple numbers first, like 6 × 8
  • Ask your child to explain each step as they go
  • Make it fun with games or challenges
  • Don't worry if it takes time to understand - it's a new method
  • Remember that the goal is to understand the process, not just get the answer
  • Encourage them to try different numbers and see if they get the same answer with normal multiplication
  • Use real-life examples like counting toys or snacks to make it relatable

Practice questions

  1. Use Russian peasant multiplication to find 14 × 19
  2. Use Russian peasant multiplication to find 11 × 13
  3. Use Russian peasant multiplication to find 16 × 21
  4. Use Russian peasant multiplication to find 9 × 15
  5. Use Russian peasant multiplication to find 7 × 12
Answers:
  1. 14 × 19 = 266
  2. 11 × 13 = 143
  3. 16 × 21 = 336
  4. 9 × 15 = 135
  5. 7 × 12 = 84

FAQ

What is Russian peasant multiplication?

Russian peasant multiplication is an ancient method of multiplying numbers using doubling and halving. You keep halving one number and doubling the other, then add up the doubled numbers that match odd halved numbers.

Why do we use this method?

This method was used by ancient peoples before calculators. It helps you understand how multiplication works and shows that there are many ways to solve a problem. It's also useful for mental math.

Is this method always faster?

No, for small numbers, normal multiplication might be faster. But for larger numbers, this method can be helpful and shows the patterns in multiplication.

Can I use this method with decimals?

No, this method only works with whole numbers. You can't halve a decimal number in this method.

Where did this method come from?

This method was used by ancient Egyptians, Greeks, and Russians. It's also called the "ancient Egyptian method" or "binary multiplication." It's a way of multiplying that doesn't require knowing all multiplication facts.