Long Multiplication
Multiply by each digit of the multiplier, shift by place value, then add partial products.
Key idea
Multiply by each digit of the multiplier, shift by place value, then add partial products.
In depth
Multiply the top number by each digit of the bottom number, shifting left for each higher place, then add the partial products. It applies the distributive property: 23 × 14 = 23×4 + 23×10.
Worked example
23 × 14: 23×4 = 92; 23×10 = 230; 92 + 230 = 322.
Real-world uses
- Calculating total cost of many items, areas of rooms in square metres and wage totals by hand
Common mistake
Forgetting the placeholder zero on the second row.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Long Multiplication?
Multiply by each digit of the multiplier, shift by place value, then add partial products. It is a topic at the intermediate level in Arithmetic & Number Sense.
Where is Long Multiplication used in real life?
Real-world examples: Calculating total cost of many items, areas of rooms in square metres and wage totals by hand.
What should I learn before Long Multiplication?
Make sure you are comfortable with Written Subtraction Algorithm, the previous topic in Arithmetic & Number Sense.
What is a common mistake with Long Multiplication?
Forgetting the placeholder zero on the second row.
How can I practise Long Multiplication?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Long Multiplication?
Move on to Long Division next.
Related intermediate topics in Arithmetic & Number Sense
- Long Division – Divide, multiply, subtract and bring down repeatedly to get the quotient.
- Factors and Multiples – Factors divide a number exactly; multiples are its products with whole numbers.
- Divisibility Rules – Quick tests: by 2 last digit even, by 3 digit-sum divisible by 3, by 5 ends 0/5, by 9 digit-sum divisible by 9.
- Prime Numbers – A prime has exactly two positive divisors: 1 and itself.
- Composite Numbers – Numbers greater than 1 with more than two factors.
- Prime Factorization – Every integer above 1 is a unique product of primes.