Master formal long multiplication method for multiplying numbers up to 4 digits by 2-digit whole numbers
Long multiplication is a formal written method for multiplying large numbers. When multiplying a 4-digit number by a 2-digit number, you break down the multiplication into manageable steps, multiply by each digit separately, then add the results together.
Essential for working out costs, measurements, and quantities in business, construction, and everyday life.
Mastering this method demonstrates your ability to handle complex calculations systematically.
The systematic approach used here is essential for algebraic multiplication and polynomial operations.
A concert venue has 3,456 seats. If tickets cost £24 each, what is the total revenue?
3456 × 24 ------ 13824 (3456 × 4) 69120 (3456 × 20) ------ 82944
Answer: £82,944
A factory produces 2,789 items per day. How many items are produced in 36 days?
2789 × 36 ------ 16734 (2789 × 6) 83670 (2789 × 30) ------ 100404
Answer: 100,404 items
Each of 45 classes raises £1,234 for charity. What is the total amount raised?
1234 × 45 ------ 6170 (1234 × 5) 49360 (1234 × 40) ------ 55530
Answer: £55,530
A delivery van travels 4,567 metres on each route. If it completes 28 routes, what is the total distance?
4567 × 28 ------ 36536 (4567 × 8) 91340 (4567 × 20) ------ 127876
Answer: 127,876 metres
Learn from typical errors students make and discover how to avoid them!
What students often do wrong:
When multiplying by the tens digit, students forget to place a zero in the ones column before writing their answer. This causes the partial products to misalign, leading to an incorrect final answer.
Correct approach: Always write a zero in the ones place before multiplying by the tens digit. This ensures proper alignment of place values.
Memory tip: Remember "Zero first for tens" - place your zero, then multiply and write your answer.
What students often do wrong:
Students forget to add the carried number or write it in the wrong place, especially when dealing with multiple carries in a single multiplication.
Correct approach: Write carried numbers small and clear above the next column. Always add them before writing your answer for that column.
Memory tip: "Multiply, add carry, write down" - follow this sequence for each digit.
Always estimate before calculating. For 3,456 × 24, round to 3,500 × 25 = 87,500. Your exact answer (82,944) should be reasonably close to this estimate. If it's very different, check your working!
You've mastered Long Multiplication (4-digit × 2-digit)!
Next: Master long division to divide large numbers by 2-digit divisors