Calculation
Long Multiplication (4-digit × 2-digit)
Year 5 · Year 6
- ✓By the end of this lesson students will be able to multiply 4-digit numbers by 2-digit numbers using the formal written method of long multiplication.
- ✓By the end of this lesson students will be able to accurately align digits according to their place value during multiplication.
- ✓By the end of this lesson students will be able to estimate answers to multiplication problems to check for reasonableness and identify potential errors.
- ✓By the end of this lesson students will be able to solve problems involving long multiplication in various contexts.
Key concepts
Long multiplication is a formal written method used to multiply larger numbers. When multiplying a 4-digit number by a 2-digit number, you break the problem down into simpler steps. First, you multiply the 4-digit number by the ones digit of the 2-digit number. Then, you multiply the 4-digit number by the tens digit of the 2-digit number, remembering to place a zero in the ones column as a placeholder because you are multiplying by a multiple of ten. Finally, you add these two partial products together to get your final answer. It is crucial to keep your digits aligned correctly according to their place value throughout the process.
Estimation is a useful skill to quickly check if your calculated answer is sensible. To estimate, you round the numbers in your multiplication problem to the nearest 10, 100, or 1000, making them easier to multiply mentally. For example, to estimate 3456 × 23, you might round 3456 to 3000 or 3500, and 23 to 20. Then you multiply these rounded numbers (e.g., 3000 × 20 = 60000 or 3500 × 20 = 70000). Your actual answer should be close to your estimate. If it's very different, it suggests you might have made a mistake in your calculation.
Key facts to remember
- 1Long multiplication is a formal written method for multiplying larger numbers.
- 2Always start by multiplying by the ones digit of the bottom number.
- 3When multiplying by the tens digit, remember to put a zero in the ones column as a placeholder.
- 4Carefully add the partial products together to get the final answer.
- 5Place value is extremely important; keep your digits aligned in columns.
- 6Estimation helps you check if your final answer is reasonable.
- 7Practise your times tables regularly as they are the foundation of multiplication.
Worked examples
Example 1
Calculate 2435 × 32.
Answer
77920
The estimated answer was 60000, and 77920 is reasonably close, so the answer is likely correct.
Example 2
A factory produces 1085 toys each day. How many toys does it produce in 26 days?
Answer
28210 toys
Pay close attention when multiplying by zero; it can be a common source of error if not handled carefully.
Example 3
Calculate 5009 × 47.
Answer
235423
The estimate of 250000 is close to 235423, confirming the calculation is likely correct. Remember to carry over correctly when digits sum to more than 9.
Common mistakes
- ✗Forgetting to include the placeholder zero when multiplying by the tens digit.
- ✗Incorrectly carrying over digits when multiplying or adding.
- ✗Misaligning digits in columns, leading to incorrect place value in partial products.
- ✗Making errors in basic multiplication facts (times tables).
- ✗Not using estimation to check the answer, missing obvious errors.
Exam tips
- ★Always show your full working out, step-by-step, as marks are often awarded for method.
- ★Use estimation before you start the detailed calculation to have a rough idea of the answer.
- ★Double-check your addition of the partial products carefully.
- ★If time allows, quickly re-do the calculation or check it with your estimate to catch any errors.
Ready to practise?
Try a problem on this topic
Snap a photo or type a question — get step-by-step working instantly.