Long Multiplication (4-digit × 2-digit)

Master formal long multiplication method for multiplying numbers up to 4 digits by 2-digit whole numbers

⏱️ 60 minutes
📊 Advanced Level
🎯 Formal long multiplication with large numbers

🎯 Learning Journey

Step 1: Set Up the Problem
Write the larger number (4-digit) above the smaller number (2-digit), aligning them by place value on the right side.
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Step 2: Multiply by the Ones Digit
Multiply the entire top number by the ones digit of the bottom number, working from right to left. Carry when needed.
⬇️
Step 3: Multiply by the Tens Digit
Multiply the entire top number by the tens digit. Place a zero in the ones column first, then write your answer starting in the tens column.
⬇️
Step 4: Add the Partial Products
Add together the two rows of numbers you created. This gives you the final answer. Check using estimation.

📖 Understanding the Topic

🎯 What You'll Learn

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.

🚀 Why This Matters

Real-World Calculations

Essential for working out costs, measurements, and quantities in business, construction, and everyday life.

Building Mathematical Confidence

Mastering this method demonstrates your ability to handle complex calculations systematically.

Foundation for Algebra

The systematic approach used here is essential for algebraic multiplication and polynomial operations.

💡 Worked Examples

Example 1: Concert Tickets

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

Example 2: Annual Production

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

Example 3: School Fundraising

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

Example 4: Distance Travelled

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

✏️ Practice Questions

Question 1: Calculate 2,345 × 23
52,935
53,935
54,935
53,835
Question 2: What is 4,128 × 34?
139,352
140,352
140,252
141,352
Question 3: A shop sells 3,672 bottles per week. How many bottles are sold in 16 weeks?
58,652
57,752
58,752
58,852
Question 4: Calculate 5,984 × 47
280,248
281,248
281,248
282,248
Question 5: What is 6,543 × 29?
188,747
189,747
189,647
190,747
Question 6: A car travels 1,856 km per month. How far does it travel in 52 months?
95,512
96,412
96,512
96,612
Question 7: Calculate 7,291 × 38
276,058
277,058
277,058
278,058
Question 8: What is 8,765 × 64?
559,960
560,860
560,960
561,960

⚠️ Common Mistakes & How to Avoid Them

Learn from typical errors students make and discover how to avoid them!

Forgetting the Placeholder Zero

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.

How to Avoid This Mistake

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.

Not Carrying Correctly

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.

How to Avoid This Mistake

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.

💡 Teacher's Tip

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!

📋 Chapter Summary

🎉 Congratulations!

You've mastered Long Multiplication (4-digit × 2-digit)!

🎯 Skills You've Developed:

✓ Set up long multiplication problems correctly with proper alignment
✓ Multiply 4-digit numbers by single digits with carrying
✓ Use placeholder zeros when multiplying by tens digit
✓ Add partial products accurately to find final answers
✓ Check answers using estimation and inverse operations

🚀 What's Next?

Next: Master long division to divide large numbers by 2-digit divisors

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