Chapter 2.14: Long Division (4-digit ÷ 2-digit)

🎯 Learning Journey

Step 1: Divide

Look at the first digits of the dividend. How many times does the divisor fit into them? Write this number above the line.

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Step 2: Multiply

Multiply the divisor by the number you just wrote. Write the result below the digits you were dividing into.

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Step 3: Subtract

Subtract the result from the number above it. Bring down the next digit from the dividend to make a new number.

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Step 4: Repeat

Repeat the divide-multiply-subtract process until you've used all digits. Any number left over is the remainder.

📖 Understanding the Topic

🎯 What You'll Learn

Long division is a systematic method for dividing large numbers. The process follows a repeating cycle: Divide, Multiply, Subtract, and Bring down (often remembered as "Dad, Mum, Sister, Brother"). This method allows you to divide any size number with accuracy.

🚀 Why This Matters

Sharing and Distributing

Essential for dividing resources, calculating per-person costs, and solving sharing problems in real life.

Problem-Solving Skills

Develops logical thinking and step-by-step problem solving that transfers to many other mathematical concepts.

Fraction Foundation

Understanding division with remainders is crucial for working with fractions and decimals.

💡 Worked Examples

Example 1: School Trip

3,456 pupils need to be divided into groups of 24. How many groups can be formed?

Answer: 144 groups

Example 2: Factory Production

A factory packages 5,628 items into boxes of 36. How many full boxes can be made?

       156 r 12
    ----------
36 | 5628
     36↓↓
     ---
     202
     180↓
     ----
     228
     216
     ---
      12

Answer: 156 full boxes with 12 items remaining

Example 3: Money Distribution

£4,284 is shared equally among 42 people. How much does each person receive?

Answer: £102 each

Example 4: Distance Per Day

A cyclist travels 2,592 km over 54 days. What is the average distance per day?

Answer: 48 km per day

✏️ Practice Questions

Question 1: Calculate 1,248 ÷ 24

51

52

53

54

Question 2: What is 3,276 ÷ 42?

76

77

78

79

Question 3: 5,184 books are packed into boxes of 36. How many full boxes?

142

144

146

148

Question 4: Calculate 6,832 ÷ 64

105

106 r 48

107

108

Question 5: What is 4,536 ÷ 54?

82

84

86

88

Question 6: £7,245 is shared among 45 people. How much each?

£159

£161

£163

£165

Question 7: Calculate 8,568 ÷ 72

117

119

121

123

Question 8: What is the remainder when 9,457 ÷ 85?

10

12

14

16

⚠️ Common Mistakes & How to Avoid Them

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

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Incorrect Estimation

What students often do wrong:

Students guess how many times the divisor fits into the dividend without proper estimation, leading to numbers that are too large (requiring correction) or too small (wasting time).

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How to Avoid This Mistake

Correct approach: Use your times tables knowledge. If dividing by 36, think about multiples of 36 (36, 72, 108, 144, etc.) to estimate accurately.

Memory tip: Round the divisor to the nearest 10 for quick mental estimation, then adjust if needed.

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Forgetting to Bring Down

What students often do wrong:

After subtracting, students forget to bring down the next digit from the dividend, causing the remaining calculation to be incorrect.

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How to Avoid This Mistake

Correct approach: After every subtraction, immediately bring down the next digit before continuing. Make this part of your automatic routine.

Memory tip: Remember "Divide, Multiply, Subtract, Bring down" - all four steps every time!

💡 Teacher's Tip

Check your answer by multiplying the quotient by the divisor and adding any remainder. The result should equal your original dividend. For example: 3,456 ÷ 24 = 144, so check: 144 × 24 = 3,456 ✓

📋 Chapter Summary

🎉 Congratulations!

You've mastered Long Division (4-digit ÷ 2-digit)!

🎯 Skills You've Developed:

✓ Apply the long division algorithm systematically

✓ Estimate quotients accurately using times tables

✓ Handle remainders correctly in division problems

✓ Verify division answers using multiplication

✓ Solve real-world problems involving division

🚀 What's Next?

Next: Learn short division methods for efficient mental and written calculation