Short Division Methods

Use short division (bus stop method) efficiently for dividing by single-digit numbers

⏱️ 45 minutes
📊 Medium Level
🎯 Efficient mental division strategies

🎯 Learning Journey

Step 1: Draw the Bus Stop
Draw the division bracket (bus stop) with the divisor outside on the left and the dividend inside underneath the bracket.
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Step 2: Divide the First Digit
Look at the first digit. How many times does the divisor go into it? Write the answer above and any remainder as a small number before the next digit.
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Step 3: Continue Through Each Digit
Divide each digit (including any carried amount), writing answers above and carrying remainders forward to the next digit.
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Step 4: Deal with Final Remainder
If there's a remainder at the end, express it as a remainder, fraction, or decimal depending on the context of the problem.

📖 Understanding the Topic

🎯 What You'll Learn

Short division (also called the bus stop method) is a compact and efficient way to divide numbers, especially by single-digit divisors. Unlike long division, you work mainly in your head, writing only the quotient above and small remainder numbers below. This method is faster once mastered and takes up less space on paper.

🚀 Why This Matters

Speed and Efficiency

Short division is much faster than long division for single-digit divisors, making it ideal for quick calculations.

Mental Arithmetic Practice

Strengthens mental calculation skills and times table recall, essential for all mathematical work.

Practical Applications

Perfect for everyday calculations like sharing costs, dividing ingredients in recipes, and splitting quantities.

💡 Worked Examples

Example 1: Sharing Sweets

846 sweets are shared equally among 6 children. How many does each child get?

    141
   -----
6 ) 8⁴4⁴6

Working:
8 ÷ 6 = 1 r 2
24 ÷ 6 = 4 r 0
6 ÷ 6 = 1

Answer: 141 sweets each

Example 2: Packaging Items

A factory has 2,736 items to pack into boxes of 8. How many boxes are needed?

    342
   -----
8 ) 2⁷3⁶6

Working:
27 ÷ 8 = 3 r 3
33 ÷ 8 = 4 r 1
16 ÷ 8 = 2

Answer: 342 boxes

Example 3: Weekly Schedule

A school year has 1,575 hours of lessons divided equally over 7 terms. How many hours per term?

    225
   -----
7 ) 1⁵5⁷5

Working:
15 ÷ 7 = 2 r 1
17 ÷ 7 = 2 r 3
35 ÷ 7 = 5

Answer: 225 hours per term

Example 4: Distributing Money

£4,563 prize money is split equally among 9 winners. How much does each person receive?

    507
   -----
9 ) 4⁵5⁰6³3

Working:
45 ÷ 9 = 5 r 0
6 ÷ 9 = 0 r 6
63 ÷ 9 = 7

Answer: £507 each

✏️ Practice Questions

Question 1: Calculate 728 ÷ 4
180
182
184
186
Question 2: What is 1,536 ÷ 6?
254
256
258
260
Question 3: 2,345 pencils are packed into boxes of 5. How many boxes?
467
469
471
473
Question 4: Calculate 3,528 ÷ 7
502
504
506
508
Question 5: What is 4,896 ÷ 8?
610
612
614
616
Question 6: 6,372 books are shared among 9 libraries. How many books per library?
706
708
710
712
Question 7: Calculate 924 ÷ 3
306
308
310
312
Question 8: What is 5,642 ÷ 7? (Give remainder)
805 r 5
806 r 0
806 r 4
807 r 1

⚠️ Common Mistakes & How to Avoid Them

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

Forgetting to Include Zero

What students often do wrong:

When a digit cannot be divided by the divisor (like 6 ÷ 8), students skip it entirely instead of writing 0 in the answer. This causes all subsequent digits to be in the wrong place value position.

How to Avoid This Mistake

Correct approach: When a digit is smaller than the divisor, write 0 above it and combine that digit with the next digit to form a larger number to divide.

Memory tip: "Zero is a number too" - include it in your answer whenever division doesn't work for a digit.

Miswriting Remainder Digits

What students often do wrong:

Students write the remainder number too large or in the wrong place, making it hard to read and leading to confusion about which digit they're currently working with.

How to Avoid This Mistake

Correct approach: Write remainder numbers small and slightly raised (like a superscript) before the next digit. Keep your working neat and organized.

Memory tip: "Small and high keeps remainders nearby" - write them small and positioned clearly.

💡 Teacher's Tip

Check your answer by multiplying the quotient by the divisor and adding any remainder. For 846 ÷ 6 = 141, check: 141 × 6 = 846 ✓ The bus stop method is faster than long division once you're confident with your times tables!

📋 Chapter Summary

🎉 Congratulations!

You've mastered Short Division Methods!

🎯 Skills You've Developed:

✓ Use the bus stop method efficiently for single-digit division
✓ Carry remainders mentally and record them correctly
✓ Include zeros in answers when appropriate
✓ Check division answers using multiplication
✓ Choose between short and long division appropriately

🚀 What's Next?

Next: Explore fractions, decimals, and percentages to extend your number understanding

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