Why is long division taught in schools?

Long division teaches important mathematical skills: understanding place value, estimation, breaking complex problems into steps, and checking work systematically. It builds number sense and mental math abilities. While calculators can divide quickly, understanding the process helps with algebra, fractions, and problem-solving. UK National Curriculum requires long division by Year 6 (ages 10-11).

Is this calculator suitable for UK primary and secondary students?

Yes! This calculator is perfect for UK students from Year 5 through GCSE. It shows step-by-step working following UK teaching methods (DMSB method), displays remainders, decimals, and mixed numbers, and provides detailed explanations. Use it to check homework, understand the process, or practice for SATs and GCSEs. It aligns with the UK National Curriculum for Mathematics.

Long Division Calculator - Step-by-Step Division

Free long division calculator with detailed step-by-step solutions. Shows remainders, decimals, and mixed numbers. Perfect for UK students Years 5-11. Updated 2025.

Long Division Calculator

Dividend (Number to be divided)

Divisor (Number to divide by)

Decimal Places (for non-whole results)

📚 Worked Examples

Example 1: Division with No Remainder

Problem: 144 ÷ 12

Step 1 (Divide): How many times does 12 go into 14? → 1 time
Write 1 above the 4

Step 2 (Multiply): 1 × 12 = 12
Write 12 under 14

Step 3 (Subtract): 14 - 12 = 2
Write 2 below

Step 4 (Bring down): Bring down the 4 to make 24

Step 5 (Repeat): How many times does 12 go into 24? → 2 times
Write 2 after the 1 to make 12
2 × 12 = 24, subtract: 24 - 24 = 0

Answer: 144 ÷ 12 = 12

Check: 12 × 12 = 144 ✓

Example 2: Division with Remainder

Problem: 157 ÷ 12

Step 1: 12 into 15 goes 1 time (1 × 12 = 12)
Subtract: 15 - 12 = 3, bring down 7 to make 37

Step 2: 12 into 37 goes 3 times (3 × 12 = 36)
Subtract: 37 - 36 = 1

Final Answer: Quotient = 13, Remainder = 1
Can be written as: 13 R 1, or 13 1/12, or 13.083...

Answer: 157 ÷ 12 = 13 R 1

Check: (13 × 12) + 1 = 156 + 1 = 157 ✓

Example 3: Division Resulting in Decimal

Problem: 25 ÷ 4

Step 1: 4 into 25 goes 6 times (6 × 4 = 24)
Subtract: 25 - 24 = 1

Step 2 (Continue with decimals): Add decimal point and 0
Bring down 0 to make 10

Step 3: 4 into 10 goes 2 times (2 × 4 = 8)
Subtract: 10 - 8 = 2
Could continue: bring down another 0 to make 20, 4 into 20 goes 5 times exactly

Answer: 25 ÷ 4 = 6.25

Check: 6.25 × 4 = 25.00 ✓

Example 4: Large Number Division

Problem: 2468 ÷ 17

Step 1: 17 into 24 goes 1 time (1 × 17 = 17)
Subtract: 24 - 17 = 7, bring down 6 to make 76

Step 2: 17 into 76 goes 4 times (4 × 17 = 68)
Subtract: 76 - 68 = 8, bring down 8 to make 88

Step 3: 17 into 88 goes 5 times (5 × 17 = 85)
Subtract: 88 - 85 = 3

Answer: 2468 ÷ 17 = 145 R 3

Check: (145 × 17) + 3 = 2465 + 3 = 2468 ✓

Example 5: Division by Powers of 10

Problem: 456 ÷ 100

Shortcut Method: When dividing by 10, 100, 1000, etc., move the decimal point left
Dividing by 100 = move decimal 2 places left

Calculation: 456.00 → Move 2 places left → 4.56

Answer: 456 ÷ 100 = 4.56

Check: 4.56 × 100 = 456 ✓

Similarly: ÷10 = move 1 left, ÷1000 = move 3 left

💡 Tips & Tricks for Long Division

The DMSB Method

Divide - How many times does divisor fit into current number?
Multiply - Multiply quotient by divisor
Subtract - Subtract product from current number
Bring down - Bring down next digit and repeat

Mental Math Shortcuts

Estimate first: Round divisor and dividend to estimate answer (helps catch errors)
Times tables: Know your times tables up to 12×12 for faster calculation
Check divisibility: Before starting, check if number is divisible (e.g., even numbers ÷2)
Powers of 10: Dividing by 10/100/1000 = move decimal left 1/2/3 places
Half and double: 48÷12 = 24÷6 = 12÷3 = 4 (keep halving both until easy)

Checking Your Work

Multiplication check: Quotient × Divisor + Remainder = Dividend
Estimation check: Does answer match your initial estimate?
Reasonableness: If 100÷10=10, then 96÷11 should be close to 10
Calculator verify: After working it out, verify with calculator

Remember These Rules

Dividend > Divisor usually: If not, quotient is decimal less than 1
Remainder < Divisor always: If not, you can divide more
Zero in quotient: It's OK to have 0 in middle of answer (e.g., 1005÷5=201)
Decimal placement: Decimal in quotient goes directly above decimal in dividend

⚠️ Common Mistakes to Avoid

❌ Mistake 1: Forgetting to bring down next digit

After subtracting, ALWAYS bring down the next digit before continuing

TIP: Draw an arrow down to the next digit as a reminder

❌ Mistake 2: Writing quotient in wrong place

Quotient digit must go directly above the last digit you're currently dividing

TIP: Line up quotient digits carefully above dividend

❌ Mistake 3: Incorrect subtraction

Double-check subtraction step - it's where most errors occur

TIP: Use addition to check: if 47-35=12, then 12+35 should equal 47

❌ Mistake 4: Choosing wrong quotient digit

WRONG: Guessing too high (e.g., 7 when actual answer is 6)

CORRECT: Estimate, try it, adjust if needed. OK to cross out and try again!

❌ Mistake 5: Not handling zeros correctly

When divisor doesn't go into current number, write 0 in quotient and bring down

Example: 1005÷5: After 10÷5=2, next is 0÷5=0, write 0, then 05÷5=1 → Answer: 201

❌ Mistake 6: Remainder larger than divisor

If remainder ≥ divisor, you can divide one more time

CHECK: Final remainder must ALWAYS be less than divisor

❌ Mistake 7: Forgetting to check answer

Always verify using (Quotient × Divisor) + Remainder = Dividend

HABIT: Make checking your last step EVERY TIME

📖 Complete Guide to Long Division

Understanding Division

Division is splitting a number into equal parts. The dividend is the number being divided, the divisor is the number you're dividing by, and the quotient is the answer. If there's an amount left over, that's the remainder. Division is the inverse operation of multiplication.

Key Division Terms

Dividend: The number being divided (inside the division bracket)
Divisor: The number you're dividing by (outside the bracket)
Quotient: The answer (written on top)
Remainder: What's left over when division isn't exact
Partial dividend: The portion of the dividend you're currently working with

When to Use Long Division

Use long division when:

Dividing by a two-digit or larger number
You need to show detailed working for homework or exams
The division doesn't work out evenly
You want to find exact remainders or decimal places
Practicing for UK SATs (Year 6) or GCSE exams

Different Ways to Express Division Results

With remainder: 17 ÷ 5 = 3 R 2 (common in primary school)
As decimal: 17 ÷ 5 = 3.4 (more precise)
As mixed number: 17 ÷ 5 = 3 2/5 (fraction form)
As improper fraction: 17 ÷ 5 = 17/5 (algebraic form)

Real-World Applications

Sharing equally: Dividing 24 sweets among 6 children (24÷6=4 each)
Finding unit price: £12 for 4 items (12÷4=£3 per item)
Time calculations: 150 minutes = how many hours? (150÷60=2.5 hours)
Recipe scaling: Recipe serves 8, but you need for 12 (portions × 12÷8)
Travel: 360 miles at 60 mph = 360÷60 = 6 hours

UK National Curriculum

In the UK, students learn division progressively:

Year 2-3: Sharing and grouping (basic division concepts)
Year 4-5: Short division with single-digit divisors
Year 5-6: Long division with two-digit divisors (required for SATs)
Year 7-9: Division with decimals, remainders as fractions
GCSE: Division in algebra, ratios, and problem-solving

❓ Frequently Asked Questions

How do you do long division step by step?

Follow the DMSB method: Divide (how many times?), Multiply (quotient × divisor), Subtract (from current number), Bring down (next digit). Repeat until no digits remain. Always check: (Quotient × Divisor) + Remainder = Dividend.

What is a remainder in division?

A remainder is what's left over when division isn't exact. For 17÷5, you get 3 with 2 left over (remainder 2). Remainders can be expressed as R2, as decimal .4, or as fraction 2/5.

How do you check if a long division answer is correct?

Use the check formula: (Quotient × Divisor) + Remainder = Dividend. For example, 456÷12=38 R0, check: (38×12)+0=456 ✓ This works for all division problems and helps catch errors.

Can you divide by zero?

No! Division by zero is undefined and impossible in mathematics. It's like asking "how many zeros make 5?" - there's no answer. Calculators show ERROR when you try this.

What's the difference between short division and long division?

Short division is for single-digit divisors (1-9) with working done mentally. Long division is for larger divisors (10+) with all steps written out clearly. Both use the same DMSB method, but long division shows more detail.

How do you do long division with decimals?

Move the decimal point in the divisor to make it a whole number, then move the dividend's decimal the same number of places. Divide normally, placing the decimal point in the quotient directly above where it appears in the dividend.

Why is long division still taught when we have calculators?

Long division builds crucial skills: place value understanding, estimation, systematic problem-solving, and number sense. These skills are essential for algebra, fractions, and mathematical thinking - not just getting an answer.

Is this calculator good for UK primary and secondary students?

Yes! Perfect for Years 5-11, showing step-by-step working following UK teaching methods. Use it to check homework, prepare for SATs or GCSEs, or understand the process better. Aligns with the UK National Curriculum.