Division Strategies
Master dividing large numbers by 1-digit divisors using short division, understand remainders, and choose the best strategy for any division problem.
What Is Division?
Division is sharing equally or grouping into equal sets. When we divide, we split a number into equal parts. For example, 24 ÷ 4 asks: "How many groups of 4 are in 24?" or "If I share 24 into 4 equal groups, how many in each group?"
Sharing (Partitioning)
Split 12 biscuits equally among 3 friends. How many each?
12 ÷ 3 = 4
Parts of a Division
84 ÷ 4 = 21
84
Dividend
(number being divided)
4
Divisor
(dividing by)
21
Quotient
(answer)
Short Division (The Bus Stop Method)
Short division is a written method for dividing larger numbers. We work through the digits from left to right, carrying remainders as we go. It is called the "bus stop" method because the division sign looks like a bus stop shelter.
How Short Division Works: 952 ÷ 4
9 ÷ 4 = 2 remainder 1. Write 2 above, carry 1.
Carry 1 makes 15. 15 ÷ 4 = 3 r 3. Carry 3.
Carry 3 makes 32. 32 ÷ 4 = 8 exactly. No remainder.
952 ÷ 4 = 238
Dealing With Remainders
Sometimes a number does not divide evenly. The amount left over is called the remainder.
Example: 47 ÷ 5
5 × 9 = 45 (close but less than 47)
47 − 45 = 2 left over
47 ÷ 5 = 9 remainder 2 (9 r 2)
When does the remainder matter?
"Pack 47 eggs into boxes of 5. How many full boxes?"
Answer: 9 full boxes (ignore remainder)
"How many eggs left over?" Answer: 2 eggs
Mental Division Strategies
Halving
Dividing by 2 is the same as finding half.
96 ÷ 2
Half of 96 = 48
Use Multiplication Facts
Division is the inverse of multiplication.
63 ÷ 7
7 × 9 = 63, so answer = 9
Chunking
Take away known multiples in chunks.
84 ÷ 6
6×10=60; 84−60=24
6×4=24; total: 14
Key Vocabulary
Dividend
The number being divided up. In 84 ÷ 4, the dividend is 84.
Divisor
The number you are dividing by. In 84 ÷ 4, the divisor is 4.
Quotient
The result of a division. In 84 ÷ 4 = 21, the quotient is 21.
Remainder
The amount left over after dividing evenly. In 47 ÷ 5 = 9 r 2, the remainder is 2.
Worked Examples
Calculate 738 ÷ 3 using short division.
Step 1: 7 ÷ 3 = 2 remainder 1. Write 2, carry 1.
Step 2: Bring in carry: 13 ÷ 3 = 4 remainder 1. Write 4, carry 1.
Step 3: Bring in carry: 18 ÷ 3 = 6 exactly. Write 6.
Answer: 738 ÷ 3 = 246
What is 365 ÷ 7? Include any remainder.
Step 1: 3 ÷ 7 = 0 r 3. Write 0, carry 3. (Or start from 36 as the first chunk.)
Step 2: 36 ÷ 7 = 5 r 1 (7 × 5 = 35). Write 5, carry 1.
Step 3: 15 ÷ 7 = 2 r 1 (7 × 2 = 14). Write 2, remainder 1.
Answer: 365 ÷ 7 = 52 remainder 1
A farmer has 504 apples to pack into bags of 6. How many full bags?
Step 1: Set up: 504 ÷ 6
Step 2: 5 ÷ 6 = 0 r 5. Use 50: 50 ÷ 6 = 8 r 2. Carry 2.
Step 3: 24 ÷ 6 = 4 exactly.
Answer: 504 ÷ 6 = 84. The farmer can fill 84 full bags.
Knowledge Check
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Key Concepts Summary
- ●Division means sharing equally or grouping into equal sets.
- ●Short division works digit by digit from left to right, carrying remainders to the next column.
- ●The remainder is the amount left over when a number does not divide evenly.
- ●Division and multiplication are inverse operations — use times tables to check your answers.
- ●Always check your answer: quotient × divisor + remainder = dividend.