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Division

Grades 4–8 Division

Division asks: "how many times does this fit into that?" — 984 ÷ 8 means "how many 8s inside 984?" Every division method is just a different bookkeeping system for the same question. Interestingly, division is naturally left-to-right already: every method starts with the biggest place value.

Method 1: long division (the classic)

Work through the big number digit by digit, left to right, asking "how many 8s fit here?" at each step:

1 2 3 _______ 8 ) 9 8 4 8 ← 8 goes into 9 once; 1 × 8 = 8 --- 1 8 ← bring down the 8 1 6 ← 8 goes into 18 twice; 2 × 8 = 16 --- 2 4 ← bring down the 4 2 4 ← 8 goes into 24 three times; 3 × 8 = 24 --- 0 Answer: 123
  1. 8 into 9 goes 1 time. Subtract 8, carry the remainder 1 to the next digit.
  2. 8 into 18 goes 2 times. Subtract 16, remainder 2.
  3. 8 into 24 goes 3 times. Subtract 24, remainder 0.
  4. Answer: 123. Check: 123 × 8 = 984. ✓

Method 2: short division (for small divisors)

Same questions, tidier layout — the carry-overs get written small between the digits instead of on their own lines:

1 2 3 _______ 8 ) 9 ¹8 ²4 9 ÷ 8 = 1 r 1 → the 1 hops onto the 8, making 18 18 ÷ 8 = 2 r 2 → the 2 hops onto the 4, making 24 24 ÷ 8 = 3 r 0 Answer: 123

Method 3: chunking (friendly numbers)

Keep subtracting easy groups of 8 until nothing's left — you choose how big each bite is:

984 ÷ 8 984 − 800 = 184 ← 100 eights 184 − 160 = 24 ← 20 more eights 24 − 24 = 0 ← 3 more eights 100 + 20 + 3 = 123

Bigger bites are faster, smaller bites are safer — both are correct. 984 − 96 (12 eights) twelve times works too; it just takes longer.

Remainders are allowed If something is left over, that's the remainder: 100 ÷ 8 = 12 remainder 4 (because 12 × 8 = 96, and 4 is left). Later you'll write it as a fraction or decimal: 100 ÷ 8 = 12.5.
Division by zero Dividing by zero isn't "zero" and it isn't infinity — it's genuinely undefined. "How many 0s fit in 984?" has no answer; no matter how many zeros you add, you never get anywhere. Any calculator or program that tries it will complain — rightly so.
Try it yourself:
  1. 96 ÷ 8  (answer: 12)
  2. 455 ÷ 7  (answer: 65)
  3. 1,296 ÷ 9  (answer: 144)

Division leans on multiplication facts — brush up in standard multiplication or left-to-right multiplication.

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