4-digit division

1Summary 重點摘要

846 ÷ 2 = 423. Start from left.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Part 1: Start from the highest placeFor 848 ÷ 4, begin at the hundreds: 8 ÷ 4 = 2, so write 2 in the quotient's hundreds place. Unlike addition and subtraction, division runs from the highest place down, left to right. Keep the direction straight from the very first step. Why opposite to addition and subtraction? Division is a process of sharing, and the biggest units must be shared out first, the smaller units after. Take care that each quotient digit sits above the digit being divided; the 2 from 8 ÷ 4 belongs over the hundreds, and written anywhere else the whole working tangles.
2. Part 2: Keep dividing each placeContinue 848 ÷ 4: tens 4 ÷ 4 = 1, so write 1 in the tens of the quotient; ones 8 ÷ 4 = 2, so write 2 in the ones. The quotient is 212. Check: 212 × 4 = 848, exactly the dividend, so the quotient is correct. Why check? Long division has many steps, and a slip in any one of them spoils the result; multiplying the quotient by the divisor is the most reliable check. Take care to find every quotient digit in order; skipping a place leaves the quotient with the wrong number of digits, and the answer goes wrong on its own.
3. Part 3: Bring down when neededFor 650 ÷ 5: hundreds 6 ÷ 5 = 1 remainder 1; bring down the tens 5 to make 15, and 15 ÷ 5 = 3; finally the ones 0 ÷ 5 = 0. The quotient is 130. Why bring down? The remainder is too small to divide alone, and joined with the next digit it becomes big enough. The final 0 must be written, or the answer wrongly becomes 13, ten times too small. Take care to bring down one digit at a time, never two, and to write each brought-down digit in its proper place, joining the remainder into a new number.
4. Part 4: Keep the quotient alignedIn 848 ÷ 4 = 212, each digit of the quotient sits over its own place: 2 over the hundreds, 1 over the tens, 2 over the ones. A slipped digit becomes a completely different number. Watch the dividend's places and write one digit per place. Why does alignment matter so much? Each quotient digit reports the result for the same place of the dividend, and a slip changes every place value, so the number goes wrong by itself. Take care that when a place cannot divide, a 0 goes into the quotient there; leaving it blank is misalignment all the same, and the next part shows a real case.
5. Part 5: Dividing with remainders927 ÷ 3: 9 ÷ 3 = 3; 2 ÷ 3 is too small, so write 0 in the tens of the quotient; bring down the 7 to make 27, and 27 ÷ 3 = 9. The quotient is 309. Also 930 ÷ 4 = 232 remainder 2, and 232 × 4 + 2 = 930 checks out. Every remainder stays smaller than the divisor, the rule of long division. Why smaller? If the remainder reached or passed the divisor, one more share could still be given, which means the quotient was written short. Take care that with a remainder, checking uses quotient × divisor + remainder; leaving out the remainder spoils the check.
6. Part 6: Word problemShare 848 sweets equally among 4 classes: 848 ÷ 4 = 212, so each class gets 212 sweets. If a remainder appears, follow what the question asks; sometimes round down, sometimes prepare one extra share. Read the question carefully before deciding. Why can the same remainder demand different treatment? The situation gives the remainder its meaning: leftover sweets may be kept, but leftover people still need another bus. Take care to answer in a full sentence with the unit; a bare number is not a complete answer, and that is the basic requirement of word problems.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• Long division runs left to right from the highest place
• Bring down the next digit when needed
• Write 0 for any place that is too small
• Remainders stay smaller than the divisor
• Check: quotient × divisor + remainder = dividend