Division (I): Equal sharing

1Summary 重點摘要

Split equally. 12 / 3 = 4.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Step 1: Know equal sharingEqual sharing means every part gets the same amount. For example, share 12 sweets equally among 3 children: each child must get the same number of sweets, nobody more and nobody less; agree on the rule before starting and take turns, so there is no argument. Fair sharing, with every part the same, is exactly what division means. A common mistake is to serve two children first, giving out 5 sweets and then 4, and only remember the third child at the end, so the shares differ. The right way is to deal in rounds, so that each child gets the same amount in every round.
2. Step 2: Deal them out in roundsThe sweets can be dealt one at a time in rounds: in round 1 each child gets 1 sweet, using 3 sweets and leaving 12 − 3 = 9; in round 2 each gets another 1, using 3 more and leaving 6; after round 3, 3 remain. Go on like this, round by round, each round using exactly the number of children, 3 sweets, until all the sweets are shared out. A common mistake is to give 2 sweets each in the first round but only 1 each in the second, dealing unevenly. The amount per child must be the same in every round, or the final shares will differ and the sharing will no longer be equal.
3. Step 3: Share until none is leftBy round 4, each child takes 1 more sweet; this round uses 3 sweets, and in all 4 × 3 = 12 have been used. Since 12 − 12 = 0, the sweets are finished and none are left over. With no remainder, 12 sweets can be shared exactly equally among 3 children, and no child gets less. A common mistake is to miscount the rounds and think the sweets ran out after three. After each round, record what is left with subtraction: 12, 9, 6, 3, 0; once the list reaches 0, you know the sweets are exactly used up and can write the answer with confidence.
4. Step 4: How many each child getsEach child received 1 sweet in each of the four rounds, 4 times in all, so each child gets 4 sweets. As a division sentence it is 12 ÷ 3 = 4: 12 is the total to share, called the dividend; 3 is the number of children, called the divisor; and 4, the amount each child gets, is called the quotient. Check once more: 4 sweets times 3 children equals 12 sweets, matching the total. A common mistake is to swap the quotient and the divisor, writing 12 ÷ 4 = 3. Be clear that 3 is the number of people sharing and 4 is the amount each person gets; the two meanings differ and must not be reversed.
5. Step 5: Check with multiplicationDivision can be checked with multiplication: 3 children with 4 sweets each gives 3 × 4 = 12, back to the original 12 sweets. If the multiplication result equals the total, the division is correct; if it does not, giving 9 or 15 for example, the quotient is wrong and must be worked out again. This method is quick and reliable: a few seconds of multiplication after each division confirms the answer. A common mistake is to add the divisor and the quotient, 3 + 4 = 7, and call that a check. The check must use multiplication, because multiplication is the inverse of division; addition cannot catch a wrong quotient.
6. Step 6: A fast way - use times tablesWith bigger numbers we need not deal round by round; think of times tables instead. For 20 ÷ 5, ask 'what times 5 makes 20?' Since 5 × 4 = 20, we know 20 ÷ 5 = 4. Likewise for 42 ÷ 7, recalling 7 × 6 = 42 shows the answer is 6. Knowing the tables well makes division much faster. A common mistake is an untrained memory of the tables, trying numbers one by one, wasting time and missing the right one, or misremembering a fact such as taking seven eights as 54 instead of 56. Read the tables a few times every day, and in a problem first think 'what times what makes this?' Division then becomes quick and accurate.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• Equal sharing means division.
• 12 ÷ 3 = 4 means 3 equal groups of 4.
• Times tables help: 4 × 3 = 12.
• Dealing round by round keeps it fair.
• Check: quotient x divisor = total.