Unit 19
Bahagi
Cikgu ada 18 biji bola. Dia membahagikan bola itu sama banyak kepada 3 kumpulan. Berapakah bola bagi setiap kumpulan?
18 ÷ 3 = ?
除 = bahagi；平分 = bahagi sama banyak
除法就是把一个数平均分成几份，求每一份有多少；或者求一个数里面有几个同样的组。题目里看到 sama banyak（一样多）、dibahagikan（分给）、“setiap … menerima 多少”（求每一份）等说法，通常要用除法；如果已经知道每份多少、要求总数，那是乘法。本单元的计算题都刚好分完；实验台里分不完剩下的，叫余数（baki）。
例子：18 个球平分给 3 组 → 18 ÷ 3 = 6。
注意：除法和乘法是相反的：3 × 6 = 18。
divide = bahagi, share equally = bahagi sama banyak
Dividing shares a number equally into groups to find how many in each, or finds how many equal groups fit. Phrases like sama banyak (the same), dibahagikan (shared) and 'setiap … menerima berapa' (how many does each get) usually tell you to divide; if each share is known and the total is asked, multiply instead. The sums in this unit share exactly; in the lab, anything left over that cannot be shared is the remainder (baki).
Example: 18 balls shared among 3 groups → 18 ÷ 3 = 6.
Watch out: division is the opposite of multiplication: 3 × 6 = 18.
Tolak berulang
Bahagi sebagai tolak berulang
18 ÷ 3
18 → 15 → 12 → 9 → 6 → 3 → 0
−3 sebanyak 6 kali
18 ÷ 3 = 6
−3 sebanyak 6 kali
18 ÷ 3 = 6
连续减 = tolak berulang
除法可以看成“一直减同一个数，直到减完为止”。18 每次减 3：15、12、9、6、3、0，一共减了 6 次，所以 18 ÷ 3 = 6。减了几次，就是商。
例子：12 ÷ 4 → 8、4、0 → 减了 3 次 → 3。
注意：数的是“减了几次”，不是最后剩下的数。
repeated subtraction = tolak berulang
Division can be seen as taking away the same number again and again until nothing is left. 18 minus 3 each time: 15, 12, 9, 6, 3, 0, which is 6 times, so 18 ÷ 3 = 6. The number of subtractions is the answer.
Example: 12 ÷ 4 → 8, 4, 0 → 3 times → 3.
Watch out: count how many times you subtracted, not what is left at the end.
Kongsi sama banyak
Pilih bilangan orang, kemudian agihkan objek satu demi satu kepada setiap orang.
平均分 = kongsi sama banyak；轮流 = secara giliran；余数 = baki
实验台把物件一个一个轮流放进每个人的盒子，确保每个人得到一样多。分完后，盒子里的数量是商；无法再平均分的物件留在下面，叫余数。选择 3、4、5 人分别观察。
例子：14 个物件分给 3 人，每人先得到相同数量，剩下的另放。
注意：不能为了分完而让其中一个人多拿，平均分时每个人必须一样多。
share equally = kongsi sama banyak; in turn = secara giliran; remainder = baki
The lab places objects into each person's box one at a time in turn so everyone receives the same amount. The number in each box is the quotient; any objects that cannot form another equal round remain below as the remainder. Try groups of 3, 4 and 5 people.
Example: when 14 objects are shared among 3 people, each person first receives an equal number and the rest stay aside.
Watch out: do not give one person extra just to use every object; equal sharing means all people receive the same number.
Semak makmal
Apakah maksud baki dalam pembahagian?
余数 = baki；平均分 = kongsi sama banyak
题目问分完以后画面下方留下的物件代表什么。回想实验台：每轮要给每个人各一个；当剩下的物件不够再进行完整一轮时，它们会留在盒子外。请选择描述这种情况的选项。
例子：可以用小圆点模拟分发，并在每一轮后检查是否人人都有相同数量。
注意：余数不是人数，也不是每个人已经得到的数量。
remainder = baki; share equally = kongsi sama banyak
The question asks what the objects left below the boxes represent. Recall that every complete round gives one object to every person. When there are too few objects for another complete round, they stay outside the boxes. Choose the option that describes this situation.
Example: model the sharing with small counters and check after each round that everyone has the same amount.
Watch out: the remainder is not the number of people or the number already received by each person.
Bahagi panjang
Bahagi dari tempat paling kiri
936 ÷ 3 = ?
Semak: 3 × 312 = 936 ✔
长除法 = bahagi panjang
除法和加减乘不一样，要从最左边的数位开始：百位 9 ÷ 3 = 3，写在百位上面；十位 3 ÷ 3 = 1；个位 6 ÷ 3 = 2。所以 936 ÷ 3 = 312。用乘法检查：3 × 312 = 936 ✔。
例子：84 ÷ 4 → 8÷4=2，4÷4=1 → 21。
注意：商的每个数字要写在对应的数位上面。
long division = bahagi panjang
Unlike adding, subtracting and multiplying, division starts from the left: hundreds 9 ÷ 3 = 3, written above the hundreds; tens 3 ÷ 3 = 1; ones 6 ÷ 3 = 2. So 936 ÷ 3 = 312. Check: 3 × 312 = 936 ✔.
Example: 84 ÷ 4 → 8÷4=2, 4÷4=1 → 21.
Watch out: write each digit of the answer above its own place.
Tukar puluh kepada sa
Bahagi dengan baki puluh
72 ÷ 3 = ?
| 2 | 4 | |
| 3) | 7 | 2 |
① 7 puluh ÷ 3 = 2 puluh baki 1 puluh
② baki 1 puluh = 10 sa
③ 10 sa + 2 sa = 12 sa
④ 12 sa ÷ 3 = 4 sa → 72 ÷ 3 = 24
十换成一 = tukar puluh kepada sa
72 ÷ 3：先除十位，7 个十除以 3，每份 2 个十，还剩 1 个十。剩下的 1 个十不能丢掉，要换成 10 个一，和原来的 2 个一合起来是 12 个一。12 ÷ 3 = 4，所以答案 24。检查：3 × 24 = 72 ✔。
例子：52 ÷ 4 → 5 个十 ÷ 4 = 1 个十余 1 个十 → 换成 10 个一，加 2 = 12 → 12 ÷ 4 = 3 → 13。
注意：余下的十要换成一，带到个位一起除。
change tens into ones = tukar puluh kepada sa
72 ÷ 3: divide the tens first. 7 tens ÷ 3 gives 2 tens each with 1 ten left. That ten is not thrown away; change it into 10 ones and add the 2 ones to make 12 ones. 12 ÷ 3 = 4, so the answer is 24. Check: 3 × 24 = 72 ✔.
Example: 52 ÷ 4 → 5 tens ÷ 4 = 1 ten with 1 ten left → 10 ones + 2 = 12 → 12 ÷ 4 = 3 → 13.
Watch out: a ten left over must be changed into ones and divided with the ones.
Corak
Bahagi 10, 100 dan 1 000
6 300 ÷ 10 = 630
6 300 ÷ 100 = 63
6 000 ÷ 1 000 = 6
除以 10、100、1 000 = bahagi 10, 100, 1 000
除以 10，每个数字都往右移一位，末尾去掉一个 0；除以 100 去掉两个 0；除以 1 000 去掉三个 0。这正好是乘 10、100、1 000 的相反。
例子：6 300 ÷ 10 = 630，6 300 ÷ 100 = 63，6 000 ÷ 1 000 = 6。
注意：这一招只适用于末尾有足够 0 的数。
divide by 10, 100, 1 000 = bahagi 10, 100, 1 000
Dividing by 10 moves every digit one place right, taking one 0 off the end; by 100 take off two zeros; by 1 000 take off three. It is the opposite of multiplying by 10, 100, 1 000.
Example: 6 300 ÷ 10 = 630, 6 300 ÷ 100 = 63, 6 000 ÷ 1 000 = 6.
Watch out: this shortcut works only when the number ends in enough zeros.
Cuba kira
84 ÷ 4 = ?
| ? | ? | |
| 4) | 8 | 4 |
从左边除起 = bahagi dari kiri
十位 8 ÷ 4 = 2，个位 4 ÷ 4 = 1，所以 84 ÷ 4 = 21。检查：4 × 21 = 84 ✔。12 是把两个数字倒过来写。除法的商要从最高位写起，所以十位的商在前面。
例子：69 ÷ 3 = 23。
注意：十位的商写在前面。
divide from the left = bahagi dari kiri
Tens 8 ÷ 4 = 2, ones 4 ÷ 4 = 1, so 84 ÷ 4 = 21. Check: 4 × 21 = 84 ✔. 12 writes the digits the wrong way round.
Example: 69 ÷ 3 = 23.
Watch out: the tens digit of the answer comes first.
Tukar ratus dan puluh
738 ÷ 6 = ?
| ? | ? | ? | |
| 6) | 7 | 3 | 8 |
连续换位 = tukar berturut-turut
百位：7 ÷ 6 = 1，余 1 个百 → 换成 10 个十，加原来的 3 个十 = 13 个十；十位：13 ÷ 6 = 2，余 1 个十 → 换成 10 个一，加 8 = 18 个一；个位：18 ÷ 6 = 3。答案 123。检查：6 × 123 = 738 ✔。
例子：735 ÷ 5 = 147。
注意：每一步剩下的都要换到右边一位，不能丢掉。
regroup again and again = tukar berturut-turut
Hundreds: 7 ÷ 6 = 1 with 1 hundred left → 10 tens, plus the 3 tens = 13 tens; tens: 13 ÷ 6 = 2 with 1 ten left → 10 ones, plus 8 = 18 ones; ones: 18 ÷ 6 = 3. The answer is 123. Check: 6 × 123 = 738 ✔.
Example: 735 ÷ 5 = 147.
Watch out: whatever is left at each step moves to the next place on the right; never drop it.
Kira secara pantas
5 400 ÷ 9 = ?
快速计算 = kira secara pantas
5 400 就是 54 个百。用乘法口诀 9 × 6 = 54，所以 54 个百 ÷ 9 = 6 个百 = 600。这类整十、整百的数，先把后面的 0 盖住，用口诀算，再把 0 补回去。检查：9 × 600 = 5 400 ✔。
例子：350 ÷ 5 → 35 个十 ÷ 5 = 7 个十 = 70。
注意：60 和 6 000 是补错了 0 的个数。
calculate quickly = kira secara pantas
5 400 is 54 hundreds. From the times table 9 × 6 = 54, so 54 hundreds ÷ 9 = 6 hundreds = 600. For numbers ending in zeros, cover the zeros, use the times table, then put the zeros back. Check: 9 × 600 = 5 400 ✔.
Example: 350 ÷ 5 → 35 tens ÷ 5 = 7 tens = 70.
Watch out: 60 and 6 000 put back the wrong number of zeros.
Bahagi 100
5 600 ÷ 100 = ?
除以 100 = bahagi 100
5 600 除以 100，末尾去掉两个 0，得到 56。560 只去掉了一个 0（那是除以 10）；506 是把 0 放错了位置。检查：56 × 100 = 5 600 ✔。除以 100 就是把每个数字往右移两位。
例子：4 200 ÷ 100 = 42。
注意：数清楚 100 有两个 0。
divide by 100 = bahagi 100
5 600 ÷ 100: take two zeros off the end to get 56. 560 takes off only one zero (that is ÷ 10); 506 puts a 0 in the wrong place. Check: 56 × 100 = 5 600 ✔.
Example: 4 200 ÷ 100 = 42.
Watch out: 100 has two zeros.
Cari kesilapan
Farid menulis 6 024 ÷ 6 = 104. Apakah jawapan yang betul?
商中间的 0 = sifar dalam hasil bahagi
千位 6 ÷ 6 = 1；百位 0 ÷ 6 = 0，这个 0 一定要写；十位 2 不够 6，写 0，和个位合成 24；24 ÷ 6 = 4。所以答案 1 004。Farid 漏写了 0。
例子：3 015 ÷ 3 = 1 005。
注意：用乘法检查：6 × 104 = 624，不是 6 024。
zeros inside the answer = sifar dalam hasil bahagi
Thousands 6 ÷ 6 = 1; hundreds 0 ÷ 6 = 0, and this 0 must be written; tens 2 is less than 6, so write 0 and combine it with the ones to make 24; 24 ÷ 6 = 4. The answer is 1 004. Farid left out the zeros.
Example: 3 015 ÷ 3 = 1 005.
Watch out: check by multiplying: 6 × 104 = 624, not 6 024.
Ringkasan
Syabas!
Bahagi sama banyak
Bahagi dari tempat paling kiri. Semak dengan darab. Bahagi 10, 100, 1 000: buang 1, 2 atau 3 sifar.
Latihan tambahan →