Unit 26
Bahagi
Pak Ali memetik 15 630 biji rambutan. Rambutan itu dimasukkan sama banyak ke dalam 10 buah bakul.
Berapakah rambutan dalam setiap bakul?
除法 = bahagi；商 = hasil bahagi；余数 = baki
把一个数量平均分成几份，求每份是多少，就要用除法。这个单元要学除以 10、100、1 000，以及五位数以内的数除以一位数和两位数，有时会有余数。
例子：60 个苹果平均放进 10 个袋子，每袋 60 ÷ 10 = 6 个。
注意：sama banyak（平均）告诉我们每份一样多；要看题目是求每一份有多少（用除法），还是求总数（用乘法）。
division = bahagi; quotient = hasil bahagi; remainder = baki
When an amount is shared equally into groups and we want the size of each group, we divide. In this unit we divide by 10, 100 and 1 000, and divide numbers up to five digits by one-digit and two-digit numbers, sometimes with a remainder.
Example: 60 apples shared equally into 10 bags gives 60 ÷ 10 = 6 in each bag.
Watch out: sama banyak tells us every share is equal; decide whether the question asks for the size of each share (divide) or for the total (multiply).
Bahagi dengan 10
Bahagi panjang: mula dari kiri
15 630 ÷ 10
| 1 | 5 | 6 | 3 | ||
| 10) | 1 | 5 | 6 | 3 | 0 |
| − | 1 | 0 | |||
| 5 | 6 | ||||
| − | 5 | 0 | |||
| 6 | 3 | ||||
| − | 6 | 0 | |||
| 3 | 0 | ||||
| − | 3 | 0 | |||
| 0 |
15 630 ÷ 10 = 1 563 → buang satu sifar
长除法 = bahagi panjang
长除法从最左边开始：先看被除数前面几位够不够除，够了就写商，乘回去、相减，再把下一位数字移下来，一直做到最后一位。除以 10 的时候，答案就是把末尾的一个 0 去掉。
例子：4 580 ÷ 10 = 458。
注意：商的每一位要写在对应的数位上方。
long division = bahagi panjang
Long division starts from the left. See whether the first digits can be divided; if so, write the quotient digit, multiply back, subtract and bring down the next digit, until the last digit is used. When dividing by 10, the answer is simply the number with its last zero removed.
Example: 4 580 ÷ 10 = 458.
Watch out: write each quotient digit above the matching place.
Bahagi dengan 100
Cara 2: cerakin dahulu
47 800 ÷ 100
47 800 = 40 000 + 7 000 + 800
40 000 ÷ 100 = 400
7 000 ÷ 100 = 70
800 ÷ 100 = 8
400 + 70 + 8 = 478
40 000 ÷ 100 = 400
7 000 ÷ 100 = 70
800 ÷ 100 = 8
400 + 70 + 8 = 478
先分解再除 = cerakin, kemudian bahagi
把被除数按数位分解成几部分，每一部分分别除以 100，最后把商加起来。这个方法和长除法得到同样的答案，而且可以看到：除以 100，就是去掉末尾两个 0。
例子：36 500 ÷ 100 = 300 + 60 + 5 = 365。
注意：只有末尾的 0 可以去掉，中间的 0 要留着。
break it down first = cerakin, kemudian bahagi
Split the number into parts by place value, divide each part by 100, and add the answers. This gives the same result as long division and shows that dividing by 100 removes the last two zeros.
Example: 36 500 ÷ 100 = 300 + 60 + 5 = 365.
Watch out: only zeros at the end can be removed; zeros in the middle stay.
Bahagi dengan 1 000
Lihat polanya
56 000 ÷ 10 · ÷ 100 · ÷ 1 000
56 000 ÷ 10 = 5 600
56 000 ÷ 100 = 560
56 000 ÷ 1 000 = 56
56 000 ÷ 100 = 560
56 000 ÷ 1 000 = 56
除以 10、100、1 000 = bahagi dengan 10, 100, 1 000
除以 10 去掉末尾一个 0，除以 100 去掉两个 0，除以 1 000 去掉三个 0。这正好和乘法相反：乘法补 0，除法去 0。
例子：92 000 ÷ 1 000 = 92。
注意：末尾的 0 不够去掉时，就会有余数，下面会学。
divide by 10, 100 and 1 000 = bahagi dengan 10, 100, 1 000
Dividing by 10 removes one zero from the end, by 100 removes two, and by 1 000 removes three. This is the opposite of multiplying, which adds zeros.
Example: 92 000 ÷ 1 000 = 92.
Watch out: when there are not enough zeros at the end, there is a remainder; we learn this later.
Bahagi dengan 1 000
Cara 1: tulis sebagai pecahan
74 000 ÷ 1 000
74 000 ÷ 1 000 = 74 0001 000 = 741 = 74
写成分数约去 0 = tulis sebagai pecahan, potong sifar
除法可以写成分数：被除数写在上面，除数写在下面。1 000 有三个 0，就在上下两个数的末尾各划掉三个 0，剩下的就是商：74 000 ÷ 1 000 = 74 ÷ 1 = 74。
例子：36 000 ÷ 1 000 → 上下各划掉三个 0 → 36。
注意：上面和下面划掉的 0 个数要一样，而且只能划末尾的 0。
write it as a fraction = tulis sebagai pecahan, potong sifar
A division can be written as a fraction, with the number being divided on top and the divisor below. 1 000 has three zeros, so cross out three zeros at the end of both numbers; what is left is the answer: 74 000 ÷ 1 000 = 74 ÷ 1 = 74.
Example: 36 000 ÷ 1 000: cross out three zeros on top and below to get 36.
Watch out: cross out the same number of zeros on top and below, and only zeros at the end.
Bahagi dan darab
Bahagi ialah songsangan darab
45 200 ÷ □ = 452
452 × 1 = 452
452 × 10 = 4 520
452 × 100 = 45 200
Jadi 45 200 ÷ 100 = 452
452 × 10 = 4 520
452 × 100 = 45 200
Jadi 45 200 ÷ 100 = 452
除法和乘法互逆 = bahagi songsangan darab
如果 452 × 100 = 45 200，那么 45 200 ÷ 100 = 452。除法算式里缺了除数时，可以改用乘法来想：商乘上哪一个数，会得到被除数？把 ×1、×10、×100 的结果一行一行列出来比较，就能找到。
例子：□ ÷ 1 000 = 64 → □ = 64 × 1 000 = 64 000。
注意：列模式时，每多乘一次 10，末尾就多一个 0。
division undoes multiplication = bahagi songsangan darab
If 452 × 100 = 45 200, then 45 200 ÷ 100 = 452. When the divisor is missing from a division sentence, think with multiplication: the answer times which number gives the starting number? List the results of × 1, × 10 and × 100 line by line and compare.
Example: □ ÷ 1 000 = 64, so □ = 64 × 1 000 = 64 000.
Watch out: in the pattern, each extra × 10 puts one more zero at the end.
Lima digit ÷ satu digit
Bahagi mengikut nilai tempat
43 752 ÷ 8
五位数除以一位数 = lima digit bahagi satu digit
从左边开始：4 不够除以 8，就看 43；43 ÷ 8 = 5 余 3，把 5 写在千位上方。把下一位 7 移下来成 37，37 ÷ 8 = 4 余 5……一直除到个位。答案 5 469。可以用 5 469 × 8 = 43 752 验算。
例子：25 616 ÷ 4 = 6 404。
注意：第一位不够除时，可以在万位上方先写 0，再和下一位一起除；读商的时候，最前面的 0 不用读。
five digits divided by one digit = lima digit bahagi satu digit
Start on the left: 4 cannot be divided by 8, so use 43. 43 ÷ 8 = 5 remainder 3; write 5 above the thousands. Bring down 7 to make 37; 37 ÷ 8 = 4 remainder 5; carry on to the ones. The answer is 5 469; check with 5 469 × 8 = 43 752.
Example: 25 616 ÷ 4 = 6 404.
Watch out: when the first digit is too small, you can write 0 above the ten thousands and divides it together with the next digit; the leading 0 is not read in the answer.
Bahagi dengan 25
Dua cara
225 ÷ 25
Cara 1: tolak 25 berulang pada garis nombor
0
50
100
150
200
225
mula
▼
▼
225 → 200 → 175 → … → 25 → 0 · 9 lompatan
Cara 2: 25 = 5 × 5
225 ÷ 5 = 45 → 45 ÷ 5 = 9
除以 25 = bahagi dengan 25
方法一：除法就是连续减，从 225 开始每次减 25，减到 0 一共减了几次，商就是几。方法二：25 = 5 × 5，所以可以先除以 5，再除以 5，每一步都比较容易。两种方法都得 9。
例子：300 ÷ 25 → 300 ÷ 5 = 60，60 ÷ 5 = 12。
注意：方法二是连除两次 5，不是除以 10。
divide by 25 = bahagi dengan 25
Method 1: division is repeated subtraction; start at 225 and take away 25 each time until you reach 0, and count the steps. Method 2: 25 = 5 × 5, so divide by 5 and then by 5 again, which is easier. Both give 9.
Example: 300 ÷ 25: 300 ÷ 5 = 60, then 60 ÷ 5 = 12.
Watch out: method 2 divides by 5 twice; it does not divide by 10.
Bahagi dengan dua digit
Bahagi panjang
68 952 ÷ 34
除以两位数 = bahagi dengan dua digit
方法和除以一位数一样，只是每一步要想“几个 34 最接近而不超过”。68 ÷ 34 = 2；移下 9，9 比 34 小，商写 0；移下 5 成 95，95 ÷ 34 = 2 余 27；移下 2 成 272，272 ÷ 34 = 8。答案 2 028。
例子：3 348 ÷ 12 = 279。
注意：不够除的时候，商一定要写 0，不能跳过。
divide by a two-digit number = bahagi dengan dua digit
The steps are the same as for one digit, but each time ask how many 34s fit without going over. 68 ÷ 34 = 2; bring down 9, which is smaller than 34, so write 0; bring down 5 to make 95, 95 ÷ 34 = 2 remainder 27; bring down 2 to make 272, 272 ÷ 34 = 8. The answer is 2 028.
Example: 3 348 ÷ 12 = 279.
Watch out: when a step is too small, write 0 in the quotient; do not skip it.
Ada baki · Cara 1
Bahagi panjang dengan 1 000
38 406 ÷ 1 000
| 3 | 8 | ||||
| 1 000) | 3 | 8 | 4 | 0 | 6 |
| − | 3 | 0 | 0 | 0 | |
| 8 | 4 | 0 | 6 | ||
| − | 8 | 0 | 0 | 0 | |
| 4 | 0 | 6 |
38 406 ÷ 1 000 = 38 baki 406
长除法求余数 = bahagi panjang dengan baki
除以 1 000 也可以用长除法：从左边开始，前三位 384 比 1 000 小，要看前四位 3 840，里面有 3 个 1 000，余 840；把 6 移下来成 8 406，里面有 8 个 1 000，余 406。所以商是 38，余数是 406。
例子：21 750 ÷ 1 000 → 商 21，余 750。
注意：余数一定要比除数 1 000 小，如果不是，就表示商还可以再大。
long division with a remainder = bahagi panjang dengan baki
Dividing by 1 000 can also be done by long division. From the left, 384 is smaller than 1 000, so use the first four digits, 3 840: it holds 3 thousands with 840 left. Bring down 6 to make 8 406, which holds 8 thousands with 406 left. The quotient is 38 and the remainder is 406.
Example: 21 750 ÷ 1 000 gives a quotient of 21 and a remainder of 750.
Watch out: the remainder must be smaller than 1 000; if it is not, the quotient can still be bigger.
Ada baki · Cara 2
Lihat pola: ÷ 10, ÷ 100, ÷ 1 000
47 385 ÷ 1 000
47 385 ÷ 10 = 4 738 baki 5
47 385 ÷ 100 = 473 baki 85
47 385 ÷ 1 000 = 47 baki 385
47 385 ÷ 100 = 473 baki 85
47 385 ÷ 1 000 = 47 baki 385
有余数的除法 = bahagi dengan baki
末尾不是 0 时，除以 10、100、1 000 会有余数。规律是：除以 10，最后一位是余数；除以 100，最后两位是余数；除以 1 000，最后三位是余数，前面的数就是商。
例子：52 614 ÷ 100 = 526 余 14。
注意：余数一定比除数小。
division with a remainder = bahagi dengan baki
If the number does not end in zeros, dividing by 10, 100 or 1 000 leaves a remainder. The pattern: ÷ 10 leaves the last digit as the remainder, ÷ 100 the last two digits, and ÷ 1 000 the last three digits; the digits in front are the quotient.
Example: 52 614 ÷ 100 = 526 remainder 14.
Watch out: the remainder is always smaller than the number you divide by.
Bina sifir
Sifir membantu membahagi
91 350 ÷ 43
1 × 43 = 43
2 × 43 = 86
3 × 43 = 129
4 × 43 = 172
5 × 43 = 215
6 × 43 = 258
7 × 43 = 301
8 × 43 = 344
9 × 43 = 387
先建乘法表 = bina sifir dahulu
除以两位数时，先把这个数的 1 到 9 倍写成表，做长除法时就能很快找到“最接近而不超过”的那一个倍数。例如要除 91 时，表里 86 最接近又不超过 91，所以商写 2。
例子：除以 26 时，先写 26、52、78、104……
注意：倍数表要一个一个加 43 往上算，不要跳着算；写完第 9 个，可以用 430 − 43 检查它对不对。
build a times table first = bina sifir dahulu
When dividing by a two-digit number, first write its 1 to 9 times table. Then in the long division you can quickly find the biggest multiple that does not go over each part.
Example: before dividing by 26, write 26, 52, 78, 104 and so on.
Watch out: build the table by adding 43 each time without skipping; check the ninth entry with 430 − 43.
Gunakan sifir
Bahagi panjang dengan sifir 43
91 350 ÷ 43 = 2 124 baki 18
| 2 | 1 | 2 | 4 | ||
| 43) | 9 | 1 | 3 | 5 | 0 |
| − | 8 | 6 | |||
| 5 | 3 | ||||
| − | 4 | 3 | |||
| 1 | 0 | 5 | |||
| − | 8 | 6 | |||
| 1 | 9 | 0 | |||
| − | 1 | 7 | 2 | ||
| 1 | 8 |
用表来除 = bahagi menggunakan sifir
每一步都去乘法表里找“不超过而且最接近”的倍数：91 里面最多有 2 个 43（86）；移下 3 成 53，最多 1 个 43；移下 5 成 105，最多 2 个（86）；移下 0 成 190，最多 4 个（172），余 18。
例子：100 ÷ 43 → 表里 86 最接近，商 2 余 14。
注意：余数 18 比 43 小，就停止。
divide using the table = bahagi menggunakan sifir
At each step find the multiple in the table that is closest without going over: 91 holds 2 lots of 43 (86); bring down 3 to make 53, which holds 1; bring down 5 to make 105, which holds 2 (86); bring down 0 to make 190, which holds 4 (172), leaving 18.
Example: 100 ÷ 43: 86 is closest, so the answer is 2 remainder 14.
Watch out: the remainder 18 is smaller than 43, so we stop.
Semak
Semak dengan darab dan tambah baki
2 124 × 43 + 18 = 91 350
Darab
| 2 | 1 | 2 | 4 | ||
| × | 4 | 3 | |||
| 6 | 3 | 7 | 2 | ||
| + | 8 | 4 | 9 | 6 | 0 |
| 9 | 1 | 3 | 3 | 2 |
Tambah baki
| 1 | |||||
| 9 | 1 | 3 | 3 | 2 | |
| + | 1 | 8 | |||
| 9 | 1 | 3 | 5 | 0 |
验算 = semak
商 × 除数 + 余数 = 被除数。2 124 × 43 = 91 332，再加余数 18，得 91 350，和原来的被除数一样，说明除法算对了。
例子：50 ÷ 7 = 7 余 1 → 7 × 7 + 1 = 50。
注意：验算时别忘了加上余数。
check = semak
quotient × divisor + remainder = the number divided. 2 124 × 43 = 91 332, and adding the remainder 18 gives 91 350, the starting number, so the division is correct.
Example: 50 ÷ 7 = 7 remainder 1, and 7 × 7 + 1 = 50.
Watch out: remember to add the remainder when checking.
Bina sifir
Sifir 53 daripada sifir 5 dan sifir 3
53 × n = 50 × n + 3 × n
1 × 53
50 + 3 = 53
50 + 3 = 53
2 × 53
100 + 6 = 106
100 + 6 = 106
3 × 53
150 + 9 = 159
150 + 9 = 159
4 × 53
200 + 12 = 212
200 + 12 = 212
5 × 53
250 + 15 = 265
250 + 15 = 265
6 × 53
300 + 18 = 318
300 + 18 = 318
7 × 53
350 + 21 = 371
350 + 21 = 371
8 × 53
400 + 24 = 424
400 + 24 = 424
9 × 53
450 + 27 = 477
450 + 27 = 477
用两个乘法表拼出新表 = bina sifir 53 daripada sifir 5 dan 3
53 = 50 + 3，所以 n 个 53 就是 n 个 50 加上 n 个 3。n 个 50 用乘法表 5 的得数再补一个 0，n 个 3 直接查乘法表 3。例如 3 × 53 = 150 + 9 = 159。这样 1 到 9 倍都能很快写出来，做 ÷ 53 的长除法时就可以查表。
例子：要建 48 的表 → 48 = 40 + 8，4 × 48 = 160 + 32 = 192。
注意：50 × n 的个位一定是 0，别忘了在乘法表 5 的得数后面补 0。
build a new table from two tables = bina sifir 53 daripada sifir 5 dan 3
53 = 50 + 3, so n lots of 53 are n lots of 50 plus n lots of 3. For n lots of 50, take the 5 times table answer and write a 0 after it; for n lots of 3, use the 3 times table. For example, 3 × 53 = 150 + 9 = 159. The 1 to 9 times entries come quickly, and the table helps in long division by 53.
Example: to build the 48 table, 48 = 40 + 8, so 4 × 48 = 160 + 32 = 192.
Watch out: 50 × n always ends in 0, so remember the 0 after the 5 times table answer.
Anggar dahulu
Adakah jawapan munasabah?
58 740 ÷ 31
Anggaran: 60 000 ÷ 30 = 2 000
| 1 | 8 | 9 | 4 | ||
| 31) | 5 | 8 | 7 | 4 | 0 |
| − | 3 | 1 | |||
| 2 | 7 | 7 | |||
| − | 2 | 4 | 8 | ||
| 2 | 9 | 4 | |||
| − | 2 | 7 | 9 | ||
| 1 | 5 | 0 | |||
| − | 1 | 2 | 4 | ||
| 2 | 6 |
1 894 baki 26 ≈ 2 000 ✔
先估计 = anggar dahulu
把被除数和除数都取成好算的整数：60 000 ÷ 30 = 2 000。准确答案 1 894 余 26 很接近 2 000，所以合理。如果算出来是 189 或 18 940，就知道一定错了。
例子：39 800 ÷ 19 ≈ 40 000 ÷ 20 = 2 000。
注意：估计是用来检查位数对不对。
estimate first = anggar dahulu
Round both numbers to easy ones: 60 000 ÷ 30 = 2 000. The exact answer, 1 894 remainder 26, is close to 2 000, so it is reasonable. An answer like 189 or 18 940 would clearly be wrong.
Example: 39 800 ÷ 19 ≈ 40 000 ÷ 20 = 2 000.
Watch out: an estimate helps you check that the answer has the right number of digits.
Kira cepat
63 000 ÷ 1 000 = ?
除以一千 = bahagi dengan seribu
除数是一千，一千有三个 0，所以把被除数末尾的三个 0 去掉，剩下的就是商。也可以写成分数，上下各划掉三个 0。做完用乘法检查：商乘一千，要回到原来的数。
例子：41 000 ÷ 1 000 = 41。
注意：去掉 0 的个数要和除数的 0 一样多，少去一个就变成除以一百了。
divide by one thousand = bahagi dengan seribu
The divisor is one thousand, which has three zeros, so remove the last three zeros of the number; what is left is the answer. You can also write a fraction and cross out three zeros on top and below. Check by multiplying: the answer times one thousand must give the starting number.
Example: 41 000 ÷ 1 000 = 41.
Watch out: remove as many zeros as the divisor has; one zero fewer would be dividing by one hundred.
Cuba
9 135 ÷ 7 = ?
商中间的 0 = sifar dalam hasil bahagi
用长除法从最左边开始：每一步先看够不够除，够就写商、乘回去、相减，再把下一位移下来。如果移下来的数比除数小，就在商的这一位写 0，再移下一位继续。最后用“商 × 除数”检查。
例子：8 048 ÷ 8 = 1 006。
注意：写 0 的那一步最容易漏掉，漏了商就少一位；0 的位置放错，商也会变。
a zero in the quotient = sifar dalam hasil bahagi
Use long division from the left. At each step see whether it can be divided; if so, write the quotient digit, multiply back, subtract and bring down the next digit. If the number brought down is smaller than the divisor, write 0 in that place of the quotient and bring down the next digit. Check with quotient × divisor.
Example: 8 048 ÷ 8 = 1 006.
Watch out: the step that needs a 0 is easy to miss, which loses a digit; putting the 0 in the wrong place also changes the answer.
Ada baki
75 213 ÷ 100 = ?
除以一百有余数 = bahagi 100 dengan baki
除以一百时，被除数的最后两位数字是余数，前面的数字就是商。可以先用一条线把最后两位隔开，线前面是商，线后面是余数。
例子：40 507 ÷ 100 = 405 余 7。
注意：除以十只隔开最后一位，除以一千隔开最后三位；看清楚除数再决定隔开几位。
divide by 100 with a remainder = bahagi 100 dengan baki
When dividing by 100, the last two digits are the remainder and the digits in front are the quotient. Draw a line before the last two digits: in front of the line is the quotient, after it is the remainder.
Example: 40 507 ÷ 100 = 405 remainder 7.
Watch out: ÷ 10 splits off only the last digit and ÷ 1 000 the last three, so read the divisor before drawing the line.
Ringkasan
Syabas!
÷
Bahagi dari kiri. Tulis 0 jika tidak cukup. Semak: hasil bahagi × pembahagi + baki.
Latihan tambahan →