Unit 17
Tolak
Sebuah stadium ada 35 482 tempat duduk. Pada satu perlawanan, 2 675 tempat duduk kosong.
Berapakah penonton yang hadir?
减法 = tolak；差 = beza
从全部座位里去掉空着的座位，剩下的就是来了的观众，这要用减法。减法也可以用来比较两个数相差多少。这个单元要学会十万以内的减法，包括连续减两个数。
例子：1 000 个座位空了 150 个，来了 1 000 − 150 = 850 人。
注意：“剩下”“相差”“多多少”“少多少”通常表示要用减法。
subtraction = tolak; difference = beza
Taking the empty seats away from all the seats tells us how many people came; that is subtraction. Subtraction also tells us how far apart two numbers are. In this unit we subtract within 100 000, including taking away two numbers in a row.
Example: 1 000 seats with 150 empty means 1 000 − 150 = 850 people came.
Watch out: words such as baki, beza, berapa lebih and berapa kurang usually mean subtract.
Bentuk lazim
Tolak dari sa, kumpul semula jika perlu
35 482 − 2 675
退位减法 = tolak dengan kumpul semula
按数位对齐后从个位减起。上面的数字比下面的小、不够减时，就向左边一位借 1：左边那一位少 1，这一位多 10，再减。红色小字就是借位以后的新数字。
例子：52 634 − 1 857：个位 4 不够减 7，借一个十变 14，14 − 7 = 7……答案 50 777。
注意：借过的那一位要记得先减 1 再计算。
subtraction with regrouping = tolak dengan kumpul semula
Line up the places and subtract from the ones. If the top digit is smaller than the bottom digit, borrow 1 from the place on the left: that place goes down by 1 and this place gets 10 more. The small red digits show the new values after borrowing.
Example: 52 634 − 1 857: 4 ones is less than 7, so regroup to 14 − 7 = 7, and so on; the answer is 50 777.
Watch out: remember that the place you borrowed from is now 1 less.
Cari kesilapan
Pengiraan manakah betul?
48 316 − 2 205
Kiraan 1 ✔
| 4 | 8 | 3 | 1 | 6 | |
| − | 2 | 2 | 0 | 5 | |
| 4 | 6 | 1 | 1 | 1 |
Kiraan 2 ✘
| 4 | 8 | 3 | 1 | 6 | |
| − | 2 | 2 | 0 | 5 | 0 |
| 2 | 6 | 2 | 6 | 6 |
对齐数位 = susun ikut nilai tempat
做竖式时，两个数要按个位对齐，不是按最左边对齐。第二种算法把 2 205 往左移了一位，变成当作 22 050 来减，所以答案错了。
例子：63 480 − 510，要把 510 的 0 放在个位下面，答案 62 970。
注意：位数少的数，前面要空出位置。
line up the place values = susun ikut nilai tempat
In a column calculation, line the numbers up by their ones, not by their left edges. The second working shifts 2 205 one place to the left, so it is really taking away 22 050, which gives a wrong answer.
Example: 63 480 − 510: put the 0 of 510 under the ones; the answer is 62 970.
Watch out: a number with fewer digits leaves empty places on the left.
Semak jawapan
Semak tolak dengan tambah
50 213 − 6 408 = 43 805
Tolak
| 4 | 9 | 12 | 0 | 13 | |
| 5 | 0 | 2 | 1 | 3 | |
| − | 6 | 4 | 0 | 8 | |
| 4 | 3 | 8 | 0 | 5 |
Semak: tambah
| 1 | 1 | 1 | |||
| 4 | 3 | 8 | 0 | 5 | |
| + | 6 | 4 | 0 | 8 | |
| 5 | 0 | 2 | 1 | 3 |
用加法验算 = semak dengan tambah
减法和加法是相反的运算。把差和减数加起来，如果等于被减数，就表示减法算对了。
例子：9 000 − 2 750 = 6 250，验算：6 250 + 2 750 = 9 000，对了。
注意：验算时加的是“减数”，不是被减数。
check with addition = semak dengan tambah
Subtraction and addition undo each other. Add the answer to the number that was taken away; if you get back the starting number, the subtraction is correct.
Example: 9 000 − 2 750 = 6 250; check: 6 250 + 2 750 = 9 000, correct.
Watch out: add the number that was taken away, not the starting number.
Anggar dahulu
Anggaran dalam ringgit
RM72 390 − RM18 640
Anggaran
RM72 390 → RM72 000
RM18 640 → RM19 000
= RM53 000
RM18 640 → RM19 000
= RM53 000
Jawapan sebenar
| 6 | 11 | 13 | |||
| 7 | 2 | 3 | 9 | 0 | |
| − | 1 | 8 | 6 | 4 | 0 |
| 5 | 3 | 7 | 5 | 0 |
RM53 750 hampir kepada RM53 000 → munasabah
先估计 = anggar dahulu
把两个金额都取整到最接近的千令吉，再心算相减得到估计值。准确答案算出来以后，和估计值比较：接近就合理。
例子：RM41 820 − RM9 150 ≈ RM42 000 − RM9 000 = RM33 000，准确答案 RM32 670，接近。
注意：金额的答案要写 RM。
estimate first = anggar dahulu
Round both amounts to the nearest thousand ringgit and subtract in your head to get an estimate. After working out the exact answer, compare it with the estimate: if it is close, it is reasonable.
Example: RM41 820 − RM9 150 ≈ RM42 000 − RM9 000 = RM33 000; the exact answer RM32 670 is close.
Watch out: money answers need RM in front.
Tolak daripada 80 000
Dua cara
80 000 − 5 347
Cara 1
| 7 | 9 | 9 | 9 | 10 | |
| 8 | 0 | 0 | 0 | 0 | |
| − | 5 | 3 | 4 | 7 | |
| 7 | 4 | 6 | 5 | 3 |
Cara 2: −1 kedua-dua
| 7 | 9 | 9 | 9 | 9 | |
| − | 5 | 3 | 4 | 6 | |
| 7 | 4 | 6 | 5 | 3 |
从整万减 = tolak daripada puluh ribu genap
方法一：一路向左借位，0 变成 9，个位变 10。方法二：两个数同时减 1，变成 79 999 − 5 346，两数的差不变，但每一位都够减，不必借位。两种方法答案一样。
例子：30 000 − 1 258 → 29 999 − 1 257 = 28 742。
注意：两个数都要减 1，只减一个就错了。
subtract from a whole ten thousand = tolak daripada puluh ribu genap
Method 1: regroup all the way along, so the zeros become 9s and the ones become 10. Method 2: take 1 from both numbers to get 79 999 − 5 346. The difference stays the same, but now every column can be subtracted without borrowing.
Example: 30 000 − 1 258 becomes 29 999 − 1 257 = 28 742.
Watch out: take 1 from both numbers, not just one of them.
Tolak daripada 50 000
Cara cerakin
50 000 − 3 628
50 000 = 40 000 + 9 000 + 900 + 90 + 10
3 628 = 3 000 + 600 + 20 + 8
9 000 − 3 000 = 6 000 · 900 − 600 = 300 · 90 − 20 = 70 · 10 − 8 = 2
40 000 + 6 000 + 300 + 70 + 2 = 46 372
分解后减 = cara cerakin
从整万数减一个数时，可以先把整万数分解成“少一个万、再加 9 000 + 900 + 90 + 10”，这样每一个数位都有足够的数可以减。再把减数也按数位分解，同一数位的部分相减，最后把所有结果加起来。
例子：30 000 − 4 215 → 30 000 = 20 000 + 9 000 + 900 + 90 + 10；9 000 − 4 000 = 5 000，900 − 200 = 700，90 − 10 = 80，10 − 5 = 5 → 20 000 + 5 000 + 700 + 80 + 5 = 25 785。
注意：分解时个位要留 10，不是 9；最后别忘了把没有被减的那一部分（整万）加回去。
subtract by breaking up = cara cerakin
To subtract from a whole ten thousand, break it up into one ten thousand less plus 9 000 + 900 + 90 + 10, so every place has enough to subtract from. Break the other number up by place value, subtract place by place, then add all the results together.
Example: 30 000 − 4 215: 30 000 = 20 000 + 9 000 + 900 + 90 + 10; 9 000 − 4 000 = 5 000, 900 − 200 = 700, 90 − 10 = 80, 10 − 5 = 5, so 20 000 + 5 000 + 700 + 80 + 5 = 25 785.
Watch out: the ones part is 10, not 9, and remember to add back the ten thousands part that was not used.
Tolak berturut-turut · Cara 1
Tolak dari kiri ke kanan
67 530 − 1 842 − 23 600
Langkah 1
| 6 | 14 | 12 | 10 | ||
| 6 | 7 | 5 | 3 | 0 | |
| − | 1 | 8 | 4 | 2 | |
| 6 | 5 | 6 | 8 | 8 |
Langkah 2
| 6 | 5 | 6 | 8 | 8 | |
| − | 2 | 3 | 6 | 0 | 0 |
| 4 | 2 | 0 | 8 | 8 |
从左到右连减 = tolak dari kiri ke kanan
连续减两个数时，可以按次序做：先从第一个数减去第二个数，得到中间答案，再从中间答案减去第三个数。每一步都是普通的减法，要注意退位。
例子：9 000 − 1 500 − 2 500 → 先 7 500，再 5 000。
注意：第二步是用中间答案去减，不是用原来的数。
subtract from left to right = tolak dari kiri ke kanan
When taking away two numbers in a row, you can go in order: take the second number from the first to get a middle answer, then take the third number from that. Each step is an ordinary subtraction, so watch the regrouping.
Example: 9 000 − 1 500 − 2 500: first 7 500, then 5 000.
Watch out: in step 2 subtract from the middle answer, not from the starting number.
Tolak berturut-turut · Cara 2
Tambah nombor yang ditolak dahulu
67 530 − 1 842 − 23 600
Langkah 1: tambah
| 1 | |||||
| 1 | 8 | 4 | 2 | ||
| + | 2 | 3 | 6 | 0 | 0 |
| 2 | 5 | 4 | 4 | 2 |
Langkah 2: tolak
| 4 | 12 | 10 | |||
| 6 | 7 | 5 | 3 | 0 | |
| − | 2 | 5 | 4 | 4 | 2 |
| 4 | 2 | 0 | 8 | 8 |
连减 = tolak berturut-turut
方法一：从左到右，先减第一个数，得数再减第二个数。方法二：先把两个要减的数加起来，再从被减数里一次减掉。两种方法答案相同。
例子：9 000 − 1 500 − 2 500 = 9 000 − 4 000 = 5 000。
注意：方法二是把两个减数“加”起来，不是相减。
subtract twice = tolak berturut-turut
Method 1: work from left to right, taking away the first number and then the second from that answer. Method 2: add the two numbers to be taken away, then subtract their total once. Both give the same answer.
Example: 9 000 − 1 500 − 2 500 = 9 000 − 4 000 = 5 000.
Watch out: in method 2 you add the two numbers being taken away; you do not subtract them.
Tolak berturut-turut
Susunan nombor yang ditolak boleh ditukar
67 530 − 23 600 − 1 842
Tolak 23 600 dahulu
| 6 | 15 | ||||
| 6 | 7 | 5 | 3 | 0 | |
| − | 2 | 3 | 6 | 0 | 0 |
| 4 | 3 | 9 | 3 | 0 |
Kemudian tolak 1 842
| 8 | 12 | 10 | |||
| 4 | 3 | 9 | 3 | 0 | |
| − | 1 | 8 | 4 | 2 | |
| 4 | 2 | 0 | 8 | 8 |
67 530 − 1 842 − 23 600 = 67 530 − 23 600 − 1 842 = 42 088
换减数次序 = tukar susunan nombor yang ditolak
连续减两个数时，两个“要减去的数”可以交换先后，答案不变，因为总共减去的量一样。可以挑比较好算的那个先减，例如先减一个整千或整百的数。但是被减数（最前面的数）一定要留在最前面，不能和减数交换。
例子：8 400 − 1 275 − 2 000 → 先减 2 000 得 6 400，再减 1 275 得 5 125；照原来次序做也是 5 125。
注意：只有减数之间可以换次序；把被减数和减数对调，结果就完全不同了。
swap the order of what is taken away = tukar susunan nombor yang ditolak
When taking away two numbers in a row, the two numbers being taken away can swap places and the answer stays the same, because the total taken away is the same. Take away the easier one first, such as a whole thousand. The starting number must stay at the front.
Example: 8 400 − 1 275 − 2 000: take 2 000 first to get 6 400, then 1 275 to get 5 125; the order as written also gives 5 125.
Watch out: only the numbers being taken away may swap; swapping the starting number changes the answer completely.
Cari nombor yang ditolak
90 146 − □ = 31 520
Tolak jawapan daripada nombor pertama.
| 8 | 9 | 11 | |||
| 9 | 0 | 1 | 4 | 6 | |
| − | 3 | 1 | 5 | 2 | 0 |
| 5 | 8 | 6 | 2 | 6 |
□ = 90 146 − 31 520 = 58 626 · Semak: 90 146 − 58 626 = 31 520 ✔
求减数 = cari nombor yang ditolak
被减数和差都知道，要求的是减去了多少：减数 = 被减数 − 差。可以用小数字想：10 − □ = 6，□ = 10 − 6 = 4。
例子：5 000 − □ = 1 200 → □ = 5 000 − 1 200 = 3 800。
注意：求出来以后放回原式验算。
find the number taken away = cari nombor yang ditolak
We know the starting number and the answer; we need how much was taken away: number taken away = starting number − answer. Think small: 10 − □ = 6, so □ = 10 − 6 = 4.
Example: 5 000 − □ = 1 200, so □ = 5 000 − 1 200 = 3 800.
Watch out: put your answer back into the sentence to check it.
Cuba kira
71 204 − 38 567 = ?
多次退位 = kumpul semula beberapa kali
这是一题需要多次借位的五位数减法。按数位对齐，从个位减起；上面的数字不够减，就向左边一位借 1（左边少 1，这一位多 10）。如果左边那一位是 0，要再往更左边借。算完用加法验算：差 + 减数 = 被减数。
例子：60 312 − 27 465：个位 2 不够减 5 要借位……答案 32 847；验算 32 847 + 27 465 = 60 312。
注意：借过的那一位要先减 1 再算；遇到 0 时要继续向左借。
regroup several times = kumpul semula beberapa kali
This five-digit subtraction needs regrouping more than once. Line up the places and subtract from the ones. If the top digit is too small, borrow 1 from the left (the left place goes down by 1 and this place gains 10); if the left place is 0, borrow from further left. Check by adding the answer and the number taken away.
Example: 60 312 − 27 465 = 32 847; check 32 847 + 27 465 = 60 312.
Watch out: a place you borrowed from is 1 less, and when you meet a 0 keep borrowing further left.
Tolak berturut
45 000 − 12 380 − 9 415 = ?
连减 = tolak berturut-turut
题目要从一个数连续减去两个数。方法一：从左到右，先减前面那个减数，得到中间结果，再减后面那个减数。方法二：先把两个减数加起来，再从被减数里一次减掉。两种方法结果一样，可以用一种算、另一种检查。
例子：20 000 − 5 000 − 3 000：方法一 15 000 − 3 000 = 12 000；方法二 20 000 − 8 000 = 12 000。
注意：第一步的中间结果不是最后答案；方法二是把两个减数“加”起来。
subtract twice = tolak berturut-turut
Take two numbers away one after the other. Method 1: go left to right, subtracting the first number and then the second from the middle answer. Method 2: add the two numbers being taken away and subtract their total once. Use one method and check with the other.
Example: 20 000 − 5 000 − 3 000: 15 000 − 3 000 = 12 000, or 20 000 − 8 000 = 12 000.
Watch out: the middle answer is not the final answer, and in method 2 you add the two numbers being taken away.
Cari nombor
62 000 − □ = 17 358
求减数 = cari nombor yang ditolak
算式里被减数和差都知道，要求“减去了多少”。用小数字想：10 − □ = 6，□ = 10 − 6 = 4。所以减数 = 被减数 − 差。从整千、整万减时可以用“两数各减 1”，就不用借位。最后放回原式检查。
例子：40 000 − □ = 15 000 → □ = 40 000 − 15 000 = 25 000；检查 40 000 − 25 000 = 15 000。
注意：求减数要用减法；把两个数加起来得到的数比被减数还大，一定不对。
find the number taken away = cari nombor yang ditolak
The starting number and the answer are known; how much was taken away? Think small: 10 − □ = 6, so □ = 10 − 6 = 4. So the number taken away = starting number − answer. From a whole thousand, take 1 from both numbers to avoid borrowing. Check in the sentence.
Example: 40 000 − □ = 15 000, so □ = 25 000; check 40 000 − 25 000 = 15 000.
Watch out: find it by subtracting; adding gives a number bigger than the starting number.
Ringkasan