Unit 4
Tambah dan Tolak Wang
Baki dalam buku simpanan Daniel ialah RM 350.60. Dia menyimpan RM 120, kemudian mengeluarkan RM 85.25.
Berapakah baki sekarang?
加减混合 = tambah dan tolak；存折 = buku simpanan；余额 = baki
这一课学一条算式里同时有加和减。Daniel 的存折原有 RM 350.60，存入 RM 120 要加，取出 RM 85.25 要减，算式是 RM 350.60 + RM 120 − RM 85.25。两步要按顺序做，不能跳着算。
例子：有 RM 20，妈妈再给 RM 5，买东西用了 RM 8，就是 20 + 5 − 8 = RM 17。
注意：存入（wang masuk）用加，取出（wang keluar）用减。
adding and subtracting = tambah dan tolak; savings book = buku simpanan; balance = baki
In this unit one number sentence has both a plus and a minus. Daniel's savings book shows RM 350.60; putting in RM 120 means adding, and taking out RM 85.25 means subtracting, so the sentence is RM 350.60 + RM 120 − RM 85.25. The two steps must be done in order, not jumped over.
Example: with RM 20, mother gives RM 5 more and RM 8 is spent: 20 + 5 − 8 = RM 17.
Watch out: money put in (wang masuk) is added; money taken out (wang keluar) is subtracted.
Dari kiri ke kanan
RM 350.60 + RM 120 − RM 85.25
Jawapan langkah 1 menjadi baris pertama langkah 2
Langkah 1: 350.60 + 120.00 = 470.60 · Langkah 2: 470.60 − 85.25 = 385.35
从左到右 = dari kiri ke kanan；第一步 = langkah 1；第二步 = langkah 2
算式里没有括号，就从左边开始算。第一步先加：350.60 + 120.00 = 470.60。第二步把 470.60 抄到新竖式的第一行，再减 85.25：sen 60 − 25 = 35，ringgit 470 − 85 = 385，余额 RM 385.35。动画里第一步的答案“移”到右边，就是提醒你要把它抄对。
例子：RM 40 + RM 15.50 − RM 20 → 先 55.50，再减 20 → RM 35.50。
注意：第一步的答案要原封不动抄到第二步，少抄一个数字就全错。
left to right = dari kiri ke kanan; first step = langkah 1; second step = langkah 2
With no brackets, start from the left. Step one adds: 350.60 + 120.00 = 470.60. Step two copies 470.60 into the first row of a new column sum and subtracts 85.25: sen 60 − 25 = 35 and ringgit 470 − 85 = 385, so the balance is RM 385.35. In the animation the first answer slides to the right to remind you to copy it exactly.
Example: RM 40 + RM 15.50 − RM 20 → first 55.50, then subtract 20 → RM 35.50.
Watch out: copy the first answer into the second step digit for digit; one missed digit spoils everything.
Cuba
RM 64.50 + RM 28.75 − RM 40.25 = ?
| 6 | 4 | . | 5 | 0 | |
| + | 2 | 8 | . | 7 | 5 |
| ? | ? | ? | ? | ? |
| ? | |||||
| − | 4 | 0 | . | 2 | 5 |
| ? | ? | ? | ? | ? |
先加后减 = tambah dahulu, kemudian tolak
第一步：64.50 + 28.75，sen 50 + 75 = 125，写 25 进 1，1 + 64 + 28 = 93，得 RM 93.25。第二步：93.25 − 40.25，sen 25 − 25 = 0，93 − 40 = 53，得 RM 53。
例子：RM 10.20 + RM 4.80 − RM 5 → 15 − 5 = RM 10。
注意：RM 52 是第一步忘了进位，得 92.25 再减出来的。
add first, then subtract = tambah dahulu, kemudian tolak
Step one: 64.50 + 28.75, sen 50 + 75 = 125, write 25 and carry 1, then 1 + 64 + 28 = 93, giving RM 93.25. Step two: 93.25 − 40.25, sen 25 − 25 = 0 and 93 − 40 = 53, giving RM 53.
Example: RM 10.20 + RM 4.80 − RM 5 → 15 − 5 = RM 10.
Watch out: RM 52 comes from forgetting the carry in step one, getting 92.25 before subtracting.
Tolak dahulu, kemudian tambah
RM 2 000 − RM 745.80 + RM 310.50
Operasi di kiri dibuat dahulu
| 2 | 0 | 0 | 0 | . | 0 | 0 | |
| − | 7 | 4 | 5 | . | 8 | 0 | |
| 1 | 2 | 5 | 4 | . | 2 | 0 |
| 1 | 2 | 5 | 4 | . | 2 | 0 | |
| + | 3 | 1 | 0 | . | 5 | 0 | |
| 1 | 5 | 6 | 4 | . | 7 | 0 |
Langkah 1: 2 000 − 745.80 = 1 254.20 · Langkah 2: 1 254.20 + 310.50 = 1 564.70
先减后加 = tolak dahulu, kemudian tambah
哪个符号在左边就先做哪个。这里减号在前，所以先减：2 000 看成 1 999 和 100 sen，100 − 80 = 20，1 999 − 745 = 1 254，得 RM 1 254.20。再加 310.50：sen 20 + 50 = 70，1 254 + 310 = 1 564，得 RM 1 564.70。
例子：RM 100 − RM 36 + RM 12 → 64 + 12 = RM 76。
注意：不可以先把 745.80 和 310.50 加起来再减，顺序错答案就错。
subtract first, then add = tolak dahulu, kemudian tambah
Whichever sign comes first on the left is done first. Here the minus comes first, so subtract: see 2 000 as 1 999 and 100 sen, 100 − 80 = 20 and 1 999 − 745 = 1 254, giving RM 1 254.20. Then add 310.50: sen 20 + 50 = 70 and 1 254 + 310 = 1 564, giving RM 1 564.70.
Example: RM 100 − RM 36 + RM 12 → 64 + 12 = RM 76.
Watch out: do not add 745.80 and 310.50 together first and then subtract; the wrong order gives the wrong answer.
Cuba
RM 500 − RM 236.40 + RM 88.60 = ?
| 5 | 0 | 0 | . | 0 | 0 | |
| − | 2 | 3 | 6 | . | 4 | 0 |
| ? | ? | ? | ? | ? | ? |
| ? | |||||
| + | 8 | 8 | . | 6 | 0 |
| ? | ? | ? | ? | ? |
顺序 = urutan
减号在左边，先减：500 看成 499 和 100 sen，100 − 40 = 60，499 − 236 = 263，得 RM 263.60。再加 88.60：sen 60 + 60 = 120，写 20 进 1，1 + 263 + 88 = 352，得 RM 352.20。
例子：RM 50 − RM 12.50 + RM 2.50 → 37.50 + 2.50 = RM 40。
注意：RM 175 是先把 236.40 和 88.60 加起来再从 500 减，顺序反了。
order = urutan
The minus is on the left, so subtract first: see 500 as 499 and 100 sen, 100 − 40 = 60 and 499 − 236 = 263, giving RM 263.60. Then add 88.60: sen 60 + 60 = 120, write 20 and carry 1, then 1 + 263 + 88 = 352, giving RM 352.20.
Example: RM 50 − RM 12.50 + RM 2.50 → 37.50 + 2.50 = RM 40.
Watch out: RM 175 comes from adding 236.40 and 88.60 first and then subtracting from 500, which is the wrong order.
Buku simpanan
Wang masuk, wang keluar, baki
Masuk → tambah · Keluar → tolak
| Tarikh | Masuk (RM) | Keluar (RM) | Baki (RM) |
|---|---|---|---|
| Baki awal | 1 250.40 | ||
| 3 Mac | 300 | 1 550.40 | |
| 9 Mac | 420.75 | 1 129.65 | |
| 15 Mac | 95.50 | 1 225.15 |
1 250.40 + 300 = 1 550.40 → 1 550.40 − 420.75 = 1 129.65 → 1 129.65 + 95.50 = 1 225.15
存入 = wang masuk；取出 = wang keluar；余额 = baki
存折一行一行看。每存入一次，余额就加上那笔钱；每取出一次，余额就减掉那笔钱。Aina 原有 1 250.40，3 Mac 存入 300 变成 1 550.40；9 Mac 取出 420.75：1 550.40 − 420.75，sen 40 不够减 75，借 1 → 140 − 75 = 65，1 549 − 420 = 1 129，变成 1 129.65；15 Mac 存入 95.50 变成 1 225.15。
例子：余额 RM 80，取出 RM 30 后是 RM 50，再存入 RM 25 就是 RM 75。
注意：每一行的余额都是从上一行的余额算出来的。
money in = wang masuk; money out = wang keluar; balance = baki
Read the savings book line by line. Each deposit is added to the balance and each withdrawal is subtracted. Aina starts with 1 250.40; on 3 Mac she puts in 300, making 1 550.40; on 9 Mac she takes out 420.75: 1 550.40 − 420.75, the 40 sen are less than 75, so borrow 1 → 140 − 75 = 65 and 1 549 − 420 = 1 129, making 1 129.65; on 15 Mac she puts in 95.50, making 1 225.15.
Example: a balance of RM 80 becomes RM 50 after taking out RM 30, then RM 75 after putting in RM 25.
Watch out: each new balance is worked out from the balance on the line above.
Cuba
Baki RM 860.25. Masuk RM 150, keluar RM 275.50. Baki baharu?
| Masuk (RM) | Keluar (RM) | Baki (RM) |
|---|---|---|
| 860.25 | ||
| 150 | ? | |
| 275.50 | ? |
新余额 = baki baharu
存入 150：860.25 + 150 = 1 010.25。取出 275.50：1 010.25 − 275.50，sen 25 不够减 50，借 1 → 125 − 50 = 75，1 009 − 275 = 734，新余额 RM 734.75。
例子：余额 RM 200，存入 RM 50，取出 RM 120.50 → 250 − 120.50 = RM 129.50。
注意：RM 735.75 是借了 1 却没有把 1 010 改成 1 009。
new balance = baki baharu
Putting in 150: 860.25 + 150 = 1 010.25. Taking out 275.50: 1 010.25 − 275.50, the 25 sen are less than 50, so borrow 1 → 125 − 50 = 75 and 1 009 − 275 = 734, so the new balance is RM 734.75.
Example: a balance of RM 200, put in RM 50, take out RM 120.50 → 250 − 120.50 = RM 129.50.
Watch out: RM 735.75 borrows 1 but leaves 1 010 unchanged instead of making it 1 009.
Anggaran
RM 1 268 + RM 435 − RM 712
Bundarkan kepada ratus terdekat
1 268 → 1 300 · 435 → 400 · 712 → 700
Anggaran: 1 300 + 400 − 700 = RM 1 000
Sebenar: 1 268 + 435 = 1 703 → 1 703 − 712 = RM 991 ✓ hampir RM 1 000
估算 = anggaran；四舍五入到百位 = bundar kepada ratus terdekat；合理 = munasabah
估算是用整百的数快速算一次，看答案合不合理。看十位：5 或以上就进到下一个百，4 或以下就舍去。1 268 的十位是 6，变 1 300；435 的十位是 3，变 400；712 的十位是 1，变 700。估算 1 300 + 400 − 700 = 1 000。真正的答案 991 跟 1 000 很接近，所以算对了。
例子：RM 548 + RM 262 → 500 + 300 = 800，真正答案 810，接近。
注意：估算不是答案，只是用来检查答案合不合理。
estimate = anggaran; rounding to the nearest hundred = bundar kepada ratus terdekat; reasonable = munasabah
An estimate is a quick sum with round hundreds to see whether the answer makes sense. Look at the tens digit: 5 or more rounds up to the next hundred, 4 or less rounds down. 1 268 has tens digit 6, so it becomes 1 300; 435 has 3, so 400; 712 has 1, so 700. The estimate is 1 300 + 400 − 700 = 1 000. The true answer 991 is close to 1 000, so it is right.
Example: RM 548 + RM 262 → 500 + 300 = 800, and the true answer 810 is close.
Watch out: an estimate is not the answer; it only checks whether the answer is reasonable.
Cuba
Anggarkan: RM 2 580 − RM 1 320 + RM 460 (ratus terdekat)
四舍五入 = bundarkan
先把每个数变成整百：2 580 的十位是 8，进到 2 600；1 320 的十位是 2，舍成 1 300；460 的十位是 6，进到 500。估算：2 600 − 1 300 = 1 300，再加 500 = RM 1 800。真正的答案是 1 720，接近 1 800。
例子：RM 349 + RM 180 → 300 + 200 = RM 500。
注意：460 要进到 500，不是舍成 400，因为十位是 6。
rounding = bundarkan
First turn each amount into a round hundred: 2 580 has tens digit 8, so it goes up to 2 600; 1 320 has 2, so it goes down to 1 300; 460 has 6, so it goes up to 500. Estimate: 2 600 − 1 300 = 1 300, then plus 500 = RM 1 800. The true answer is 1 720, close to 1 800.
Example: RM 349 + RM 180 → 300 + 200 = RM 500.
Watch out: 460 rounds up to 500, not down to 400, because its tens digit is 6.
Cari nombor yang tiada
RM 450 + ? − RM 120.50 = RM 600
Kerja ke belakang dari jawapan
RM 450 + ? − RM 120.50 = RM 600
Sebelum tolak 120.50: 600 + 120.50 = 720.50
450 + ? = 720.50 → ? = 720.50 − 450 = RM 270.50
Semak: 450 + 270.50 − 120.50 = RM 600 ✓
倒推 = kerja ke belakang；未知数 = nombor yang tiada
方框在中间，可以从答案往回推。最后得 600，是减了 120.50 之后的，所以减之前是 600 + 120.50 = 720.50。720.50 又是 450 加上方框得来的，所以方框是 720.50 − 450 = 270.50。倒推时，原来是减的就变加，原来是加的就变减。最后代回去：450 + 270.50 = 720.50，720.50 − 120.50 = 600，对了。
例子：RM 30 + □ − RM 10 = RM 50 → 50 + 10 = 60，60 − 30 = RM 30。
注意：倒推时符号要反过来，不可以照抄原来的加减。
working backwards = kerja ke belakang; missing number = nombor yang tiada
When the box is in the middle, start from the answer and go back. The final 600 came after subtracting 120.50, so before that step the value was 600 + 120.50 = 720.50. That 720.50 came from 450 plus the box, so the box is 720.50 − 450 = 270.50. Going backwards, a subtraction becomes an addition and an addition becomes a subtraction. Put it back: 450 + 270.50 = 720.50 and 720.50 − 120.50 = 600, correct.
Example: RM 30 + □ − RM 10 = RM 50 → 50 + 10 = 60, then 60 − 30 = RM 30.
Watch out: reverse each sign when working backwards; do not copy the plus and minus as they stand.
Cuba
? − RM 85 + RM 40 = RM 255
从答案往回算 = kerja ke belakang daripada jawapan
最后一步是加 40 得 255，倒推就减 40：255 − 40 = 215。上一步是减 85 得 215，倒推就加 85：215 + 85 = 300。方框是 RM 300。检查：300 − 85 = 215，215 + 40 = 255。
例子：□ − RM 20 + RM 5 = RM 60 → 60 − 5 = 55，55 + 20 = RM 75。
注意：RM 210 是照抄原来的符号算的，倒推时要把符号反过来。
going back from the answer = kerja ke belakang daripada jawapan
The last step added 40 to get 255, so going back we subtract 40: 255 − 40 = 215. The step before subtracted 85 to get 215, so going back we add 85: 215 + 85 = 300. The box is RM 300. Check: 300 − 85 = 215 and 215 + 40 = 255.
Example: □ − RM 20 + RM 5 = RM 60 → 60 − 5 = 55, then 55 + 20 = RM 75.
Watch out: RM 210 keeps the signs as written; when going back, every sign must be reversed.
Padankan
Jawapan yang betul
配对答案 = padankan jawapan
每条算式都从左做到右。30 + 20 = 50，50 − 15 = 35。100 − 40 = 60，60 + 25 = 85。12.50 + 7.50 = 20，20 − 5 = 15。60 − 18 = 42，42 − 2 = 40。
例子：RM 8 + RM 2 − RM 6 → 10 − 6 = RM 4。
注意：两步都是减的时候，也一样从左边先做。
matching answers = padankan jawapan
Work each sentence from left to right. 30 + 20 = 50, then 50 − 15 = 35. 100 − 40 = 60, then 60 + 25 = 85. 12.50 + 7.50 = 20, then 20 − 5 = 15. 60 − 18 = 42, then 42 − 2 = 40.
Example: RM 8 + RM 2 − RM 6 → 10 − 6 = RM 4.
Watch out: when both steps are subtractions, still begin from the left.
Ringkasan
Syabas!
kiri → kanan · masuk + · keluar − · anggar dengan ratus
Buat operasi dari kiri ke kanan; jawapan langkah 1 menjadi baris pertama langkah 2. Wang masuk ditambah, wang keluar ditolak. Bundarkan kepada ratus untuk menganggar. Cari nombor yang tiada dengan kerja ke belakang.
Latihan tambahan →