Unit 8
Tambah dan Tolak Masa
Cikgu Farah merakam video kelas selama 2 jam 35 minit. Dia merakam lagi 1 jam 40 minit, kemudian memadam 50 minit.
Berapa lamakah video itu sekarang?
加减混合 = tambah dan tolak；两步 = dua langkah
这一课学一条算式里同时有加和减的时间计算。Farah 老师先录了 2 小时 35 分，又加录 1 小时 40 分，要加；后来删掉 50 分，要减。算式是 2 jam 35 minit + 1 jam 40 minit − 50 minit，要分两步，从左边算到右边。
例子：先玩 20 minit，再玩 15 minit，后来少玩 5 minit，就是 20 + 15 − 5 = 30 minit。
注意：多录、加上用加法；删掉、少了用减法。
adding and subtracting = tambah dan tolak; two steps = dua langkah
In this unit one number sentence has both adding and subtracting of time. Cikgu Farah records 2 hours 35 minutes, then records 1 hour 40 minutes more, which means adding, and later deletes 50 minutes, which means subtracting. The sentence 2 jam 35 minit + 1 jam 40 minit − 50 minit is worked in two steps from left to right.
Example: playing 20 minit, then 15 minit more, then 5 minit less gives 20 + 15 − 5 = 30 minit.
Watch out: recording more means add; deleting or cutting means subtract.
Dari kiri ke kanan
45 minit + 30 minit − 20 minit
Buat operasi di sebelah kiri dahulu
Langkah 1
45 + 30
= 75 minit
= 75 minit
Langkah 2
75 − 20
= 55 minit
= 55 minit
50 saat − 15 saat + 25 saat → 35 + 25 = 60 saat = 1 minit
从左到右 = dari kiri ke kanan
算式里有加也有减、又没有括号时，从左边开始一步一步算。45 minit + 30 minit − 20 minit：第一步 45 + 30 = 75 minit，第二步 75 − 20 = 55 minit。答案 55 minit。
例子：50 saat − 15 saat + 25 saat → 35 + 25 = 60 saat，刚好是 1 minit。
注意：第一步的答案可以先不化成 jam，等最后才整理也可以。
left to right = dari kiri ke kanan
When a sentence has both plus and minus and no brackets, work step by step starting from the left. For 45 minit + 30 minit − 20 minit, step 1 is 45 + 30 = 75 minutes and step 2 is 75 − 20 = 55 minutes. The answer is 55 minit.
Example: 50 saat − 15 saat + 25 saat → 35 + 25 = 60 saat, which is exactly 1 minit.
Watch out: the step 1 answer may stay as minutes for now and be tidied into hours at the end.
Dua langkah bentuk lazim
2 jam 35 minit + 1 jam 40 minit − 50 minit
Jawapan langkah 1 menjadi baris pertama langkah 2
Langkah 1: kumpul semula (75 − 60) · Langkah 2: pinjam 1 jam (60 + 15)
两步竖式 = dua langkah bentuk lazim
第一步做加法：35 + 40 = 75 minit，满 60，写 15，进 1；jam 1 + 2 + 1 = 4，得 4 jam 15 minit。把这个答案抄到第二个竖式的第一行。第二步做减法：15 不够减 50，借 1 jam，60 + 15 = 75，75 − 50 = 25；jam 4 − 1 = 3。答案 3 jam 25 minit。
例子：1 jam 50 minit + 20 minit − 30 minit → 2 jam 10 minit − 30 minit → 1 jam 40 minit。
注意：同一题里第一步可能进位、第二步可能借位，两种都是 60。
two-step column method = dua langkah bentuk lazim
Step 1 is the addition: 35 + 40 = 75 minutes, which reaches 60, so write 15 and carry 1; the hours give 1 + 2 + 1 = 4, so step 1 makes 4 jam 15 minit. Copy this answer as the first row of the second column sum. Step 2 is the subtraction: 15 cannot take away 50, so borrow 1 hour, 60 + 15 = 75 and 75 − 50 = 25; the hours give 4 − 1 = 3. The answer is 3 jam 25 minit.
Example: 1 jam 50 minit + 20 minit − 30 minit → 2 jam 10 minit − 30 minit → 1 jam 40 minit.
Watch out: one question may carry in step 1 and borrow in step 2, and both use 60.
Cuba
3 jam 25 minit + 2 jam 50 minit − 1 jam 30 minit = ?
| jam | minit | |
|---|---|---|
| 3 | 25 | |
| + | 2 | 50 |
| ? | ? |
Langkah 2: jawapan − 1 jam 30 minit
先加后减 = tambah dahulu, kemudian tolak
第一步：25 + 50 = 75，写 15 进 1，3 + 2 + 1 = 6 → 6 jam 15 minit。第二步：15 不够减 30，借 1 jam，75 − 30 = 45，5 − 1 = 4 → 4 jam 45 minit。
例子：1 jam 30 minit + 1 jam 40 minit − 2 jam → 3 jam 10 minit − 2 jam = 1 jam 10 minit。
注意：5 jam 45 minit 是借了 1 jam 却没有把 6 改成 5。
add first, then subtract = tambah dahulu, kemudian tolak
Step 1: 25 + 50 = 75, write 15 and carry 1, and 3 + 2 + 1 = 6, giving 6 jam 15 minit. Step 2: 15 cannot take away 30, so borrow 1 hour: 75 − 30 = 45 and 5 − 1 = 4, giving 4 jam 45 minit.
Example: 1 jam 30 minit + 1 jam 40 minit − 2 jam → 3 jam 10 minit − 2 jam = 1 jam 10 minit.
Watch out: 5 jam 45 minit borrows an hour but never changes the 6 into 5.
Tolak dahulu, kemudian tambah
9 minit 10 saat − 3 minit 45 saat + 2 minit 30 saat
Tolak ada di kiri, jadi tolak dahulu
| minit | saat | |
|---|---|---|
| 8 | 70 | |
| 10 | ||
| − | 3 | 45 |
| 5 | 25 |
| minit | saat | |
|---|---|---|
| 5 | 25 | |
| + | 2 | 30 |
| 7 | 55 |
先减后加 = tolak dahulu, kemudian tambah
这题减号在左边，所以先减。第一步：10 saat 不够减 45 saat，借 1 minit，9 变 8，60 + 10 = 70，70 − 45 = 25，8 − 3 = 5，得 5 minit 25 saat。第二步：5 minit 25 saat + 2 minit 30 saat，25 + 30 = 55，5 + 2 = 7，得 7 minit 55 saat。
例子：6 minit − 2 minit 30 saat + 1 minit 10 saat → 3 minit 30 saat + 1 minit 10 saat = 4 minit 40 saat。
注意：哪个符号在左边就先做哪个，不是一定先加。
subtract first, then add = tolak dahulu, kemudian tambah
Here the minus sign comes first, so subtract first. Step 1: 10 seconds cannot take away 45 seconds, so borrow 1 minute; 9 becomes 8, 60 + 10 = 70, 70 − 45 = 25 and 8 − 3 = 5, giving 5 minit 25 saat. Step 2: 5 minit 25 saat + 2 minit 30 saat; 25 + 30 = 55 and 5 + 2 = 7, giving 7 minit 55 saat.
Example: 6 minit − 2 minit 30 saat + 1 minit 10 saat → 3 minit 30 saat + 1 minit 10 saat = 4 minit 40 saat.
Watch out: do whichever sign comes first on the left; adding does not always go first.
Cuba
12 minit 20 saat − 5 minit 40 saat + 3 minit 15 saat = ?
左边先算 = kiri dahulu
第一步减：20 不够减 40，借 1 minit，80 − 40 = 40，11 − 5 = 6 → 6 minit 40 saat。第二步加：40 + 15 = 55，6 + 3 = 9 → 9 minit 55 saat。
例子：10 minit − 4 minit + 2 minit 20 saat = 8 minit 20 saat。
注意：3 minit 25 saat 是先把后面两个加起来再减，次序错了。
the left side first = kiri dahulu
Step 1 subtracts: 20 cannot take away 40, so borrow 1 minute; 80 − 40 = 40 and 11 − 5 = 6, giving 6 minit 40 saat. Step 2 adds: 40 + 15 = 55 and 6 + 3 = 9, giving 9 minit 55 saat.
Example: 10 minit − 4 minit + 2 minit 20 saat = 8 minit 20 saat.
Watch out: 3 minit 25 saat adds the last two times first and then subtracts, which is the wrong order.
Tertib penting
50 minit − 20 minit + 30 minit
Kiri ke kanan: 60 minit, bukan 0
Betul ✓
50 − 20 = 30
30 + 30 = 60 minit
30 + 30 = 60 minit
Salah ✗
20 + 30 = 50
50 − 50 = 0
50 − 50 = 0
60 minit = 1 jam
运算次序 = tertib operasi
为什么一定要从左到右？看 50 − 20 + 30：照次序先减 50 − 20 = 30，再加 30 + 30 = 60 minit，也就是 1 jam。如果先算后面的 20 + 30 = 50，再 50 − 50 = 0，答案完全不一样。所以加减混合没有括号时，一定照左到右的次序。
例子：30 minit − 10 minit + 5 minit = 25 minit，不是 15 minit。
注意：交换步骤会改变答案，不能随便先算后面的。
order of steps = tertib operasi
Why must we go from left to right? Look at 50 − 20 + 30. In order, 50 − 20 = 30 and then 30 + 30 = 60 minutes, which is 1 hour. If we add 20 + 30 = 50 first and then do 50 − 50 = 0, the answer is completely different. So with plus and minus and no brackets, always follow the left-to-right order.
Example: 30 minit − 10 minit + 5 minit = 25 minit, not 15 minit.
Watch out: swapping the steps changes the answer, so do not jump to the right-hand part first.
Cuba
40 minit − 15 minit + 25 minit = ?
照次序算 = ikut tertib
先算左边：40 − 15 = 25 minit，再加 25：25 + 25 = 50 minit。
例子：35 minit − 5 minit + 10 minit = 40 minit。
注意：0 minit 是先算 15 + 25 = 40 再用 40 − 40，次序错了；80 minit 是三个数全加起来。
following the order = ikut tertib
Start on the left: 40 − 15 = 25 minutes, then add 25 to get 25 + 25 = 50 minutes.
Example: 35 minit − 5 minit + 10 minit = 40 minit.
Watch out: 0 minit comes from doing 15 + 25 = 40 first and then 40 − 40, and 80 minit comes from adding all three numbers.
Masalah harian
Latihan bola sepak
1 jam 30 minit + 45 minit − 35 minit
| jam | minit | |
|---|---|---|
| 1 | 30 | |
| + | 45 | |
| 2 | 15 |
| jam | minit | |
|---|---|---|
| 2 | 15 | |
| − | 35 | |
| 1 | 40 |
ditambah → + · dipendekkan → −
应用题 = masalah harian
足球训练原本安排 1 jam 30 minit，教练加长 45 minit（加），后来下雨缩短 35 minit（减）。第一步：30 + 45 = 75 minit，写 15 进 1，得 2 jam 15 minit。第二步：15 不够减 35，借 1 jam，75 − 35 = 40，2 − 1 = 1，得 1 jam 40 minit。
例子：派对 2 jam，延长 30 minit，又提早 15 minit 结束 → 2 jam 15 minit。
注意：看清楚题目里哪个词是加（ditambah），哪个词是减（dipendekkan）。
word problem = masalah harian
Football training was planned for 1 jam 30 minit; the coach adds 45 minutes (plus), and later rain cuts it by 35 minutes (minus). Step 1: 30 + 45 = 75 minutes, write 15 and carry 1, giving 2 jam 15 minit. Step 2: 15 cannot take away 35, so borrow 1 hour: 75 − 35 = 40 and 2 − 1 = 1, giving 1 jam 40 minit.
Example: a party of 2 jam is extended by 30 minit and then ends 15 minit early → 2 jam 15 minit.
Watch out: decide which word means add (ditambah) and which means subtract (dipendekkan).
Cuba
Perjalanan bas dijadualkan 3 jam 40 minit. Bas lewat 25 minit kerana hujan, kemudian jalan pintas menjimatkan 50 minit. Berapa lamakah perjalanan itu?
迟到和节省 = lewat dan jimat
迟到 25 minit 要加：40 + 25 = 65，写 5 进 1 → 4 jam 5 minit。走捷径节省 50 minit 要减：5 不够减 50，借 1 jam，65 − 50 = 15，4 − 1 = 3 → 3 jam 15 minit。
例子：飞机 2 jam，迟 20 minit，顺风快 10 minit → 2 jam 10 minit。
注意：2 jam 25 minit 是把迟到也当成减法了。
late and saving time = lewat dan jimat
Being 25 minutes late means adding: 40 + 25 = 65, write 5 and carry 1, giving 4 jam 5 minit. The shortcut saves 50 minutes, so subtract: 5 cannot take away 50, so borrow 1 hour, 65 − 50 = 15 and 4 − 1 = 3, giving 3 jam 15 minit.
Example: a 2 jam flight that is 20 minit late but 10 minit faster with the wind → 2 jam 10 minit.
Watch out: 2 jam 25 minit treats being late as a subtraction too.
Padankan
Jawapan dua langkah
配对两步答案 = padankan jawapan dua langkah
30 + 40 = 70，70 − 10 = 60 minit = 1 jam。2 jam − 50 minit = 1 jam 10 minit，再加 20 = 1 jam 30 minit。45 + 45 = 90，90 − 30 = 60 saat = 1 minit。1 jam 20 minit − 40 minit = 40 minit，再加 1 jam = 1 jam 40 minit。
例子：20 minit + 50 minit − 10 minit = 1 jam。
注意：每一题都要先做左边那一步。
matching two-step answers = padankan jawapan dua langkah
30 + 40 = 70 and 70 − 10 = 60 minutes = 1 jam. 2 jam − 50 minit = 1 jam 10 minit, and adding 20 gives 1 jam 30 minit. 45 + 45 = 90 and 90 − 30 = 60 seconds = 1 minit. 1 jam 20 minit − 40 minit = 40 minit, and adding 1 hour gives 1 jam 40 minit.
Example: 20 minit + 50 minit − 10 minit = 1 jam.
Watch out: in every sentence, do the left-hand step first.
Ringkasan
Syabas!
kiri → kanan · langkah 1 → salin → langkah 2
Kira dari kiri ke kanan. Jawapan langkah 1 menjadi baris pertama langkah 2. Kumpul semula atau pinjam dengan 60.
Latihan tambahan →