Unit 12
Selesaikan Masalah
Keluarga Farid memandu dari Kota Kinabalu ke Sandakan. Mereka memandu 2 jam 40 minit, berehat 35 minit di Ranau, kemudian memandu lagi 3 jam 15 minit.
Berapakah jumlah masa perjalanan itu?
解决问题 = selesaikan masalah；中途休息 = berehat；旅程 = perjalanan
这一课学用四个步骤解时间应用题。Farid 一家从亚庇开车去山打根：先开 2 jam 40 minit，在兰瑙休息 35 minit，再开 3 jam 15 minit。问整趟路程用了多少时间。休息的时间也在路上，所以也要算进去。我们会把三段时间画成长条，一段接一段，就不会漏掉休息。
例子：走路去学校 15 minit，在店里停 5 minit，再走 10 minit，一共 30 minit。
注意：很多人只加开车的两段，忘了休息的 35 minit。
solving problems = selesaikan masalah; to take a rest = berehat; journey = perjalanan
In this unit we solve time word problems in four steps. Farid's family drives from Kota Kinabalu to Sandakan: 2 jam 40 minit of driving, a 35-minute rest in Ranau, then 3 jam 15 minit more. How long is the whole journey? The rest happens during the trip, so it counts too. Drawing the three parts as bars, end to end, keeps the rest from being missed.
Example: walking 15 minutes to school, stopping 5 minutes at a shop and walking 10 minutes more takes 30 minutes in all.
Watch out: many pupils add only the two driving parts and forget the 35-minute rest.
Empat langkah
Diberi → Dicari → Cara → Semak
Untuk setiap masalah masa
1. Diberi
semua masa dalam soalan, termasuk rehat
2. Dicari
jumlah masa? beza masa? waktu tiba?
3. Cara
model bar → ayat matematik → kira (60 minit = 1 jam)
4. Semak
operasi songsang: tambah ↔ tolak, darab ↔ bahagi
Gariskan setiap masa dalam soalan. Bulatkan perkataan rehat.
已知 = Diberi；所求 = Dicari；方法 = Cara；检查 = Semak
时间应用题也用四步。Diberi：把题目里所有时间列出来，休息、等待的时间也要列。Dicari：问的是一共多久、相差多久，还是几点到达？Cara：画长条、写算式、计算，记得满 60 minit 进 1 jam。Semak：用相反的运算检查。
例子：算出一共 6 jam 30 minit，就用 6 jam 30 minit 减回其中一段，看看对不对。
注意：先把题目里的“休息”圈起来，它最容易被漏掉。
given = Diberi; to find = Dicari; method = Cara; check = Semak
Time problems use the same four steps. Diberi: list every time in the question, including rests and waiting. Dicari: does it ask for the total time, the difference, or the arrival time? Cara: draw bars, write the number sentence and work it out, remembering that 60 minit make 1 jam. Semak: check with the opposite operation.
Example: after getting a total of 6 jam 30 minit, subtract one of the parts again to see whether the rest comes back.
Watch out: circle the word rehat first, because the rest time is the easiest part to lose.
Diberi dan Dicari
Lukis model bar
Tiga bahagian disambung: pandu, rehat, pandu
Rehat juga sebahagian daripada perjalanan → tambah ketiga-tiga bahagian
条形模型 = model bar；三段 = tiga bahagian；接起来 = disambung
先写 Diberi：开车 2 jam 40 minit，休息 35 minit，再开车 3 jam 15 minit。Dicari：整趟路程的总时间。画模型时，三段按先后接成一条：第一段开车、中间休息、最后一段开车。休息那段比较短，但一样是这条长条的一部分。整条的长度就是答案。
例子：上课 40 minit、休息 20 minit、再上课 30 minit，长条也是三段接起来，共 1 jam 30 minit。
注意：休息段用不同颜色画，提醒自己不要漏算。
bar model = model bar; three parts = tiga bahagian; joined end to end = disambung
Write Diberi first: drive 2 jam 40 minit, rest 35 minit, drive 3 jam 15 minit. Dicari: the time for the whole journey. In the model the three parts sit in order on one bar: driving, the rest in the middle, then driving again. The rest part is shorter, but it is still part of the bar, and the length of the whole bar is the answer.
Example: a 40-minute lesson, a 20-minute break and a 30-minute lesson also make one bar of three parts, 1 hour 30 minutes long.
Watch out: colour the rest part differently as a reminder not to leave it out.
Cara dan Semak
Tambah tiga masa
minit dahulu: 60 minit = 1 jam
| jam | minit | |
|---|---|---|
| 1 | ||
| 2 | 40 | |
| 35 | ||
| + | 3 | 15 |
| 6 | 30 |
40 + 35 + 15 = 90 minit
= 1 jam 30 minit
Tiba: 7:30 pagi + 6 jam 30 minit
= 2:00 petang
Semak: 6 jam 30 minit − 3 jam 15 minit − 35 minit = 2 jam 40 minit ✓
竖式 = bentuk lazim；进位 = kumpul semula；到达时刻 = waktu tiba
三段时间用竖式加，jam 对 jam，minit 对 minit。先加 minit：40 + 35 + 15 = 90 minit，90 minit 是 1 jam 30 minit，所以 minit 栏写 30，进 1 到 jam 栏。再加 jam：1 + 2 + 0 + 3 = 6。总时间 6 jam 30 minit。早上 7:30 pagi 出发，加 6 jam 30 minit，就是下午 2:00 petang 到。检查：总时间减回两段，剩下的刚好是第一段 2 jam 40 minit。
例子：1 jam 50 minit + 20 minit → 70 minit = 1 jam 10 minit → 写 10 进 1 → 2 jam 10 minit。
注意：minit 满 60 才进 1，不是满 100。
column form = bentuk lazim; regrouping = kumpul semula; arrival time = waktu tiba
Add the three times in columns, hours under hours and minutes under minutes. Minutes first: 40 + 35 + 15 = 90 minit, which is 1 jam 30 minit, so write 30 in the minute column and carry 1 to the hours. Then the hours: 1 + 2 + 0 + 3 = 6. The total is 6 jam 30 minit. Leaving at 7:30 pagi and adding 6 jam 30 minit gives an arrival at 2:00 petang. Check: taking the other two parts away from the total leaves exactly the first part, 2 jam 40 minit.
Example: 1 jam 50 minit + 20 minit → 70 minutes = 1 hour 10 minutes → write 10, carry 1 → 2 jam 10 minit.
Watch out: carry 1 hour only when the minutes reach 60, not 100.
Cuba
Kak Mira menjahit 1 jam 25 minit, berehat 20 minit, kemudian menjahit lagi 50 minit. Berapakah jumlah masa dari mula hingga siap?
从开始到完成 = dari mula hingga siap
问的是从开始到完成，所以休息的 20 minit 也要算。minit：25 + 20 + 50 = 95 minit = 1 jam 35 minit。jam：1 + 1 = 2。答案 2 jam 35 minit。2 jam 15 minit 是漏了休息；1 jam 95 minit 是没有把 60 minit 换成 1 jam。
例子：画画 30 minit，休息 10 minit，再画 45 minit，一共 1 jam 25 minit。
注意：答案里的 minit 不可以超过 59。
from start to finish = dari mula hingga siap
The question asks from start to finish, so the 20-minute rest counts too. Minutes: 25 + 20 + 50 = 95 minit = 1 jam 35 minit. Hours: 1 + 1 = 2. The answer is 2 jam 35 minit. 2 jam 15 minit leaves out the rest, and 1 jam 95 minit forgets to turn 60 minutes into 1 hour.
Example: drawing for 30 minutes, resting 10 minutes and drawing 45 minutes more takes 1 hour 25 minutes.
Watch out: the minutes in an answer can never be more than 59.
Tolak masa rehat
Berapa lama benar-benar bekerja?
8:00 pagi hingga 12:30 tengah hari, rehat 40 minit
| jam | minit | |
|---|---|---|
| 3 | 90 | |
| − | 40 | |
| 3 | 50 |
30 minit tidak cukup →
pinjam 1 jam = 60 minit
90 − 40 = 50
Semak: 3 jam 50 minit + 40 minit = 4 jam 30 minit ✓
扣掉休息 = tolak masa rehat；借位 = pinjam
第一步先求从 8:00 pagi 到 12:30 tengah hari 有多长：8 点到 12 点是 4 jam，再加 30 minit，共 4 jam 30 minit。第二步把休息扣掉：30 minit 减 40 minit 不够，向 jam 借 1，1 jam 是 60 minit，30 + 60 = 90，90 − 40 = 50；jam 剩 3。真正工作 3 jam 50 minit。检查：3 jam 50 minit + 40 minit = 4 jam 30 minit。
例子：2 jam 10 minit − 25 minit → 借 1 jam → 70 − 25 = 45 → 1 jam 45 minit。
注意：借 1 jam 是借 60 minit，不是借 100。
taking away the rest = tolak masa rehat; borrowing = pinjam
Step one finds how long 8:00 pagi to 12:30 tengah hari is: 8 o'clock to 12 o'clock is 4 hours, plus 30 minutes, so 4 jam 30 minit. Step two removes the rest: 30 minutes minus 40 is not possible, so borrow 1 hour, which is 60 minutes; 30 + 60 = 90 and 90 − 40 = 50, leaving 3 hours. He really works 3 jam 50 minit. Check: 3 jam 50 minit + 40 minit = 4 jam 30 minit.
Example: 2 jam 10 minit − 25 minit → borrow 1 hour → 70 − 25 = 45 → 1 jam 45 minit.
Watch out: borrowing 1 hour gives 60 minutes, not 100.
Cuba
Satu pertandingan catur berlangsung 2 jam 15 minit. Masa itu termasuk 25 minit rehat. Berapakah masa pemain benar-benar bermain?
包括休息 = termasuk rehat
“包括 25 minit 休息”表示休息在 2 jam 15 minit 里面，要减掉。15 − 25 不够，向 jam 借 1：15 + 60 = 75，75 − 25 = 50；jam 剩 1。答案 1 jam 50 minit。2 jam 10 minit 是把 25 − 15 倒过来减；2 jam 40 minit 是把休息加上去。
例子：球赛 1 jam 30 minit，含休息 15 minit，真正比赛 1 jam 15 minit。
注意：题目说 termasuk，休息已经在总时间里，要减不要加。
including the rest = termasuk rehat
Including a 25-minute rest means the rest is inside the 2 jam 15 minit, so it must be taken away. 15 − 25 will not go, so borrow 1 hour: 15 + 60 = 75 and 75 − 25 = 50, leaving 1 hour. The answer is 1 jam 50 minit. 2 jam 10 minit subtracts 25 − 15 the wrong way round, and 2 jam 40 minit adds the rest instead.
Example: a match of 1 hour 30 minutes with a 15-minute break has 1 hour 15 minutes of real play.
Watch out: termasuk means the rest is already inside the total, so subtract it, never add.
Darab, kemudian tambah
Latihan menari seminggu
40 minit × 5 hari, kemudian Sabtu 1 jam 30 minit
Langkah 1: 40 minit × 5 = 200 minit = 3 jam 20 minit
Langkah 2: 3 jam 20 minit + 1 jam 30 minit = 4 jam 50 minit
先乘后加 = darab dahulu, kemudian tambah
星期一到星期五每天练 40 minit，是 5 段一样长的时间，用乘法：40 × 5 = 200 minit。200 minit 里有 3 个 60，还剩 20，所以是 3 jam 20 minit。星期六另外练 1 jam 30 minit，第二步加上去：3 jam 20 minit + 1 jam 30 minit = 4 jam 50 minit。检查：4 jam 50 minit − 1 jam 30 minit = 3 jam 20 minit，200 ÷ 5 = 40。
例子：每天走路 30 minit，走 4 天是 2 jam，再加星期日 45 minit，共 2 jam 45 minit。
注意：星期六那段不一样长，不能一起乘 6。
multiply first, then add = darab dahulu, kemudian tambah
Monday to Friday, 40 minutes a day, is 5 equal parts, so multiply: 40 × 5 = 200 minit. 200 minutes holds three 60s with 20 left over, so it is 3 jam 20 minit. Saturday's practice of 1 jam 30 minit is different, so step two adds it: 3 jam 20 minit + 1 jam 30 minit = 4 jam 50 minit. Check: 4 jam 50 minit − 1 jam 30 minit = 3 jam 20 minit, and 200 ÷ 5 = 40.
Example: walking 30 minutes a day for 4 days is 2 hours; adding 45 minutes on Sunday makes 2 hours 45 minutes.
Watch out: Saturday's part is a different length, so you cannot simply multiply by 6.
Cuba
Encik Kumar memandu lori untuk 3 hantaran dalam 4 jam 30 minit. Setiap hantaran sama panjang dan termasuk 15 minit memunggah barang. Berapakah masa memandu untuk setiap hantaran?
先除后减 = bahagi dahulu, kemudian tolak
第一步：4 jam 30 minit = 270 minit，270 ÷ 3 = 90 minit = 1 jam 30 minit，这是每趟送货的时间。第二步：每趟里有 15 minit 卸货，开车时间是 1 jam 30 minit − 15 minit = 1 jam 15 minit。1 jam 30 minit 是忘了扣卸货；1 jam 25 minit 是只从总数扣了一次 15 minit 再除，但每趟都有卸货。
例子：2 jam 煮 4 锅汤，每锅一样久，每锅含 5 minit 洗锅，真正煮 25 minit。
注意：“每一趟都有”的时间，要在除完之后，从每一份里扣。
divide first, then subtract = bahagi dahulu, kemudian tolak
Step one: 4 jam 30 minit = 270 minutes, and 270 ÷ 3 = 90 minutes = 1 jam 30 minit, the time for each delivery. Step two: each delivery includes 15 minutes of unloading, so the driving time is 1 jam 30 minit − 15 minit = 1 jam 15 minit. 1 jam 30 minit forgets the unloading, and 1 jam 25 minit takes 15 minutes off the total only once before dividing, although every trip has unloading.
Example: cooking 4 pots of soup in 2 hours at the same pace, each including 5 minutes of washing up, leaves 25 minutes of real cooking per pot.
Watch out: time that happens in every share must be taken off each share after dividing.
Padankan
Masalah dan cara pengiraan
题目配算式 = padankan masalah dengan cara
“走、休息、再走”是三段接起来，用加法，答案 2 jam 15 minit。“3 jam 包括 30 minit 休息”要把休息扣掉，用减法，得 2 jam 30 minit。“每天 25 minit，4 天”用乘法，得 1 jam 40 minit。“4 jam 画 4 幅一样久的画，每幅含 10 minit 收拾”先除后减：60 − 10 = 50 minit。
例子：“每节课一样长”就想到除法；“中途停了”就想到要把停的时间加进去。
注意：同样是休息，“中途休息”是加，“包括休息”是减，要看清楚题目怎么说。
matching problems to methods = padankan masalah dengan cara
Walk, rest, walk again is three parts joined, so add them, giving 2 jam 15 minit. A 3-hour class including a 30-minute break needs the break removed, giving 2 jam 30 minit. 25 minutes a day for 4 days is multiplying, giving 1 jam 40 minit. Four equal paintings in 4 hours, each with 10 minutes of tidying, means divide then subtract: 60 − 10 = 50 minutes.
Example: lessons of equal length suggest dividing; a stop on the way suggests adding the stop.
Watch out: a rest in the middle of a trip is added, but a rest included in a total is subtracted, so read the wording carefully.
Ringkasan
Syabas!
Diberi → Dicari → Cara → Semak
Senaraikan semua masa, termasuk rehat. Lukis model bar. Rehat di tengah perjalanan: tambah. Termasuk rehat: tolak. 60 minit = 1 jam. Semak dengan operasi songsang.
Latihan tambahan →