Unit 7
Tolak Masa
Perjalanan kereta api mengambil masa 4 jam 15 minit. Perjalanan bas pula 1 jam 40 minit.
Berapakah beza masa antara kedua-dua perjalanan?
时间减法 = tolak masa；相差 = beza masa
这一课学用一段时间减去另一段时间。火车要 4 小时 15 分，巴士只要 1 小时 40 分，相差多久，就是用长的时间减去短的时间。时间是六十进位，所以借位时借来的是 60，不是 10。
例子：看电影用了 50 minit，看卡通用了 20 minit，相差 30 minit。
注意：求 beza masa 一定是长的减短的，答案不会是负数。
subtracting time = tolak masa; time difference = beza masa
In this unit we take one length of time away from another. A train trip takes 4 hours 15 minutes and a bus trip only 1 hour 40 minutes; to find how much longer the train takes, we subtract the shorter time from the longer one. Time works in sixties, so when we borrow we get 60, not 10.
Example: a film of 50 minit and a cartoon of 20 minit differ by 30 minit.
Watch out: for beza masa, always take the shorter time from the longer one.
Tanpa pinjam
5 jam 50 minit − 2 jam 20 minit
Tolak minit dahulu, kemudian jam
| jam | minit | |
|---|---|---|
| 5 | 50 | |
| − | 2 | 20 |
| 3 | 30 |
Minit: 50 − 20 = 30 · Jam: 5 − 2 = 3
不退位减法 = tolak tanpa pinjam
时间减法也用分栏竖式：jam 对 jam，minit 对 minit。先减右边的 minit：50 − 20 = 30，上面的数比下面大，够减。再减左边的 jam：5 − 2 = 3。答案 3 jam 30 minit。
例子：48 minit − 15 minit = 33 minit，只有一个单位，像普通减法一样。
注意：一定从小单位（右边）开始减，先看够不够减，再动手。
subtracting without borrowing = tolak tanpa pinjam
Time subtraction also uses columns, with hours under hours and minutes under minutes. Subtract the minutes on the right first: 50 − 20 = 30, and the top number is bigger, so there is enough. Then the hours on the left: 5 − 2 = 3. The answer is 3 jam 30 minit.
Example: 48 minit − 15 minit = 33 minit; with one unit it is just ordinary subtraction.
Watch out: always start from the smaller unit on the right and check whether there is enough before you subtract.
Pinjam 1 jam = 60 minit
4 jam 15 minit − 1 jam 40 minit
15 minit tidak cukup untuk tolak 40 minit
Pinjam 1 jam → 60 minit + 15 minit = 75 minit → 75 − 40 = 35
借位 = pinjam；借 1 当 60
15 minit 不够减 40 minit，要向 jam 栏借 1。4 jam 借走 1 jam，剩 3 jam。借来的 1 jam 是 60 minit，加上原来的 15 minit，变成 75 minit。75 − 40 = 35，写 35。jam 栏：3 − 1 = 2。答案 2 jam 35 minit。
例子：3 jam 10 minit − 1 jam 25 minit → 借 1 → 70 − 25 = 45 → 2 − 1 = 1 → 1 jam 45 minit。
注意：借来的是 60，不是 10 或 100；借了之后 jam 栏也要少 1。
borrowing = pinjam; borrow 1 as 60
15 minutes is not enough to take away 40 minutes, so we borrow 1 from the hour column. 4 jam becomes 3 jam. The borrowed hour is 60 minutes, and together with the 15 minutes already there it makes 75 minutes. 75 − 40 = 35, so write 35. Hour column: 3 − 1 = 2. The answer is 2 jam 35 minit.
Example: 3 jam 10 minit − 1 jam 25 minit → borrow 1 → 70 − 25 = 45 → 2 − 1 = 1 → 1 jam 45 minit.
Watch out: the borrowed amount is 60, not 10 or 100, and the hour column must go down by 1.
Cuba
6 jam 10 minit − 2 jam 35 minit = ?
| jam | minit | |
|---|---|---|
| 6 | 10 | |
| − | 2 | 35 |
| ? | ? |
先看够不够减 = semak cukup atau tidak
10 minit 不够减 35 minit，向 jam 借 1：6 变 5，minit 变成 60 + 10 = 70。70 − 35 = 35。jam：5 − 2 = 3。答案 3 jam 35 minit。
例子：5 jam 5 minit − 1 jam 20 minit → 65 − 20 = 45 → 4 − 1 = 3 → 3 jam 45 minit。
注意：4 jam 25 minit 是用 35 − 10 倒过来减，这是常见错误。
checking whether there is enough = semak cukup atau tidak
10 minutes cannot take away 35 minutes, so borrow 1 hour: 6 becomes 5 and the minutes become 60 + 10 = 70. Then 70 − 35 = 35, and the hours give 5 − 2 = 3. The answer is 3 jam 35 minit.
Example: 5 jam 5 minit − 1 jam 20 minit → 65 − 20 = 45 → 4 − 1 = 3 → 3 jam 45 minit.
Watch out: 4 jam 25 minit comes from doing 35 − 10 upside down, a very common slip.
Minit dan saat
8 minit 12 saat − 3 minit 47 saat
Pinjam 1 minit = 60 saat
| minit | saat | |
|---|---|---|
| 7 | 72 | |
| 12 | ||
| − | 3 | 47 |
| 4 | 25 |
60 + 12 = 72 saat → 72 − 47 = 25 · 7 − 3 = 4
分秒借位 = pinjam minit
saat 栏 12 不够减 47，向 minit 栏借 1 minit。8 minit 变成 7 minit，借来的 1 minit 是 60 saat，60 + 12 = 72 saat。72 − 47 = 25，写 25。minit：7 − 3 = 4。答案 4 minit 25 saat。
例子：6 minit 20 saat − 2 minit 50 saat → 80 − 50 = 30 → 5 − 2 = 3 → 3 minit 30 saat。
注意：竖式上把 8 划掉写 7，可以提醒自己已经借过了。
borrowing a minute = pinjam minit
In the seconds column, 12 cannot take away 47, so borrow 1 minute from the minutes column. 8 minit becomes 7 minit, and the borrowed minute is 60 seconds, so 60 + 12 = 72 saat. 72 − 47 = 25, so write 25. Minutes: 7 − 3 = 4. The answer is 4 minit 25 saat.
Example: 6 minit 20 saat − 2 minit 50 saat → 80 − 50 = 30 → 5 − 2 = 3 → 3 minit 30 saat.
Watch out: crossing out the 8 and writing 7 above it reminds you that you have already borrowed.
Cuba
10 minit 5 saat − 4 minit 38 saat = ?
| minit | saat | |
|---|---|---|
| 10 | 5 | |
| − | 4 | 38 |
| ? | ? |
借 1 minit = pinjam 1 minit
5 saat 不够减 38 saat，借 1 minit：10 变 9，saat 变成 60 + 5 = 65。65 − 38 = 27。minit：9 − 4 = 5。答案 5 minit 27 saat。
例子：7 minit 8 saat − 2 minit 30 saat → 68 − 30 = 38 → 6 − 2 = 4 → 4 minit 38 saat。
注意：5 minit 67 saat 是借了 100，不是 60。
borrowing 1 minute = pinjam 1 minit
5 seconds cannot take away 38 seconds, so borrow 1 minute: 10 becomes 9 and the seconds become 60 + 5 = 65. Then 65 − 38 = 27, and the minutes give 9 − 4 = 5. The answer is 5 minit 27 saat.
Example: 7 minit 8 saat − 2 minit 30 saat → 68 − 30 = 38 → 6 − 2 = 4 → 4 minit 38 saat.
Watch out: 5 minit 67 saat comes from borrowing 100 instead of 60.
Tolak dua kali
5 jam 30 minit − 1 jam 45 minit − 2 jam 10 minit
Tolak satu demi satu, dari kiri ke kanan
| jam | minit | |
|---|---|---|
| 4 | 90 | |
| 30 | ||
| − | 1 | 45 |
| 3 | 45 |
| jam | minit | |
|---|---|---|
| 3 | 45 | |
| − | 2 | 10 |
| 1 | 35 |
连减 = tolak dua kali
两个减号要一个一个做。第一步：5 jam 30 minit − 1 jam 45 minit，30 不够减 45，借 1 jam，90 − 45 = 45，jam 4 − 1 = 3，得 3 jam 45 minit。第二步：用这个答案再减 2 jam 10 minit，45 − 10 = 35，3 − 2 = 1，得 1 jam 35 minit。
例子：55 minit − 18 minit − 22 minit → 37 − 22 = 15 minit。
注意：第一步的答案要抄对，第二步才会对。
subtracting twice = tolak dua kali
With two minus signs, do them one at a time. Step 1: 5 jam 30 minit − 1 jam 45 minit; 30 is not enough for 45, so borrow 1 hour, 90 − 45 = 45 and 4 − 1 = 3, giving 3 jam 45 minit. Step 2: take 2 jam 10 minit from that answer; 45 − 10 = 35 and 3 − 2 = 1, giving 1 jam 35 minit.
Example: 55 minit − 18 minit − 22 minit → 37 − 22 = 15 minit.
Watch out: copy the answer of step 1 correctly, or step 2 will be wrong too.
Cuba
50 saat − 12 saat − 19 saat = ?
单位相同的连减 = tolak berturut-turut
先算 50 − 12 = 38 saat，再算 38 − 19 = 19 saat。答案 19 saat。
例子：40 minit − 15 minit − 5 minit → 25 − 5 = 20 minit。
注意：31 saat 只算了 12 + 19，还没有拿 50 去减。
subtracting one after another = tolak berturut-turut
First 50 − 12 = 38 seconds, then 38 − 19 = 19 seconds. The answer is 19 saat.
Example: 40 minit − 15 minit − 5 minit → 25 − 5 = 20 minit.
Watch out: 31 saat is only 12 + 19; it has not yet been taken away from 50.
Beza masa
Amir 3 minit 20 saat · Ben 2 minit 45 saat
Beza = masa panjang − masa pendek
Amir
Ben
beza = 35 saat ↑
| minit | saat | |
|---|---|---|
| 2 | 80 | |
| 20 | ||
| − | 2 | 45 |
| 0 | 35 |
时间差 = beza masa
比较两个人用的时间，用条形图看：长条多出来的那一段就是相差的时间。Amir 跑 3 minit 20 saat，Ben 跑 2 minit 45 saat。20 不够减 45，借 1 minit，80 − 45 = 35；minit 2 − 2 = 0。所以相差 35 saat。
例子：做功课 1 jam 10 minit 和 50 minit 相差 20 minit。
注意：大单位减到 0 时可以不写，答案就写 35 saat。
time difference = beza masa
To compare two people's times, look at the bars: the extra piece on the longer bar is the difference. Amir runs for 3 minit 20 saat and Ben for 2 minit 45 saat. 20 cannot take away 45, so borrow 1 minute: 80 − 45 = 35, and the minutes give 2 − 2 = 0. The difference is 35 saat.
Example: homework times of 1 jam 10 minit and 50 minit differ by 20 minit.
Watch out: when the big unit comes to 0 you may leave it out and just write 35 saat.
Cuba
Kelas tarian 1 jam 30 minit. Kelas piano 55 minit. Berapa lamakah kelas tarian lebih panjang?
多多少时间 = lebih panjang berapa
求差：1 jam 30 minit − 55 minit。30 不够减 55，借 1 jam：60 + 30 = 90 minit，90 − 55 = 35。jam：1 − 1 = 0。答案 35 minit。
例子：游泳课 1 jam 15 minit 比画画课 40 minit 多 35 minit。
注意：1 jam 25 minit 是倒过来用 55 − 30 算出来的。
how much longer = lebih panjang berapa
Find the difference: 1 jam 30 minit − 55 minit. 30 is not enough for 55, so borrow 1 hour: 60 + 30 = 90 minutes, and 90 − 55 = 35. Hours: 1 − 1 = 0. The answer is 35 minit.
Example: a swimming class of 1 jam 15 minit is 35 minit longer than a drawing class of 40 minit.
Watch out: 1 jam 25 minit comes from working out 55 − 30 the wrong way round.
Padankan
Baki masa yang betul
配对差 = padankan baki
1 jam 就是 60 minit，60 − 20 = 40 minit。3 jam 15 minit − 1 jam 30 minit：借 1 jam，75 − 30 = 45，2 − 1 = 1，得 1 jam 45 minit。5 minit 10 saat − 40 saat：借 1 minit，70 − 40 = 30，得 4 minit 30 saat。45 − 45 = 0，所以只剩 2 jam。
例子：2 jam − 30 minit = 1 jam 30 minit。
注意：整小时减分钟，也要先把 1 jam 换成 60 minit。
matching the answers = padankan baki
1 jam is 60 minutes, so 60 − 20 = 40 minit. For 3 jam 15 minit − 1 jam 30 minit, borrow 1 hour: 75 − 30 = 45 and 2 − 1 = 1, giving 1 jam 45 minit. For 5 minit 10 saat − 40 saat, borrow 1 minute: 70 − 40 = 30, giving 4 minit 30 saat. 45 − 45 = 0, so only 2 jam is left.
Example: 2 jam − 30 minit = 1 jam 30 minit.
Watch out: when a whole hour loses some minutes, first change 1 jam into 60 minit.
Ringkasan
Syabas!
tidak cukup → pinjam 1 = 60 → tolak
Tolak unit kecil dahulu. Jika tidak cukup, pinjam 1 unit besar dan tambah 60. Jangan lupa unit besar berkurang 1.
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