Unit 3
Tolak Panjang
Pokok kelapa di halaman sekolah tingginya 8 m 20 cm. Pokok pisang pula 3 m 65 cm.
Berapakah beza tinggi kedua-dua pokok itu?
长度减法 = tolak panjang；相差 = beza
这一课学用一个长度减去另一个长度。学校的椰子树高 8 m 20 cm，香蕉树高 3 m 65 cm，两棵树相差多高，就用高的减矮的。长度是一百进位，借位时借来的是 100 cm。
例子：一支 18 cm 的铅笔比一支 12 cm 的铅笔长 6 cm。
注意：求 beza 一定是大的减小的，答案不会是负数。
subtracting lengths = tolak panjang; difference = beza
In this unit we take one length away from another. The school coconut tree is 8 m 20 cm tall and the banana tree is 3 m 65 cm; to find how much taller the coconut tree is, subtract the shorter height from the taller one. Lengths work in hundreds, so a borrowed metre gives 100 cm.
Example: an 18 cm pencil is 6 cm longer than a 12 cm pencil.
Watch out: for beza, always take the smaller length from the bigger one.
Unit yang sama
Gunung Kinabalu 4 095 m · Gunung Trus Madi 2 642 m
Beza tinggi = 4 095 m − 2 642 m
| m | |
|---|---|
| 4 095 | |
| − | 2 642 |
| 1 453 |
Beza tinggi: 1 453 m
同单位相减 = tolak unit yang sama
京那巴鲁山高 4 095 m，Trus Madi 山高 2 642 m，两个都是 m，就像普通减法列竖式：个位 5 − 2 = 3；十位 9 − 4 = 5；百位 0 不够减 6，向千位借 1，10 − 6 = 4；千位 3 − 2 = 1。两座山相差 1 453 m。
例子：教室走廊长 845 cm，旗杆台长 320 cm，相差 525 cm。
注意：这里的借位是普通减法借 1 当 10，因为单位只有一个。
subtracting the same unit = tolak unit yang sama
Mount Kinabalu is 4 095 m high and Mount Trus Madi is 2 642 m high. Both are in metres, so subtract like ordinary numbers in columns: ones 5 − 2 = 3; tens 9 − 4 = 5; hundreds 0 cannot take away 6, so borrow 1 thousand, 10 − 6 = 4; thousands 3 − 2 = 1. The difference is 1 453 m.
Example: a corridor of 845 cm and a stage of 320 cm differ by 525 cm.
Watch out: here the borrowing is the ordinary kind, 1 for 10, because there is only one unit.
Cuba
900 cm − 465 cm = ?
| cm | |
|---|---|
| 900 | |
| − | 465 |
| ? |
从 0 借位 = pinjam melalui sifar
900 的十位和个位都是 0，要先向百位借：9 变 8，十位变 10，再借 1 给个位，十位剩 9，个位变 10。个位 10 − 5 = 5，十位 9 − 6 = 3，百位 8 − 4 = 4。答案 435 cm。
例子：700 cm − 238 cm = 462 cm。
注意：565 cm 是不借位、直接用下面的数减上面的数，是常见错误。
borrowing across zeros = pinjam melalui sifar
Both the tens and ones of 900 are 0, so borrow from the hundreds first: 9 becomes 8 and the tens become 10; then lend 1 to the ones, leaving 9 tens and 10 ones. Ones 10 − 5 = 5, tens 9 − 6 = 3, hundreds 8 − 4 = 4. The answer is 435 cm.
Example: 700 cm − 238 cm = 462 cm.
Watch out: 565 cm comes from taking the top digit away from the bottom one without borrowing, a common slip.
Tanpa pinjam
6 m 85 cm − 2 m 40 cm
Tolak cm dahulu, kemudian m
| m | cm | |
|---|---|---|
| 6 | 85 | |
| − | 2 | 40 |
| 4 | 45 |
cm: 85 − 40 = 45 · m: 6 − 2 = 4
不退位减法 = tolak tanpa pinjam
复名数相减也用分栏竖式：m 对 m，cm 对 cm。先减右边的 cm：85 − 40 = 45，上面的数比下面大，够减。再减左边的 m：6 − 2 = 4。答案 4 m 45 cm。
例子：9 m 70 cm − 5 m 30 cm = 4 m 40 cm。
注意：一定先从 cm 栏开始，先看上面的 cm 够不够减，再动手。
subtracting without borrowing = tolak tanpa pinjam
Lengths with two units are also subtracted in columns, metres under metres and centimetres under centimetres. Subtract the cm on the right first: 85 − 40 = 45, and the top number is bigger, so there is enough. Then the metres: 6 − 2 = 4. The answer is 4 m 45 cm.
Example: 9 m 70 cm − 5 m 30 cm = 4 m 40 cm.
Watch out: always begin with the cm column and check whether the top number is big enough before subtracting.
Pinjam 1 m = 100 cm
8 m 20 cm − 3 m 65 cm
20 cm tidak cukup untuk tolak 65 cm
Pinjam 1 m → 100 cm + 20 cm = 120 cm → 120 − 65 = 55
借位 = pinjam；借 1 当 100
20 cm 不够减 65 cm，要向 m 栏借 1。8 m 借走 1 m，剩 7 m。借来的 1 m 是 100 cm，加上原来的 20 cm，变成 120 cm。120 − 65 = 55，写 55。m 栏：7 − 3 = 4。两棵树相差 4 m 55 cm。
例子：5 m 10 cm − 2 m 40 cm → 借 1 → 110 − 40 = 70 → 4 − 2 = 2 → 2 m 70 cm。
注意：借来的是 100，不是 10；借了以后 m 栏也要少 1。
borrowing = pinjam; borrow 1 as 100
20 cm is not enough to take away 65 cm, so borrow 1 from the metre column. 8 m becomes 7 m. The borrowed metre is 100 cm, and with the 20 cm already there it makes 120 cm. 120 − 65 = 55, so write 55. Metre column: 7 − 3 = 4. The trees differ by 4 m 55 cm.
Example: 5 m 10 cm − 2 m 40 cm → borrow 1 → 110 − 40 = 70 → 4 − 2 = 2 → 2 m 70 cm.
Watch out: the borrowed amount is 100, not 10, and the metre column must go down by 1.
Cuba
7 m 15 cm − 2 m 48 cm = ?
| m | cm | |
|---|---|---|
| 7 | 15 | |
| − | 2 | 48 |
| ? | ? |
先看够不够减 = semak cukup atau tidak
15 cm 不够减 48 cm，向 m 借 1：7 变 6，cm 变成 100 + 15 = 115。115 − 48 = 67。m：6 − 2 = 4。答案 4 m 67 cm。
例子：6 m 5 cm − 1 m 30 cm → 105 − 30 = 75 → 5 − 1 = 4 → 4 m 75 cm。
注意：5 m 33 cm 是倒过来用 48 − 15；4 m 52 cm 是借了 100 却忘了加上原来的 15。
checking whether there is enough = semak cukup atau tidak
15 cm cannot take away 48 cm, so borrow 1 m: 7 becomes 6 and the centimetres become 100 + 15 = 115. Then 115 − 48 = 67, and the metres give 6 − 2 = 4. The answer is 4 m 67 cm.
Example: 6 m 5 cm − 1 m 30 cm → 105 − 30 = 75 → 5 − 1 = 4 → 4 m 75 cm.
Watch out: 5 m 33 cm does 48 − 15 the wrong way round, and 4 m 52 cm borrows 100 but forgets to add the 15.
Tolak dua kali
10 m − 3 m 45 cm − 2 m 30 cm
Tolak satu demi satu
| m | cm | |
|---|---|---|
| 9 | 100 | |
| 0 | ||
| − | 3 | 45 |
| 6 | 55 |
| m | cm | |
|---|---|---|
| 6 | 55 | |
| − | 2 | 30 |
| 4 | 25 |
连减 = tolak dua kali
两个减号要一个一个做。第一步：10 m − 3 m 45 cm，10 m 的 cm 是 0，不够减 45，借 1 m，100 − 45 = 55，m 栏 9 − 3 = 6，得 6 m 55 cm。第二步：用这个答案再减 2 m 30 cm，55 − 30 = 25，6 − 2 = 4，得 4 m 25 cm。
例子：800 cm − 250 cm − 150 cm → 550 − 150 = 400 cm。
注意：整米的数要先在 cm 栏写 0，才看得出要借位。
subtracting twice = tolak dua kali
With two minus signs, do them one at a time. Step 1: 10 m − 3 m 45 cm; 10 m has 0 cm, which cannot take away 45, so borrow 1 m: 100 − 45 = 55 and 9 − 3 = 6, giving 6 m 55 cm. Step 2: take 2 m 30 cm from that answer; 55 − 30 = 25 and 6 − 2 = 4, giving 4 m 25 cm.
Example: 800 cm − 250 cm − 150 cm → 550 − 150 = 400 cm.
Watch out: write 0 in the cm column for a whole number of metres so you can see that borrowing is needed.
Cuba
950 cm − 275 cm − 380 cm = ?
单位相同的连减 = tolak berturut-turut
先算 950 − 275 = 675 cm，再算 675 − 380 = 295 cm。答案 295 cm。
例子：600 m − 150 m − 200 m → 450 − 200 = 250 m。
注意：675 cm 只做了第一步，还要再减 380。
subtracting one after another = tolak berturut-turut
First 950 − 275 = 675 cm, then 675 − 380 = 295 cm. The answer is 295 cm.
Example: 600 m − 150 m − 200 m → 450 − 200 = 250 m.
Watch out: 675 cm only finishes step 1; you still have to take away 380.
Beza panjang
Kereta A 4 m 35 cm · Kereta B 3 m 80 cm
Beza = panjang − pendek
Kereta A
Kereta B
beza = 55 cm ↑
| m | cm | |
|---|---|---|
| 3 | 135 | |
| 35 | ||
| − | 3 | 80 |
| 0 | 55 |
长度差 = beza panjang
比较两辆车有多长，可以看条形图：长的那条多出来的一段就是相差的长度。A 车 4 m 35 cm，B 车 3 m 80 cm。35 不够减 80，借 1 m，135 − 80 = 55；m 栏 3 − 3 = 0。所以相差 55 cm。
例子：书桌长 1 m 20 cm，椅子宽 45 cm，相差 75 cm。
注意：m 减到 0 时可以不写，答案就写 55 cm。
difference in length = beza panjang
To compare two cars, look at the bars: the extra piece on the longer bar is the difference. Car A is 4 m 35 cm and car B is 3 m 80 cm. 35 cannot take away 80, so borrow 1 m: 135 − 80 = 55, and the metres give 3 − 3 = 0. The difference is 55 cm.
Example: a desk 1 m 20 cm long and a chair 45 cm wide differ by 75 cm.
Watch out: when the metres come to 0 you may leave them out and simply write 55 cm.
Cuba
Seutas tali panjangnya 5 m. Ali memotong 1 m 75 cm daripadanya. Berapakah panjang tali yang tinggal?
剩下的长度 = panjang yang tinggal
剪掉一段就是减法：5 m − 1 m 75 cm。5 m 写成 5 m 0 cm，0 不够减 75，借 1 m：100 − 75 = 25；m 栏 4 − 1 = 3。剩 3 m 25 cm。
例子：3 m 的布剪掉 1 m 40 cm，剩 1 m 60 cm。
注意：4 m 25 cm 是借了 1 m 却没有把 5 变成 4。
the length left = panjang yang tinggal
Cutting a piece off means subtracting: 5 m − 1 m 75 cm. Write 5 m as 5 m 0 cm; 0 cannot take away 75, so borrow 1 m: 100 − 75 = 25, and the metres give 4 − 1 = 3. The rope left is 3 m 25 cm.
Example: cutting 1 m 40 cm from 3 m of cloth leaves 1 m 60 cm.
Watch out: 4 m 25 cm borrows the metre but forgets to change 5 into 4.
Padankan
Baki panjang yang betul
配对差 = padankan baki panjang
1 m 就是 100 cm，100 − 35 = 65 cm。5 m 20 cm − 2 m 50 cm：借 1 m，120 − 50 = 70，4 − 2 = 2，得 2 m 70 cm。80 − 80 = 0，所以只剩 7 m。600 − 245 = 355 cm。
例子：2 m − 60 cm = 1 m 40 cm。
注意：整米减厘米，也要先把 1 m 换成 100 cm 再减。
matching the answers = padankan baki panjang
1 m is 100 cm, so 100 − 35 = 65 cm. For 5 m 20 cm − 2 m 50 cm, borrow 1 m: 120 − 50 = 70 and 4 − 2 = 2, giving 2 m 70 cm. 80 − 80 = 0, so only 7 m is left. 600 − 245 = 355 cm.
Example: 2 m − 60 cm = 1 m 40 cm.
Watch out: when centimetres are taken from whole metres, first change 1 m into 100 cm.
Ringkasan
Syabas!
tidak cukup → pinjam 1 m = 100 cm → tolak
Tolak cm dahulu. Jika tidak cukup, pinjam 1 m dan tambah 100 cm. Jangan lupa lajur m berkurang 1.
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