Unit 10
Darab Jisim
Ibu membeli 3 peket oat. Jisim setiap peket ialah 1 kg 400 g.
Berapakah jumlah jisim oat itu?
质量乘法 = darab jisim；每包 = setiap peket
这一课学一个质量乘以一位数。妈妈买 3 包燕麦，每包一样重，都是 1 kg 400 g，求总质量就是 1 kg 400 g × 3，比连加三次快。乘的时候克和公斤都要乘。
例子：每包糖 1 kg，买 4 包，就是 1 kg × 4 = 4 kg。
注意：克乘出来满 1 000 g，要换成公斤进位。
multiplying mass = darab jisim; each packet = setiap peket
In this unit we multiply a mass by a one-digit number. Mother buys 3 packets of oats, each with the same mass of 1 kg 400 g, so the total is 1 kg 400 g × 3, which is quicker than adding it three times. Both the grams and the kilograms must be multiplied.
Example: 4 bags of sugar at 1 kg each make 1 kg × 4 = 4 kg.
Watch out: when the grams multiply to 1 000 g or more, change them into kilograms and carry.
Satu unit
250 g × 3 · 12 kg × 4
Darab seperti biasa, tulis unitnya
| g | |
|---|---|
| 250 | |
| × | 3 |
| 750 |
| kg | |
|---|---|
| 12 | |
| × | 4 |
| 48 |
单名数乘法 = darab satu unit
只有克或只有公斤时，照普通乘法做：250 × 3，个位 0 × 3 = 0，十位 5 × 3 = 15 写 5 进 1，百位 2 × 3 + 1 = 7，得 750 g。12 × 4 = 48，得 48 kg。乘数写在个位下面。
例子：120 g × 4 = 480 g；21 kg × 3 = 63 kg。
注意：乘完记得写单位，克还是克，公斤还是公斤。
multiplying one unit = darab satu unit
With only grams or only kilograms, multiply as usual: in 250 × 3, the ones give 0 × 3 = 0, the tens give 5 × 3 = 15 so write 5 and carry 1, and the hundreds give 2 × 3 + 1 = 7, making 750 g. 12 × 4 = 48, making 48 kg. The multiplier sits under the ones digit.
Example: 120 g × 4 = 480 g; 21 kg × 3 = 63 kg.
Watch out: write the unit after multiplying; grams stay grams and kilograms stay kilograms.
Cuba
350 g × 4 = ?
| g | |
|---|---|
| 350 | |
| × | 4 |
| ? |
积超过 1 000 g = hasil lebih 1 000 g
350 × 4 = 1 400 g。1 400 g 里有一个 1 000 g，就是 1 kg，剩下 400 g，答案 1 kg 400 g。
例子：300 g × 5 = 1 500 g = 1 kg 500 g。
注意：14 kg 是用 100 来换的，克换公斤要用 1 000。
a product over 1 000 g = hasil lebih 1 000 g
350 × 4 = 1 400 g. There is one lot of 1 000 g in 1 400 g, which is 1 kg, with 400 g left, so the answer is 1 kg 400 g.
Example: 300 g × 5 = 1 500 g = 1 kg 500 g.
Watch out: 14 kg comes from changing with 100; grams change into kilograms with 1 000.
Bentuk lazim
2 kg 130 g × 3
Darab gram dahulu, kemudian kilogram
| kg | g | |
|---|---|---|
| 2 | 130 | |
| × | 3 | |
| 6 | 390 |
g: 130 × 3 = 390 · kg: 2 × 3 = 6
分栏乘法 = darab dalam dua lajur
复名数乘一位数，乘数写在克栏下面，但是两栏都要乘它。先乘克：130 × 3 = 390，不满 1 000，直接写。再乘公斤：2 × 3 = 6。答案 6 kg 390 g。
例子：1 kg 210 g × 4 → 210 × 4 = 840 → 1 × 4 = 4 → 4 kg 840 g。
注意：只乘了克、忘了乘公斤，就会得到 2 kg 390 g 这种错答案。
multiplying in two columns = darab dalam dua lajur
When kg and g are multiplied by a one-digit number, the multiplier is written under the gram column, but both columns are multiplied by it. Grams first: 130 × 3 = 390, below 1 000, so write it down. Then kilograms: 2 × 3 = 6. The answer is 6 kg 390 g.
Example: 1 kg 210 g × 4 → 210 × 4 = 840 → 1 × 4 = 4 → 4 kg 840 g.
Watch out: multiplying only the grams and forgetting the kilograms gives a wrong answer such as 2 kg 390 g.
Kumpul semula
1 kg 400 g × 3
Hasil gram cukup 1 000 → 1 kg
1 200 g = 1 kg 200 g → tulis 200, bawa 1 · 1 × 3 + 1 = 4
乘完再进位 = darab, kemudian kumpul semula
先乘克：400 × 3 = 1 200 g，满了 1 000。1 200 g = 1 kg 200 g，克栏写 200，把 1 kg 进到公斤栏。再乘公斤：1 × 3 = 3，加上进来的 1，得 4。3 包燕麦一共 4 kg 200 g。
例子：2 kg 500 g × 3 → 500 × 3 = 1 500 → 写 500 进 1 → 2 × 3 + 1 = 7 → 7 kg 500 g。
注意：进位的 1 是在公斤乘完之后才加，不是先加再乘。
multiply, then regroup = darab, kemudian kumpul semula
Multiply the grams first: 400 × 3 = 1 200 g, which reaches 1 000. 1 200 g = 1 kg 200 g, so write 200 in the gram column and carry 1 kg to the kilogram column. Then multiply the kilograms: 1 × 3 = 3, plus the carried 1 makes 4. The 3 packets of oats weigh 4 kg 200 g in total.
Example: 2 kg 500 g × 3 → 500 × 3 = 1 500 → write 500, carry 1 → 2 × 3 + 1 = 7 → 7 kg 500 g.
Watch out: the carried 1 is added after multiplying the kilograms, not before.
Cuba
2 kg 350 g × 4 = ?
| kg | g | |
|---|---|---|
| 2 | 350 | |
| × | 4 | |
| ? | ? |
满千进一 = kumpul semula 1 000 g
克：350 × 4 = 1 400，写 400，进 1。公斤：2 × 4 = 8，加进位 1 得 9。答案 9 kg 400 g。
例子：1 kg 300 g × 4 → 300 × 4 = 1 200 → 写 200 进 1 → 1 × 4 + 1 = 5 → 5 kg 200 g。
注意：8 kg 400 g 忘了进位；8 kg 1 400 g 没有把 1 000 g 换成 1 kg。
carrying a thousand = kumpul semula 1 000 g
Grams: 350 × 4 = 1 400, write 400 and carry 1. Kilograms: 2 × 4 = 8, plus the carried 1 makes 9. The answer is 9 kg 400 g.
Example: 1 kg 300 g × 4 → 300 × 4 = 1 200 → write 200, carry 1 → 1 × 4 + 1 = 5 → 5 kg 200 g.
Watch out: 8 kg 400 g forgets the carry, and 8 kg 1 400 g leaves 1 000 g unchanged into 1 kg.
Bawa lebih daripada 1
3 kg 625 g × 4
2 500 g = 2 kg 500 g → bawa 2
| kg | g | |
|---|---|---|
| 2 | ||
| 3 | 625 | |
| × | 4 | |
| 14 | 500 |
625 × 4 = 2 500 → tulis 500, bawa 2 · 3 × 4 + 2 = 14
进 2 或 3 = bawa 2 atau 3
克乘出来可能有好几个 1 000。625 × 4 = 2 500 g，里面有两个 1 000，所以是 2 kg 500 g：克栏写 500，向公斤栏进 2。公斤：3 × 4 = 12，加 2 得 14。答案 14 kg 500 g。
例子：800 g × 4 = 3 200 g → 写 200 进 3 → 3 kg 200 g。
注意：进几就看克的积里有几个 1 000，不一定都是进 1。
carrying 2 or 3 = bawa 2 atau 3
The gram product can contain several thousands. 625 × 4 = 2 500 g, which holds two lots of 1 000, so it is 2 kg 500 g: write 500 in the gram column and carry 2 to the kilograms. Kilograms: 3 × 4 = 12, plus 2 makes 14. The answer is 14 kg 500 g.
Example: 800 g × 4 = 3 200 g → write 200, carry 3 → 3 kg 200 g.
Watch out: the number carried equals how many thousands are in the gram product, so it is not always 1.
Cuba
1 kg 750 g × 5 = ?
| kg | g | |
|---|---|---|
| 1 | 750 | |
| × | 5 | |
| ? | ? |
进 3 = bawa 3
克：750 × 5 = 3 750 g，有三个 1 000，写 750，进 3。公斤：1 × 5 = 5，加 3 得 8。答案 8 kg 750 g。
例子：1 kg 600 g × 5 → 600 × 5 = 3 000 → 写 0 进 3 → 5 + 3 = 8 → 8 kg。
注意：6 kg 750 g 只进了 1；3 750 g 里有 3 kg，要进 3。
carrying 3 = bawa 3
Grams: 750 × 5 = 3 750 g, which holds three thousands, so write 750 and carry 3. Kilograms: 1 × 5 = 5, plus 3 makes 8. The answer is 8 kg 750 g.
Example: 1 kg 600 g × 5 → 600 × 5 = 3 000 → write 0, carry 3 → 5 + 3 = 8 → 8 kg.
Watch out: 6 kg 750 g carries only 1, but 3 750 g contains 3 kg, so 3 must be carried.
Masalah harian
6 botol jem × 450 g
Beri jawapan dalam kg dan g
| g | |
|---|---|
| 450 | |
| × | 6 |
| 2 700 |
2 700 g = 2 000 g + 700 g = 2 kg 700 g
应用题 = masalah harian；每瓶 = setiap botol
6 瓶果酱，每瓶 450 g，总质量就是 450 g × 6 = 2 700 g。题目要 kg 和 g，就把 2 700 g 拆成 2 000 g 和 700 g，写成 2 kg 700 g。
例子：每包米粉 400 g，买 5 包 → 2 000 g = 2 kg。
注意：“每个一样重，有几个”就用乘法，不要把 450 和 6 相加。
word problem = masalah harian; each bottle = setiap botol
With 6 bottles of jam at 450 g each, the total mass is 450 g × 6 = 2 700 g. The question wants kg and g, so split 2 700 g into 2 000 g and 700 g and write 2 kg 700 g.
Example: 5 packets of rice vermicelli at 400 g each → 2 000 g = 2 kg.
Watch out: equal masses repeated a number of times call for multiplying, not for adding 450 and 6.
Cuba
Ada 8 peket gula. Jisim setiap peket ialah 750 g. Berapakah jumlah jisim gula itu?
整千克 = gram ribu bulat
750 g × 8 = 6 000 g。6 000 g 刚好是 6 个 1 000 g，所以是 6 kg，克的部分是 0。
例子：250 g × 4 = 1 000 g = 1 kg。
注意：60 kg 是除以 100 得来的；5 kg 600 g 是把 750 × 8 算错了。
a whole number of kilograms = gram ribu bulat
750 g × 8 = 6 000 g. That is exactly six lots of 1 000 g, so it is 6 kg with no grams left over.
Example: 250 g × 4 = 1 000 g = 1 kg.
Watch out: 60 kg comes from dividing by 100, and 5 kg 600 g is a slip in working out 750 × 8.
Padankan
Hasil darab jisim
配对积 = padankan hasil darab
500 × 2 = 1 000 g = 1 kg。1 kg 200 g × 3：200 × 3 = 600，1 × 3 = 3 → 3 kg 600 g。2 kg 600 g × 2：600 × 2 = 1 200 → 写 200 进 1 → 2 × 2 + 1 = 5 → 5 kg 200 g。4 × 9 = 36 kg。
例子：1 kg 100 g × 5 = 5 kg 500 g。
注意：先看克的积有没有满 1 000，再决定要不要进位。
matching products = padankan hasil darab
500 × 2 = 1 000 g = 1 kg. 1 kg 200 g × 3: 200 × 3 = 600 and 1 × 3 = 3 → 3 kg 600 g. 2 kg 600 g × 2: 600 × 2 = 1 200 → write 200, carry 1 → 2 × 2 + 1 = 5 → 5 kg 200 g. 4 × 9 = 36 kg.
Example: 1 kg 100 g × 5 = 5 kg 500 g.
Watch out: check whether the gram product reaches 1 000 before deciding to carry.
Ringkasan
Syabas!
g × → kumpul semula setiap 1 000 g → kg × + bawa
Darab gram dahulu. Setiap 1 000 g jadi 1 kg dan dibawa ke lajur kg. Darab kg, kemudian tambah yang dibawa.
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