Unit 5
Darab Wang
Harga sebuah bakul hadiah ialah RM 38.60. Puan Rani membeli 4 buah bakul hadiah.
Berapakah jumlah harga yang perlu dibayar?
乘钱 = darab wang；单价 = harga seunit；数量 = kuantiti；总价 = jumlah harga
这一课学金额乘以一个数。买几件一样的东西，总价就是单价乘数量。一个礼篮 RM 38.60，买 4 个，就是 RM 38.60 × 4。乘钱时 sen 和 ringgit 分开乘，sen 满 100 就换成 ringgit。
例子：一支笔 RM 1.20，买 3 支，总价 RM 1.20 × 3 = RM 3.60。
注意：只有每件价钱一样时才用乘法，价钱不同就要用加法。
multiplying money = darab wang; unit price = harga seunit; quantity = kuantiti; total price = jumlah harga
In this unit we multiply an amount of money by a number. When several items cost the same, the total is the unit price times the quantity. One gift basket is RM 38.60 and 4 are bought, so the total is RM 38.60 × 4. We multiply the sen and the ringgit separately, and every 100 sen becomes 1 ringgit.
Example: a pen costs RM 1.20 and 3 pens cost RM 1.20 × 3 = RM 3.60.
Watch out: multiply only when every item has the same price; different prices need addition.
Bentuk lazim
RM 38.60 × 4
Darab sen dahulu, 100 sen jadi 1 ringgit
60 sen × 4 = 240 sen = RM 2 + 40 sen → tulis 40, bawa 2 ke ringgit
竖式乘法 = bentuk lazim darab；进位 = kumpul semula
乘钱先乘 sen：60 sen × 4 = 240 sen。240 sen 等于 2 ringgit 40 sen，所以 sen 的位置写 40，把 2 ringgit 进到左边。再乘 ringgit：38 × 4 = 152，加上进位的 2 得 154。答案 RM 154.40。一位一位乘也是一样：0 × 4 = 0，6 × 4 = 24 写 4 进 2。
例子：RM 12.30 × 3 → 30 × 3 = 90 sen，12 × 3 = 36 → RM 36.90。
注意：sen 乘出来满 100 才进到 ringgit，进的是几个 100 就进几。
column multiplication = bentuk lazim darab; regrouping = kumpul semula
Multiply the sen first: 60 sen × 4 = 240 sen. 240 sen is 2 ringgit 40 sen, so write 40 in the sen place and carry 2 ringgit to the left. Then multiply the ringgit: 38 × 4 = 152, plus the carried 2 makes 154. The answer is RM 154.40. Digit by digit it works the same: 0 × 4 = 0, then 6 × 4 = 24, write 4 and carry 2.
Example: RM 12.30 × 3 → 30 × 3 = 90 sen and 12 × 3 = 36 → RM 36.90.
Watch out: carry to the ringgit only when the sen reach 100, and carry one for each full hundred.
Cuba
RM 24.75 × 3 = ?
| 2 | 4 | . | 7 | 5 | |
| × | 3 | ||||
| ? | ? | ? | ? | ? |
sen 乘后进位 = sen didarab, kumpul semula
先乘 sen：75 × 3 = 225 sen = 2 ringgit 25 sen，写 25，进 2。再乘 ringgit：24 × 3 = 72，加 2 得 74。答案 RM 74.25。
例子：RM 8.45 × 2 → 45 × 2 = 90 sen，8 × 2 = 16 → RM 16.90。
注意：RM 72.25 是忘了把进位的 2 加到 ringgit。
carrying after multiplying the sen = sen didarab, kumpul semula
Multiply the sen first: 75 × 3 = 225 sen = 2 ringgit 25 sen, write 25 and carry 2. Then the ringgit: 24 × 3 = 72, plus 2 makes 74. The answer is RM 74.25.
Example: RM 8.45 × 2 → 45 × 2 = 90 sen and 8 × 2 = 16 → RM 16.90.
Watch out: RM 72.25 is what you get when the carried 2 is not added to the ringgit.
Nilai yang lebih besar
RM 1 236.50 × 7
Darab setiap digit dari kanan ke kiri
| 1 | 2 | 4 | 3 | ||||
| 1 | 2 | 3 | 6 | . | 5 | 0 | |
| × | 7 | ||||||
| 8 | 6 | 5 | 5 | . | 5 | 0 |
0×7=0 · 5×7=35 → 5 bawa 3 · 6×7+3=45 → 5 bawa 4 · 3×7+4=25 → 5 bawa 2 · 2×7+2=16 → 6 bawa 1 · 1×7+1=8
逐位相乘 = darab setiap digit；从右到左 = dari kanan ke kiri
金额大的时候，一位一位乘，从最右边开始。0 × 7 = 0；5 × 7 = 35，写 5 进 3；6 × 7 = 42，加 3 是 45，写 5 进 4；3 × 7 = 21，加 4 是 25，写 5 进 2；2 × 7 = 14，加 2 是 16，写 6 进 1；1 × 7 = 7，加 1 是 8。小数点对着上面的小数点写下来，答案 RM 8 655.50。
例子：RM 2 103.20 × 3 → 0, 6, 9, 0, 3, 6 → RM 6 309.60。
注意：答案的小数点要跟上面的小数点在同一条直线上，sen 保持两位。
multiplying digit by digit = darab setiap digit; right to left = dari kanan ke kiri
For a larger amount, multiply one digit at a time starting from the right. 0 × 7 = 0; 5 × 7 = 35, write 5 and carry 3; 6 × 7 = 42, plus 3 is 45, write 5 and carry 4; 3 × 7 = 21, plus 4 is 25, write 5 and carry 2; 2 × 7 = 14, plus 2 is 16, write 6 and carry 1; 1 × 7 = 7, plus 1 is 8. Put the decimal point directly under the one above, giving RM 8 655.50.
Example: RM 2 103.20 × 3 → 0, 6, 9, 0, 3, 6 → RM 6 309.60.
Watch out: the decimal point in the answer sits in the same column as the one above, and the sen keep two digits.
Cuba
RM 2 145.25 × 4 = ?
| 2 | 1 | 4 | 5 | . | 2 | 5 | |
| × | 4 | ||||||
| ? | ? | ? | ? | ? | ? | ? |
sen 刚好 100 = sen cukup 100
25 sen × 4 = 100 sen，刚好是 RM 1，sen 写 00，进 1。ringgit：2 145 × 4 = 8 580，加 1 得 8 581。答案 RM 8 581，sen 是 00 所以不用写。
例子：RM 3.50 × 2 → 50 × 2 = 100 sen = RM 1 → 7 + 1 = RM 8。
注意：RM 8 580 是忘了进位的 1；RM 8 581.25 是把 25 sen 原样留下，没有乘。
sen making exactly 100 = sen cukup 100
25 sen × 4 = 100 sen, exactly RM 1, so write 00 in the sen place and carry 1. Ringgit: 2 145 × 4 = 8 580, plus 1 gives 8 581. The answer is RM 8 581, and the sen are 00 so nothing more is written.
Example: RM 3.50 × 2 → 50 × 2 = 100 sen = RM 1 → 7 + 1 = RM 8.
Watch out: RM 8 580 leaves out the carried 1, and RM 8 581.25 keeps the 25 sen without multiplying them.
Darab 10, 100, 1000
RM 6.25 × 10, × 100, × 1000
Titik perpuluhan bergerak ke kanan
× 10 → 1 tempat · × 100 → 2 tempat · × 1000 → 3 tempat, isi 0
小数点右移 = titik perpuluhan bergerak ke kanan；位 = tempat
乘 10、100、1000 不用竖式，只要移小数点。乘 10 移 1 位：6.25 变 62.50。乘 100 移 2 位：6.25 变 625。乘 1000 移 3 位：6.25 只有两位小数，移第三位时没有数字，就补一个 0，变 6 250。乘数有几个 0，小数点就向右移几位。
例子：RM 4.80 × 10 = RM 48；RM 4.80 × 100 = RM 480；RM 4.80 × 1000 = RM 4 800。
注意：小数点是向右移，不是向左；移错方向钱就变少了。
decimal point moves right = titik perpuluhan bergerak ke kanan; place = tempat
Multiplying by 10, 100 or 1000 needs no column sum; just move the decimal point. Times 10 moves it 1 place: 6.25 becomes 62.50. Times 100 moves it 2 places: 6.25 becomes 625. Times 1000 moves it 3 places: 6.25 has only two decimal digits, so fill the empty place with a 0, giving 6 250. The number of zeros tells how many places to move.
Example: RM 4.80 × 10 = RM 48; RM 4.80 × 100 = RM 480; RM 4.80 × 1000 = RM 4 800.
Watch out: the point moves to the right, not the left; moving the wrong way makes the money smaller.
Cuba
RM 4.80 × 100 = ?
乘 100 = darab 100；两个 0 = dua sifar
100 有两个 0，所以小数点向右移两位：4.80 → 48.0 → 480。移完之后 sen 是 00，答案写成整数 RM 480 就可以。
例子：RM 2.35 × 100 = RM 235。
注意：RM 48 只移了一位，那是乘 10；RM 4 800 移了三位，那是乘 1000。
times 100 = darab 100
100 has two zeros, so the decimal point moves two places to the right: 4.80 → 48.0 → 480. The answer is RM 480.
Example: RM 2.35 × 100 = RM 235.
Watch out: RM 48 moves only one place, which is times 10; RM 4 800 moves three places, which is times 1000.
Jadual darab 10, 100, 1000
RM 2.40 dan RM 3.05
Isi sifar di tempat kosong
| Nilai | × 10 | × 100 | × 1000 |
|---|---|---|---|
| RM 2.40 | RM 24 | RM 240 | RM 2 400 |
| RM 3.05 | RM 30.50 | RM 305 | RM 3 050 |
3.05 × 1000 → 3050 → RM 3 050: sifar di tengah tidak boleh dibuang
乘法表 = jadual darab；中间的 0 = sifar di tengah
看表就能发现规律：同一个金额乘 10、100、1000，数字不变，只是小数点一直往右跑。RM 2.40 变成 24、240、2 400。RM 3.05 变成 30.50、305、3 050。3.05 中间那个 0 是十 sen 位的 0，移动小数点时要留着，不能丢。
例子：RM 1.08 × 100 = RM 108，不是 RM 18。
注意：乘 10 之后 sen 只剩一位时，要补 0 写成两位，例如 30.50。
multiplication table = jadual darab; middle zero = sifar di tengah
The table shows the pattern: the digits stay the same and only the decimal point keeps moving right. RM 2.40 becomes 24, 240 and 2 400. RM 3.05 becomes 30.50, 305 and 3 050. The 0 in the middle of 3.05 is the tens-of-sen digit and must stay when the point moves.
Example: RM 1.08 × 100 = RM 108, not RM 18.
Watch out: after times 10, if only one sen digit is left, add a 0 to keep two digits, as in 30.50.
Cuba
RM 9.20 × 1000 = ?
乘 1000 = darab 1000
1000 有三个 0，小数点向右移三位。9.20 的小数只有两位，第三位没有数字，补一个 0：9.20 → 9200。答案 RM 9 200。
例子：RM 1.50 × 1000 = RM 1 500。
注意：RM 9 020 是把补的 0 放错位置，0 要补在最后面。
times 1000 = darab 1000
1000 has three zeros, so the decimal point moves three places to the right. 9.20 has only two decimal digits, so the third place gets a 0: 9.20 → 9200. The answer is RM 9 200.
Example: RM 1.50 × 1000 = RM 1 500.
Watch out: RM 9 020 puts the extra 0 in the wrong place; it belongs at the very end.
Harga seunit × kuantiti
8 buah kalkulator, RM 18.90 sebuah
Jumlah harga = harga seunit × kuantiti
| 1 | 8 | . | 9 | 0 | ||
| × | 8 | |||||
| 1 | 5 | 1 | . | 2 | 0 |
90 sen × 8 = 720 sen = RM 7 + 20 sen → bawa 7 · 18 × 8 + 7 = 151
应用题 = masalah；每件 = sebuah／seunit
买 8 个一样价钱的计算器，总价 = 单价 × 数量 = RM 18.90 × 8。sen：90 × 8 = 720 sen = 7 ringgit 20 sen，写 20，进 7。ringgit：18 × 8 = 144，加 7 得 151。总价 RM 151.20。
例子：5 本练习簿，每本 RM 2.60 → 60 × 5 = 300 sen = RM 3，2 × 5 + 3 = 13 → RM 13。
注意：进位可能不只 1，720 sen 要进 7。
word problem = masalah; each = sebuah / seunit
Buying 8 calculators at the same price, the total = unit price × quantity = RM 18.90 × 8. Sen: 90 × 8 = 720 sen = 7 ringgit 20 sen, write 20 and carry 7. Ringgit: 18 × 8 = 144, plus 7 gives 151. The total is RM 151.20.
Example: 5 exercise books at RM 2.60 each → 60 × 5 = 300 sen = RM 3, then 2 × 5 + 3 = 13 → RM 13.
Watch out: the carry can be more than 1; 720 sen means carrying 7.
Cuba
Harga sehelai baju ialah RM 32.50. Berapakah harga 6 helai baju?
| 3 | 2 | . | 5 | 0 | |
| × | 6 | ||||
| ? | ? | ? | ? | ? |
6 件衣服的总价 = jumlah harga 6 helai baju
总价 = RM 32.50 × 6。sen：50 × 6 = 300 sen = RM 3，sen 写 00，进 3。ringgit：32 × 6 = 192，加 3 得 195。答案 RM 195。
例子：4 双袜子，每双 RM 4.50 → 50 × 4 = 200 sen = RM 2，16 + 2 = RM 18。
注意：RM 192 是忘了加进位的 3。
total for 6 shirts = jumlah harga 6 helai baju
The total is RM 32.50 × 6. Sen: 50 × 6 = 300 sen = RM 3, write 00 and carry 3. Ringgit: 32 × 6 = 192, plus 3 gives 195. The answer is RM 195.
Example: 4 pairs of socks at RM 4.50 each → 50 × 4 = 200 sen = RM 2, then 16 + 2 = RM 18.
Watch out: RM 192 leaves out the carried 3.
Padankan
Hasil darab yang betul
配对积 = padankan hasil darab
同一个 RM 1.50 乘 10、100、1000，答案是 15、150、1 500，只是小数点越移越右。RM 12.25 × 2：25 × 2 = 50 sen，12 × 2 = 24，得 RM 24.50。
例子：RM 0.50 × 10 = RM 5；RM 0.50 × 100 = RM 50。
注意：乘 10 之后 1.50 变 15.0，末尾的 0 可以不写。
matching products = padankan hasil darab
The same RM 1.50 times 10, 100 and 1000 gives 15, 150 and 1 500, with the decimal point moving further right each time. RM 12.25 × 2: 25 × 2 = 50 sen and 12 × 2 = 24, giving RM 24.50.
Example: RM 0.50 × 10 = RM 5; RM 0.50 × 100 = RM 50.
Watch out: after times 10, 1.50 becomes 15.0, and the final 0 can be dropped.
Ringkasan
Syabas!
sen dahulu → 100 sen = 1 ringgit · ×10 / ×100 / ×1000 → gerak titik
Darab sen dahulu; 100 sen jadi 1 ringgit. Darab ringgit dan tambah bawaan. Darab 10, 100, 1000: titik perpuluhan bergerak 1, 2, 3 tempat ke kanan. Jumlah harga = harga seunit × kuantiti.
Latihan tambahan →