Unit 5
Bahagi Panjang
Kak Ana ada seutas reben 7 m 50 cm.
Dia memotongnya kepada 3 bahagian yang sama panjang.
Berapakah panjang setiap bahagian?
长度除法 = bahagi panjang；一样长 = sama panjang
这一课学把一个长度平均分成几段。Ana 姐姐有一条 7 m 50 cm 的丝带，剪成 3 段一样长，每段多长，就是 7 m 50 cm ÷ 3。除的时候先除 m，m 除不完的部分换成 cm 再除。
例子：一条 90 cm 的绳子平均剪成 3 段，每段 30 cm。
注意：除不完的 m 不能丢掉，它要换成 cm 继续分。
dividing length = bahagi panjang; equal lengths = sama panjang
In this unit we cut a length into equal pieces. Kak Ana has a ribbon 7 m 50 cm long and cuts it into 3 equal pieces; each piece is 7 m 50 cm ÷ 3. We divide the metres first, and any metre left over is changed into centimetres and divided too.
Example: a 90 cm string cut into 3 equal pieces gives 30 cm each.
Watch out: a leftover metre must not be thrown away; it becomes centimetres and is shared as well.
Satu unit sahaja
486 cm ÷ 2 · 3 m ÷ 4
Jika m tidak cukup, tukar kepada cm
cm
486 ÷ 2
= 243 cm
= 243 cm
m → cm
3 m = 300 cm
300 ÷ 4 = 75 cm
300 ÷ 4 = 75 cm
3 × 100 = 300 · semak: 75 × 4 = 300 ✓
单名数除法 = bahagi satu unit
只有一个单位、又能除尽时，就像普通除法：486 ÷ 2，4 ÷ 2 = 2，8 ÷ 2 = 4，6 ÷ 2 = 3，得 243 cm。如果米太少不够除，例如 3 m ÷ 4，就先把 3 m 换成 300 cm，再算 300 ÷ 4 = 75 cm。
例子：2 m ÷ 5 → 200 cm ÷ 5 = 40 cm。
注意：换单位时乘的是 100，不是 10。
dividing one unit = bahagi satu unit
With only one unit that divides evenly, use ordinary division: for 486 ÷ 2, 4 ÷ 2 = 2, 8 ÷ 2 = 4 and 6 ÷ 2 = 3, giving 243 cm. If there are too few metres to share, as in 3 m ÷ 4, first change 3 m into 300 cm and then work out 300 ÷ 4 = 75 cm.
Example: 2 m ÷ 5 → 200 cm ÷ 5 = 40 cm.
Watch out: when changing units, multiply by 100, not by 10.
Baki × 100
7 m 50 cm ÷ 3
Baki meter ditukar kepada sentimeter
baki 1 m → 1 × 100 + 50 = 150 cm → 150 ÷ 3 = 50
余数换成厘米 = baki × 100
先除 m：7 ÷ 3 = 2 余 1，商的 m 栏写 2。余下的 1 m 不能丢，1 m = 100 cm，把它加到原来的 50 cm 里，变成 150 cm。再除：150 ÷ 3 = 50，商的 cm 栏写 50。每段丝带 2 m 50 cm。
例子：5 m 40 cm ÷ 2 → 5 ÷ 2 = 2 余 1 → 100 + 40 = 140 → 140 ÷ 2 = 70 → 2 m 70 cm。
注意：要在竖式旁边写清楚 + 100，提醒自己余数已经换成厘米了。
changing the remainder = baki × 100
Divide the metres first: 7 ÷ 3 = 2 remainder 1, so write 2 in the m place of the answer. The leftover metre must not be lost; 1 m = 100 cm, and adding it to the 50 cm already there makes 150 cm. Then 150 ÷ 3 = 50, so write 50 in the cm place. Each piece of ribbon is 2 m 50 cm.
Example: 5 m 40 cm ÷ 2 → 5 ÷ 2 = 2 r 1 → 100 + 40 = 140 → 140 ÷ 2 = 70 → 2 m 70 cm.
Watch out: write the + 100 clearly beside your working so you remember the remainder has become centimetres.
Cuba
9 m 60 cm ÷ 4 = ?
| m | cm | |
|---|---|---|
| ? | ? | |
| 4) | 9 | 60 |
余 1 米 = baki 1 m
9 ÷ 4 = 2 余 1。余下 1 m = 100 cm，100 + 60 = 160 cm，160 ÷ 4 = 40。答案 2 m 40 cm。
例子：5 m 50 cm ÷ 5 → 5 ÷ 5 = 1 → 50 ÷ 5 = 10 → 1 m 10 cm。
注意：2 m 15 cm 是把余数丢了，只算 60 ÷ 4；240 m 是商的单位写错了。
a leftover metre = baki 1 m
9 ÷ 4 = 2 remainder 1. The leftover 1 m is 100 cm; 100 + 60 = 160 cm and 160 ÷ 4 = 40. The answer is 2 m 40 cm.
Example: 5 m 50 cm ÷ 5 → 5 ÷ 5 = 1 → 50 ÷ 5 = 10 → 1 m 10 cm.
Watch out: 2 m 15 cm throws the remainder away and only does 60 ÷ 4, while 240 m puts the wrong unit on the answer.
Baki 2 m
8 m 40 cm ÷ 3
Baki 2 m = 200 cm
| m | cm | |
|---|---|---|
| 2 | 80 | |
| 3) | 8 | 40 |
baki 2 m = 2 × 100 = 200 cm → 200 + 40 = 240 → 240 ÷ 3 = 80
余 2 米 = baki 2 m
8 ÷ 3 = 2 余 2。余下的不是 1 m，而是 2 m，所以要换成 2 × 100 = 200 cm，再加原来的 40 cm，得 240 cm。240 ÷ 3 = 80。答案 2 m 80 cm。
例子：7 m 20 cm ÷ 4 → 7 ÷ 4 = 1 余 3 → 300 + 20 = 320 → 320 ÷ 4 = 80 → 1 m 80 cm。
注意：余数是几，就加几个 100；余 2 加 200，不是加 100。
a remainder of 2 m = baki 2 m
8 ÷ 3 = 2 remainder 2. This time 2 m are left, not 1, so change them into 2 × 100 = 200 cm and add the 40 cm already there to get 240 cm. Then 240 ÷ 3 = 80. The answer is 2 m 80 cm.
Example: 7 m 20 cm ÷ 4 → 7 ÷ 4 = 1 r 3 → 300 + 20 = 320 → 320 ÷ 4 = 80 → 1 m 80 cm.
Watch out: add as many hundreds as the remainder; a remainder of 2 adds 200, not 100.
Cuba
6 m 30 cm ÷ 5 = ?
| m | cm | |
|---|---|---|
| ? | ? | |
| 5) | 6 | 30 |
余数乘 100 = baki darab 100
6 ÷ 5 = 1 余 1。余下 1 m = 100 cm，100 + 30 = 130 cm，130 ÷ 5 = 26。答案 1 m 26 cm。
例子：4 m 20 cm ÷ 3 → 4 ÷ 3 = 1 余 1 → 120 ÷ 3 = 40 → 1 m 40 cm。
注意：1 m 6 cm 丢了余数；1 m 8 cm 是把余数 1 m 当成 10 cm。
multiplying the remainder by 100 = baki darab 100
6 ÷ 5 = 1 remainder 1. The leftover 1 m is 100 cm; 100 + 30 = 130 cm and 130 ÷ 5 = 26. The answer is 1 m 26 cm.
Example: 4 m 20 cm ÷ 3 → 4 ÷ 3 = 1 r 1 → 120 ÷ 3 = 40 → 1 m 40 cm.
Watch out: 1 m 6 cm loses the remainder, and 1 m 8 cm treats the leftover 1 m as only 10 cm.
m tidak cukup dibahagi
2 m 70 cm ÷ 6
Tukar semua kepada cm
| m | cm | |
|---|---|---|
| 0 | 45 | |
| 6) | 2 | 70 |
2 m 70 cm = 270 cm → 270 ÷ 6 = 45 cm
米不够除 = m tidak cukup dibahagi
2 ÷ 6 不够除，商的 m 栏写 0，2 m 全部变成余数。把 2 m 70 cm 换成 200 + 70 = 270 cm，再算 270 ÷ 6 = 45。答案 45 cm，m 是 0 可以不写。
例子：1 m 20 cm ÷ 4 → 120 cm ÷ 4 = 30 cm。
注意：不可以只算 70 ÷ 6，前面的 2 m 也要一起分。
too few metres to share = m tidak cukup dibahagi
2 ÷ 6 cannot be shared, so the metre part of the answer is 0 and the whole 2 m becomes the remainder. Change 2 m 70 cm into 200 + 70 = 270 cm and work out 270 ÷ 6 = 45. The answer is 45 cm, and the 0 m need not be written.
Example: 1 m 20 cm ÷ 4 → 120 cm ÷ 4 = 30 cm.
Watch out: do not just divide 70 by 6; the 2 m in front must be shared too.
Cuba
1 m 60 cm ÷ 5 = ?
| m | cm | |
|---|---|---|
| ? | ? | |
| 5) | 1 | 60 |
全部化成厘米再除 = tukar semua kepada cm
1 ÷ 5 不够除，所以把 1 m 60 cm 全部换成 160 cm，160 ÷ 5 = 32。答案 32 cm。
例子：3 m 50 cm ÷ 7 → 350 cm ÷ 7 = 50 cm。
注意：12 cm 只算了 60 ÷ 5，丢了 1 m；3 m 2 cm 是把 32 拆错了单位。
changing everything to cm first = tukar semua kepada cm
1 ÷ 5 cannot be shared, so change all of 1 m 60 cm into 160 cm; 160 ÷ 5 = 32. The answer is 32 cm.
Example: 3 m 50 cm ÷ 7 → 350 cm ÷ 7 = 50 cm.
Watch out: 12 cm only does 60 ÷ 5 and loses the 1 m, while 3 m 2 cm splits 32 into the wrong units.
Semak dengan darab
2 m 50 cm × 3
Hasil bahagi × pembahagi = panjang asal
| m | cm | |
|---|---|---|
| 1 | ||
| 2 | 50 | |
| × | 3 | |
| 7 | 50 |
2 m 50 cm × 3 = 7 m 50 cm ✓ sama dengan panjang asal
用乘法验算 = semak dengan darab
除法和乘法是一对。7 m 50 cm ÷ 3 = 2 m 50 cm，验算时算 2 m 50 cm × 3：50 × 3 = 150 cm = 1 m 50 cm，写 50 进 1；2 × 3 + 1 = 7。得到 7 m 50 cm，跟原来的丝带一样长，所以答案对了。
例子：1 m 26 cm × 5 = 6 m 30 cm，所以 6 m 30 cm ÷ 5 = 1 m 26 cm 是对的。
注意：乘回来如果不等于原来的长度，就要回去找哪一步错了。
checking with multiplication = semak dengan darab
Division and multiplication are partners. Since 7 m 50 cm ÷ 3 = 2 m 50 cm, check with 2 m 50 cm × 3: 50 × 3 = 150 cm = 1 m 50 cm, so write 50 and carry 1; then 2 × 3 + 1 = 7. We get 7 m 50 cm, the same length as the ribbon, so the answer is right.
Example: 1 m 26 cm × 5 = 6 m 30 cm, so 6 m 30 cm ÷ 5 = 1 m 26 cm is correct.
Watch out: if multiplying back does not give the starting length, go back and look for the wrong step.
Cuba
Pak Din membina pagar kandang kuda sepanjang 18 m 40 cm. Pagar itu dibahagi kepada 4 bahagian yang sama panjang. Berapakah panjang setiap bahagian?
马棚围篱 = pagar kandang kuda
“分成一样长的 4 段”就是除以 4：18 ÷ 4 = 4 余 2，余下 2 m = 200 cm，200 + 40 = 240 cm，240 ÷ 4 = 60。每段 4 m 60 cm。
例子：12 m 60 cm ÷ 3 = 4 m 20 cm。
注意：4 m 10 cm 丢了余数；4 m 15 cm 是把余数 2 m 当成 20 cm。
a fence for the horse stable = pagar kandang kuda
Cutting into 4 equal parts means dividing by 4: 18 ÷ 4 = 4 remainder 2; the leftover 2 m is 200 cm, 200 + 40 = 240 cm and 240 ÷ 4 = 60. Each part is 4 m 60 cm.
Example: 12 m 60 cm ÷ 3 = 4 m 20 cm.
Watch out: 4 m 10 cm drops the remainder, and 4 m 15 cm treats the leftover 2 m as only 20 cm.
Padankan
Hasil bahagi panjang
配对商 = padankan hasil bahagi panjang
6 ÷ 2 = 3，40 ÷ 2 = 20 → 3 m 20 cm。5 ÷ 4 = 1 余 1 → 100 ÷ 4 = 25 → 1 m 25 cm。90 ÷ 3 = 30 cm。4 ÷ 5 不够除 → 450 cm ÷ 5 = 90 cm。
例子：8 m 80 cm ÷ 4 = 2 m 20 cm。
注意：没有余数时，m 和 cm 各自除就好。
matching quotients = padankan hasil bahagi panjang
6 ÷ 2 = 3 and 40 ÷ 2 = 20 → 3 m 20 cm. 5 ÷ 4 = 1 r 1 → 100 ÷ 4 = 25 → 1 m 25 cm. 90 ÷ 3 = 30 cm. 4 ÷ 5 cannot be shared → 450 cm ÷ 5 = 90 cm.
Example: 8 m 80 cm ÷ 4 = 2 m 20 cm.
Watch out: with no remainder, just divide the metres and the centimetres separately.
Ringkasan
Syabas!
bahagi m → baki × 100 + cm → bahagi lagi
Bahagi m dahulu. Tukar baki kepada cm (× 100) dan tambah. Bahagi lagi, kemudian semak dengan darab.
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