Unit 12

Bahagi Jisim

Pak Abu ada 7 kg 500 g kacang hijau. Dia membungkusnya ke dalam 3 bungkusan yang sama jisim.
Berapakah jisim setiap bungkusan?

质量除法 = bahagi jisim；平均分装 = bungkus sama banyak 这一课学把一个质量平均分成几份。Abu 伯伯有 7 kg 500 g 绿豆，要平均装成 3 包，每包多重，就是 7 kg 500 g ÷ 3。先除公斤，公斤除不完的部分换成克再除。例子：900 g 的糖平均分成 3 包，每包 300 g。注意：剩下的公斤不能丢掉，要乘 1 000 换成克继续分。

dividing mass = bahagi jisim; packing equal amounts = bungkus sama banyak In this unit we share a mass into equal parts. Pak Abu has 7 kg 500 g of mung beans to pack into 3 bags of equal mass, so each bag holds 7 kg 500 g ÷ 3. We divide the kilograms first, and any kilogram left over is changed into grams and divided too. Example: 900 g of sugar shared into 3 bags gives 300 g in each. Watch out: a leftover kilogram must not be thrown away; multiply it by 1 000 and keep sharing it as grams.

Satu unit

900 g ÷ 3 · 2 kg ÷ 4

Jika kg tidak cukup dibahagi, tukar kepada g

g

900 ÷ 3
= 300 g

kg → g

2 kg = 2 000 g
2 000 ÷ 4 = 500 g

2 × 1 000 = 2 000 · semak: 500 × 4 = 2 000 ✓

单名数除法 = bahagi satu unit 只有克又能除尽时，用乘法表倒过来想：900 ÷ 3 = 300，因为 3 × 300 = 900。公斤太少不够除的时候，例如 2 kg ÷ 4，就先把 2 kg 换成 2 000 g，再算 2 000 ÷ 4 = 500 g。例子：1 kg ÷ 2 → 1 000 g ÷ 2 = 500 g。注意：公斤换成克是乘 1 000，不是乘 100。

dividing one unit = bahagi satu unit With grams only and an even share, use the times table backwards: 900 ÷ 3 = 300, because 3 × 300 = 900. When there are too few kilograms to share, as in 2 kg ÷ 4, first change 2 kg into 2 000 g and then work out 2 000 ÷ 4 = 500 g. Example: 1 kg ÷ 2 → 1 000 g ÷ 2 = 500 g. Watch out: kilograms become grams by multiplying by 1 000, not by 100.

Cuba

3 kg ÷ 5 = ?

	kg	g
	?	?
5)	3	0

公斤不够除 = kg tidak cukup dibahagi 3 ÷ 5 不够除，先把 3 kg 换成 3 000 g。3 000 ÷ 5 = 600，答案 600 g。检查：600 × 5 = 3 000 g = 3 kg。例子：2 kg ÷ 5 = 2 000 g ÷ 5 = 400 g。注意：60 g 是把 3 kg 当成 300 g 来除，换错了。

too few kilograms to share = kg tidak cukup dibahagi 3 ÷ 5 does not work, so first change 3 kg into 3 000 g. 3 000 ÷ 5 = 600, so the answer is 600 g. Check: 600 × 5 = 3 000 g = 3 kg. Example: 2 kg ÷ 5 = 2 000 g ÷ 5 = 400 g. Watch out: 60 g treats 3 kg as only 300 g, which is the wrong change of unit.

Tiada baki

8 kg 600 g ÷ 2

Bahagi kg dahulu, kemudian g

	kg	g
	4	300
2)	8	600

kg: 8 ÷ 2 = 4 · g: 600 ÷ 2 = 300

长除法 = bahagi bentuk lazim 除数写在左边，商写在上面，公斤一栏、克一栏。先除公斤：8 ÷ 2 = 4，刚好除尽，没有余数。再除克：600 ÷ 2 = 300。答案 4 kg 300 g。例子：6 kg 900 g ÷ 3 → 6 ÷ 3 = 2 → 900 ÷ 3 = 300 → 2 kg 300 g。注意：商的公斤要写在公斤栏上面，克写在克栏上面，不要写错栏。

long division = bahagi bentuk lazim The divisor goes on the left and the answer on top, with one column for kilograms and one for grams. Divide the kilograms first: 8 ÷ 2 = 4 exactly, with nothing left over. Then divide the grams: 600 ÷ 2 = 300. The answer is 4 kg 300 g. Example: 6 kg 900 g ÷ 3 → 6 ÷ 3 = 2 → 900 ÷ 3 = 300 → 2 kg 300 g. Watch out: write the kilogram part of the answer above the kg column and the gram part above the g column.

Baki × 1 000

7 kg 500 g ÷ 3

Baki kg ditukar kepada g

baki 1 kg → 1 000 g + 500 g = 1 500 g → 1 500 ÷ 3 = 500

余数化成克 = baki × 1 000 先除公斤：7 ÷ 3 = 2 余 1，商的公斤栏写 2。余下的 1 kg 不能丢，1 kg = 1 000 g，跟原来的 500 g 合起来是 1 500 g。再除：1 500 ÷ 3 = 500，商的克栏写 500。每包绿豆 2 kg 500 g。例子：5 kg 200 g ÷ 2 → 5 ÷ 2 = 2 余 1 → 1 000 + 200 = 1 200 → 1 200 ÷ 2 = 600 → 2 kg 600 g。注意：余数要乘 1 000；乘 100 的话克会少很多。

changing the remainder = baki × 1 000 Divide the kilograms first: 7 ÷ 3 = 2 remainder 1, so write 2 above the kg column. The leftover 1 kg must not be lost; 1 kg = 1 000 g, and together with the 500 g already there it makes 1 500 g. Then 1 500 ÷ 3 = 500, written above the g column. Each bag of mung beans holds 2 kg 500 g. Example: 5 kg 200 g ÷ 2 → 5 ÷ 2 = 2 r 1 → 1 000 + 200 = 1 200 → 1 200 ÷ 2 = 600 → 2 kg 600 g. Watch out: multiply the remainder by 1 000; using 100 would leave far too few grams.

Cuba

9 kg 200 g ÷ 4 = ?

	kg	g
	?	?
4)	9	200

余 1 公斤 = baki 1 kg 9 ÷ 4 = 2 余 1。余下 1 kg = 1 000 g，1 000 + 200 = 1 200 g，1 200 ÷ 4 = 300。答案 2 kg 300 g。例子：7 kg 400 g ÷ 2 → 7 ÷ 2 = 3 余 1 → 1 400 ÷ 2 = 700 → 3 kg 700 g。注意：2 kg 50 g 把余数丢了，只算 200 ÷ 4；2 kg 75 g 把余数乘了 100。

one kilogram left over = baki 1 kg 9 ÷ 4 = 2 remainder 1. The leftover 1 kg is 1 000 g; 1 000 + 200 = 1 200 g and 1 200 ÷ 4 = 300. The answer is 2 kg 300 g. Example: 7 kg 400 g ÷ 2 → 7 ÷ 2 = 3 r 1 → 1 400 ÷ 2 = 700 → 3 kg 700 g. Watch out: 2 kg 50 g drops the remainder and only does 200 ÷ 4, while 2 kg 75 g multiplies the remainder by 100.

Jisim bersih

Jisim bersih = jisim kasar − jisim bekas

Tolak jisim bekas sebelum membahagi

1. Jisim bersih

2 kg 650 g − 250 g
= 2 kg 400 g

2. Bahagi 4

2 400 g ÷ 4
= 600 g

Jisim bersih = jisim tanpa kotak atau bekas

净重 = jisim bersih；毛重 = jisim kasar 包装上的净重，是里面东西本身的质量，不包括盒子或袋子。这盒江鱼仔连盒子一共 2 kg 650 g，空盒子 250 g，净重是 2 kg 650 g − 250 g = 2 kg 400 g。要平均装进 4 个罐子，用净重来分：2 400 g ÷ 4 = 600 g。例子：一袋米连袋子 5 kg 100 g，袋子 100 g，净重 5 kg。注意：先减掉盒子再除；直接拿 2 kg 650 g 去除，会把盒子也分进去。

net mass = jisim bersih; gross mass = jisim kasar The net mass on a label is the mass of the food itself, without the box or bag. This box of anchovies weighs 2 kg 650 g with its box, and the empty box is 250 g, so the net mass is 2 kg 650 g − 250 g = 2 kg 400 g. To share it equally into 4 containers, divide the net mass: 2 400 g ÷ 4 = 600 g. Example: a bag of rice weighs 5 kg 100 g with the bag, the bag is 100 g, so the net mass is 5 kg. Watch out: take the box away before dividing; dividing 2 kg 650 g straight away shares out the box as well.

Cuba

Sebakul udang berjisim 5 kg 300 g bersama bakulnya. Bakul kosong 500 g. Udang itu dibahagi sama banyak kepada 4 orang. Berapakah jisim udang setiap orang?

先求净重再除 = jisim bersih dahulu, kemudian bahagi 净重：5 kg 300 g − 500 g = 4 kg 800 g。再平均分给 4 人：4 ÷ 4 = 1，800 ÷ 4 = 200，每人 1 kg 200 g。例子：一桶鱼连桶 3 kg 400 g，桶 400 g，分给 3 人 → 3 kg ÷ 3 = 1 kg。注意：1 kg 325 g 是连篮子一起分了；4 kg 800 g 是只求了净重，忘了除。

net mass first, then divide = jisim bersih dahulu, kemudian bahagi Net mass: 5 kg 300 g − 500 g = 4 kg 800 g. Then share it among 4 people: 4 ÷ 4 = 1 and 800 ÷ 4 = 200, so each person gets 1 kg 200 g. Example: a pail of fish weighs 3 kg 400 g with the pail, the pail is 400 g, and 3 people share it → 3 kg ÷ 3 = 1 kg each. Watch out: 1 kg 325 g shares out the basket too, and 4 kg 800 g finds the net mass but forgets to divide.

Semak dengan darab

2 kg 500 g × 3

Hasil bahagi × pembahagi = jisim asal

	kg	g
	1
	2	500
×		3
	7	500

2 kg 500 g × 3 = 7 kg 500 g ✓ sama dengan jisim asal

用乘法验算 = semak dengan darab 除法和乘法互相检查。7 kg 500 g ÷ 3 = 2 kg 500 g，验算时算 2 kg 500 g × 3：500 × 3 = 1 500 g，写 500 进 1；2 × 3 + 1 = 7。得到 7 kg 500 g，跟 Abu 伯伯原来的绿豆一样多，答案对了。例子：1 kg 200 g × 4 = 4 kg 800 g，所以 4 kg 800 g ÷ 4 = 1 kg 200 g 是对的。注意：乘回来如果对不上原来的质量，就回头检查余数有没有乘 1 000。

checking with multiplication = semak dengan darab Division and multiplication check each other. Since 7 kg 500 g ÷ 3 = 2 kg 500 g, check with 2 kg 500 g × 3: 500 × 3 = 1 500 g, so write 500 and carry 1; then 2 × 3 + 1 = 7. We get 7 kg 500 g, the same amount of mung beans Pak Abu started with, so the answer is right. Example: 1 kg 200 g × 4 = 4 kg 800 g, so 4 kg 800 g ÷ 4 = 1 kg 200 g is correct. Watch out: if multiplying back does not give the starting mass, go back and see whether the remainder was multiplied by 1 000.

Padankan

Hasil bahagi jisim

配对商 = padankan hasil bahagi 6 ÷ 3 = 2 kg。4 kg 800 g ÷ 4：4 ÷ 4 = 1，800 ÷ 4 = 200 → 1 kg 200 g。1 kg ÷ 5 = 1 000 g ÷ 5 = 200 g。5 kg 400 g ÷ 6：5 不够除 6，全换成 5 400 g，5 400 ÷ 6 = 900 g。例子：3 kg 600 g ÷ 4 = 3 600 g ÷ 4 = 900 g。注意：公斤比除数小的时候，商没有公斤，答案只有克。

matching quotients = padankan hasil bahagi 6 ÷ 3 = 2 kg. 4 kg 800 g ÷ 4: 4 ÷ 4 = 1 and 800 ÷ 4 = 200 → 1 kg 200 g. 1 kg ÷ 5 = 1 000 g ÷ 5 = 200 g. 5 kg 400 g ÷ 6: 5 is smaller than 6, so change it all to 5 400 g, and 5 400 ÷ 6 = 900 g. Example: 3 kg 600 g ÷ 4 = 3 600 g ÷ 4 = 900 g. Watch out: when the kilograms are fewer than the divisor, the answer has no kilograms, only grams.

Ringkasan

Syabas!

kg ÷ → baki × 1 000 + g → ÷ lagi

Bahagi kg dahulu. Tukar baki kg kepada g (× 1 000) dan tambah. Bahagi lagi. Tolak jisim bekas untuk dapat jisim bersih. Semak dengan darab.

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