Unit 6

Bahagi Wang

Hadiah pertandingan RM 95 dikongsi sama rata oleh 4 orang murid.
Berapakah wang yang diterima oleh setiap murid?

分钱 = bahagi wang；平均分 = agih sama banyak；每人 = setiap orang 这一课学把金额平均分成几份。奖金 RM 95 由 4 个人平分，每人拿多少，就是 RM 95 ÷ 4。分钱时先分 ringgit，ringgit 分不完的部分换成 sen 再分，所以答案常常有 sen。例子：RM 10 由 4 个人平分，每人 RM 2.50。注意：平分的意思是每份一样多，不是随便分。

dividing money = bahagi wang; share equally = agih sama banyak; each person = setiap orang In this unit we split an amount of money into equal parts. A prize of RM 95 shared by 4 pupils means RM 95 ÷ 4. We divide the ringgit first, and any ringgit left over is changed into sen and divided again, so the answer often has sen. Example: RM 10 shared equally by 4 people gives RM 2.50 each. Watch out: sharing equally means every part is the same size, not just any split.

Bentuk lazim

RM 95 ÷ 4

Tulis 95.00, bahagi ringgit dahulu, baki tukar kepada sen

Baki RM 3 = 300 sen → teruskan bahagi · titik pada hasil bahagi sebaris dengan titik di bawah

长除法 = bentuk lazim bahagi；余数 = baki；落下来 = turunkan 除钱先把 RM 95 写成 95.00，这样 ringgit 除完还可以继续除 sen。9 ÷ 4 = 2 余 1，落下 5 变 15，15 ÷ 4 = 3 余 3。余下的 RM 3 其实是 300 sen，所以在商写上小数点（对着下面的小数点），落下 0 变 30，30 ÷ 4 = 7 余 2，再落下 0 变 20，20 ÷ 4 = 5。答案 RM 23.75。例子：RM 50 ÷ 4 → 5 ÷ 4 = 1 余 1 → 10 ÷ 4 = 2 余 2 → 20 ÷ 4 = 5 → RM 12.50。注意：商的小数点一定要跟被除数的小数点在同一条直线上。

long division = bentuk lazim bahagi; remainder = baki; bring down = turunkan To divide money, first write RM 95 as 95.00 so that we can carry on into the sen after the ringgit. 9 ÷ 4 = 2 remainder 1; bring down 5 to make 15; 15 ÷ 4 = 3 remainder 3. The RM 3 left over is really 300 sen, so we place a decimal point in the quotient directly above the one below, bring down 0 to make 30, 30 ÷ 4 = 7 remainder 2, bring down 0 to make 20, and 20 ÷ 4 = 5. The answer is RM 23.75. Example: RM 50 ÷ 4 → 5 ÷ 4 = 1 r 1 → 10 ÷ 4 = 2 r 2 → 20 ÷ 4 = 5 → RM 12.50. Watch out: the decimal point in the quotient must sit in the same column as the point in the dividend.

Cuba

RM 87 ÷ 5 = ?

	?	?	?	?	?
5)	8	7	.	0	0

余数换 sen = baki tukar kepada sen 把 RM 87 写成 87.00 来除。8 ÷ 5 = 1 余 3，落下 7 变 37，37 ÷ 5 = 7 余 2。余下的 RM 2 是 200 sen，点上小数点后落下 0 变 20，20 ÷ 5 = 4，再落下 0，0 ÷ 5 = 0。所以每份是 RM 17.40。例子：RM 61 ÷ 5 → 6 ÷ 5 = 1 余 1 → 11 ÷ 5 = 2 余 1 → 10 ÷ 5 = 2 → RM 12.20。注意：sen 要写两位，4 之后的 0 不能漏，RM 17.04 是把 4 写错位置。

changing the remainder into sen = baki tukar kepada sen Write RM 87 as 87.00 before dividing. 8 ÷ 5 = 1 remainder 3; bring down 7 to make 37; 37 ÷ 5 = 7 remainder 2. The RM 2 left is 200 sen, so put the decimal point, bring down 0 to make 20, 20 ÷ 5 = 4, then bring down the last 0 and 0 ÷ 5 = 0. Each share is RM 17.40. Example: RM 61 ÷ 5 → 6 ÷ 5 = 1 r 1 → 11 ÷ 5 = 2 r 1 → 10 ÷ 5 = 2 → RM 12.20. Watch out: sen always have two digits; the 0 after the 4 must stay, and RM 17.04 puts the 4 in the wrong place.

Nilai yang lebih besar

RM 1 245.60 ÷ 3

Bahagi digit demi digit dari kiri ke kanan

1 < 3 → ambil 12 · titik pada hasil bahagi terus di atas titik · sen mesti dua digit: .20

一位一位除 = bahagi digit demi digit；从左到右 = dari kiri ke kanan 金额大的时候，从最左边开始，一位一位除。1 比 3 小，不够除，就看 12：12 ÷ 3 = 4。落下 4，4 ÷ 3 = 1 余 1。落下 5 变 15，15 ÷ 3 = 5。到了小数点，就在商上点一个小数点。落下 6，6 ÷ 3 = 2；落下 0，0 ÷ 3 = 0。答案 RM 415.20。例子：RM 2 048.40 ÷ 4 → 20 ÷ 4 = 5，4 ÷ 4 = 1，8 ÷ 4 = 2，4 ÷ 4 = 1，0 ÷ 4 = 0 → RM 512.10。注意：最后的 0 ÷ 3 = 0 也要写出来，sen 才会是两位。

dividing digit by digit = bahagi digit demi digit; from left to right = dari kiri ke kanan For a larger amount, start at the left and divide one digit at a time. 1 is smaller than 3, so take 12: 12 ÷ 3 = 4. Bring down 4; 4 ÷ 3 = 1 remainder 1. Bring down 5 to make 15; 15 ÷ 3 = 5. At the decimal point, place a point in the quotient. Bring down 6; 6 ÷ 3 = 2. Bring down 0; 0 ÷ 3 = 0. The answer is RM 415.20. Example: RM 2 048.40 ÷ 4 → 20 ÷ 4 = 5, 4 ÷ 4 = 1, 8 ÷ 4 = 2, 4 ÷ 4 = 1, 0 ÷ 4 = 0 → RM 512.10. Watch out: the final 0 ÷ 3 = 0 must still be written, so that the sen keep two digits.

Cuba

RM 2 530.80 ÷ 8 = ?

	?	?	?	?	?	?	?
8)	2	5	3	0	.	8	0

除数 8 = pembahagi 8 2 比 8 小，先看 25：25 ÷ 8 = 3 余 1。落下 3 变 13，13 ÷ 8 = 1 余 5。落下 0 变 50，50 ÷ 8 = 6 余 2。点上小数点。落下 8 变 28，28 ÷ 8 = 3 余 4。落下 0 变 40，40 ÷ 8 = 5。答案 RM 316.35。例子：RM 1 620.40 ÷ 8 → 16 ÷ 8 = 2，2 ÷ 8 = 0 余 2，20 ÷ 8 = 2 余 4，44 ÷ 8 = 5 余 4，40 ÷ 8 = 5 → RM 202.55。注意：RM 31.635 的小数点放错了位置，钱的 sen 只有两位。

divisor 8 = pembahagi 8 2 is less than 8, so start with 25: 25 ÷ 8 = 3 remainder 1. Bring down 3 to make 13; 13 ÷ 8 = 1 remainder 5. Bring down 0 to make 50; 50 ÷ 8 = 6 remainder 2. Place the decimal point. Bring down 8 to make 28; 28 ÷ 8 = 3 remainder 4. Bring down 0 to make 40; 40 ÷ 8 = 5. The answer is RM 316.35. Example: RM 1 620.40 ÷ 8 → 16 ÷ 8 = 2, 2 ÷ 8 = 0 r 2, 20 ÷ 8 = 2 r 4, 44 ÷ 8 = 5 r 4, 40 ÷ 8 = 5 → RM 202.55. Watch out: RM 31.635 has the decimal point in the wrong place; money never has three sen digits.

Bahagi 10, 100, 1000

RM 4 250 ÷ 10, ÷ 100, ÷ 1000

Titik perpuluhan bergerak ke kiri

Nilai	÷ 10	÷ 100	÷ 1000
RM 4 250	RM 425	RM 42.50	RM 4.25
RM 780	RM 78	RM 7.80	RM 0.78

÷ 10 → titik ke kiri 1 tempat · ÷ 100 → 2 tempat · ÷ 1000 → 3 tempat

小数点左移 = titik perpuluhan bergerak ke kiri；位 = tempat 除以 10、100、1000 不用长除法，只要把小数点向左移。RM 4 250 本来是 4 250.00。÷ 10 移 1 位变 425.0，就是 RM 425。÷ 100 移 2 位变 42.50。÷ 1000 移 3 位变 4.250，就是 RM 4.25。除数有几个 0，小数点就向左移几位。例子：RM 780 ÷ 10 = RM 78；÷ 100 = RM 7.80；÷ 1000 = RM 0.78。注意：除法是向左移，跟乘法相反；移错方向钱会变多。

decimal point moves left = titik perpuluhan bergerak ke kiri; place = tempat Dividing by 10, 100 or 1000 needs no long division; just move the decimal point to the left. RM 4 250 is really 4 250.00. ÷ 10 moves it 1 place to give 425.0, which is RM 425. ÷ 100 moves it 2 places to give 42.50. ÷ 1000 moves it 3 places to give 4.250, which is RM 4.25. The number of zeros in the divisor tells how many places to move. Example: RM 780 ÷ 10 = RM 78; ÷ 100 = RM 7.80; ÷ 1000 = RM 0.78. Watch out: division moves the point left, the opposite of multiplication; moving the wrong way makes the money bigger.

Cuba

RM 3 600 ÷ 100 = ?

除以 100 = bahagi 100；两个 0 = dua sifar 100 有两个 0，小数点向左移两位：3 600.00 → 360.0 → 36.00。sen 是 00，所以写成 RM 36 就可以。例子：RM 1 500 ÷ 100 = RM 15。注意：RM 360 只移了一位，那是 ÷ 10；RM 3.60 移了三位，那是 ÷ 1000。

dividing by 100 = bahagi 100; two zeros = dua sifar 100 has two zeros, so the decimal point moves two places to the left: 3 600.00 → 360.0 → 36.00. The sen are 00, so the answer is written as RM 36. Example: RM 1 500 ÷ 100 = RM 15. Watch out: RM 360 moves only one place, which is ÷ 10; RM 3.60 moves three places, which is ÷ 1000.

Harga seunit

6 botol jus berharga RM 25.80

Harga seunit = jumlah harga ÷ kuantiti

jumlah harga

RM 25.80

kuantiti

6 botol

harga seunit

RM 25.80 ÷ 6
= RM 4.30

25 ÷ 6 = 4 baki 1 → titik → 18 ÷ 6 = 3 → 0 ÷ 6 = 0 → RM 4.30

单价 = harga seunit；总价 = jumlah harga；数量 = kuantiti 知道几件东西的总价，要找一件的价钱，就用除法：单价 = 总价 ÷ 数量。6 瓶果汁 RM 25.80，一瓶就是 RM 25.80 ÷ 6。25 ÷ 6 = 4 余 1，点上小数点，落下 8 变 18，18 ÷ 6 = 3，落下 0，0 ÷ 6 = 0。一瓶 RM 4.30。例子：3 本簿子 RM 7.50，一本 RM 7.50 ÷ 3 = RM 2.50。注意：这里的 30 sen 是 .30，不是 .3。

unit price = harga seunit; total price = jumlah harga; quantity = kuantiti When we know the total price of several items and want the price of one, we divide: unit price = total ÷ quantity. 6 bottles of juice cost RM 25.80, so one bottle is RM 25.80 ÷ 6. 25 ÷ 6 = 4 remainder 1; place the point; bring down 8 to make 18; 18 ÷ 6 = 3; bring down 0; 0 ÷ 6 = 0. One bottle is RM 4.30. Example: 3 exercise books cost RM 7.50, so one is RM 7.50 ÷ 3 = RM 2.50. Watch out: thirty sen is written .30, never .3.

Cuba

Harga 8 buah buku ialah RM 46. Berapakah harga sebuah buku?

求单价 = cari harga seunit 8 本书 RM 46，一本就是 RM 46 ÷ 8。写成 46.00：46 ÷ 8 = 5 余 6，点上小数点，落下 0 变 60，60 ÷ 8 = 7 余 4，落下 0 变 40，40 ÷ 8 = 5。一本书 RM 5.75。例子：4 支笔 RM 7，一支 RM 7 ÷ 4 = RM 1.75。注意：RM 368 是 46 × 8，题目问一本的价钱，要用除法。

finding the unit price = cari harga seunit 8 books cost RM 46, so one book is RM 46 ÷ 8. Write 46.00: 46 ÷ 8 = 5 remainder 6; place the point; bring down 0 to make 60; 60 ÷ 8 = 7 remainder 4; bring down 0 to make 40; 40 ÷ 8 = 5. One book is RM 5.75. Example: 4 pens cost RM 7, so one pen is RM 7 ÷ 4 = RM 1.75. Watch out: RM 368 is 46 × 8; the question asks for one book, so we divide.

Padankan

Hasil bahagi yang betul

配对商 = padankan hasil bahagi 同一个 RM 60，÷ 4 是 15，÷ 10 是 6，÷ 100 是 0.60：除以 10 和 100 只要把小数点向左移 1 位和 2 位。RM 90 ÷ 5：9 ÷ 5 = 1 余 4，40 ÷ 5 = 8，得 RM 18。例子：RM 40 ÷ 100 = RM 0.40；RM 40 ÷ 8 = RM 5。注意：60 ÷ 100 不到 1 ringgit，答案要写 RM 0.60，前面的 0 不能省。

matching quotients = padankan hasil bahagi The same RM 60 gives 15 when ÷ 4, 6 when ÷ 10 and 0.60 when ÷ 100: dividing by 10 and 100 only moves the point 1 and 2 places left. RM 90 ÷ 5: 9 ÷ 5 = 1 remainder 4, then 40 ÷ 5 = 8, giving RM 18. Example: RM 40 ÷ 100 = RM 0.40; RM 40 ÷ 8 = RM 5. Watch out: 60 ÷ 100 is less than 1 ringgit, so the answer is written RM 0.60 with the leading 0.

Ringkasan

Syabas!

tulis .00 → bahagi ringgit → baki jadi sen → titik sebaris · ÷10 / ÷100 / ÷1000 → titik ke kiri

Tulis nilai wang dengan .00. Bahagi ringgit dahulu; baki ditukar kepada sen dan teruskan. Titik pada hasil bahagi sebaris dengan titik di bawah. Bahagi 10, 100, 1000: titik bergerak 1, 2, 3 tempat ke kiri. Harga seunit = jumlah harga ÷ kuantiti.

Latihan tambahan →