Unit 7
Kadaran
Pak Abu menjual mangga: 3 biji RM6.
Aina mahu membeli 5 biji. Berapakah harganya?

比例 = kadaran
买东西时,买得越多,付的钱也越多,而且是按同样的倍数增加,这就是比例关系。这个单元学一个很好用的方法:单一法(kaedah unitari)。先求出“一个”的价值,再乘上要的数量。钱、长度、重量、容量都可以用。
例子:2 支笔 RM4,先求 1 支 RM2,再算 6 支是 RM12。
注意:先除后乘,两个步骤的次序不能乱。
proportion = kadaran
When you buy more, you pay more, and the cost grows by the same number of times; this is a proportion. In this unit you learn a very useful method, the unitary method (kaedah unitari): first find the value of one, then multiply by the amount you want. It works for money, length, mass and volume.
Example: 2 pens cost RM4, so 1 pen costs RM2 and 6 pens cost RM12.
Watch out: divide first, then multiply; do not mix up the order of the two steps.
Maksud kadaran
Bertambah dengan kali yang sama
| Bilangan mangga | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| Harga | RM2 | RM4 | RM6 | RM8 |
bilangan × 2 → harga × 2 · bilangan × 3 → harga × 3
成正比 = berkadaran
看表格:芒果的数目变成 2 倍,价钱也变成 2 倍;数目变成 3 倍,价钱也变成 3 倍。两个数量一起按同样的倍数变化,就说它们成比例。因为每一个芒果都一样价钱,所以能这样算。
例子:1 本簿子 RM3,4 本就是 RM12。
注意:只有每一件价钱都一样时,才可以用比例来算。
in proportion = berkadaran
Look at the table: when the number of mangoes doubles, the price doubles; when the number triples, the price triples. When two quantities change by the same number of times together, they are in proportion. This works because every mango costs the same.
Example: 1 exercise book costs RM3, so 4 cost RM12.
Watch out: you can use proportion only when every item has the same value.
Kaedah unitari
Cari nilai 1 unit dahulu
3 biji RM6 → 1 biji RM2 → 5 biji RM10
单一法 = kaedah unitari
第一步“除”:已知 3 个芒果 RM6,用 RM6 ÷ 3,求出 1 个芒果 RM2。第二步“乘”:要买 5 个,就用 RM2 × 5 = RM10。先找“一个”,再求“很多个”,所以叫单一法。
例子:4 个面包 RM8,1 个 RM2,7 个 RM14。
注意:第一步除以的是已知的数量,第二步乘以的是要求的数量。
unitary method = kaedah unitari
Step 1, divide: 3 mangoes cost RM6, so RM6 ÷ 3 gives RM2 for 1 mango. Step 2, multiply: for 5 mangoes, RM2 × 5 = RM10. You find 'one' first, then 'many', which is why it is called the unitary method.
Example: 4 buns cost RM8, so 1 bun is RM2 and 7 buns are RM14.
Watch out: in step 1 divide by the amount you know; in step 2 multiply by the amount you want.
Wang dengan sen
4 tin susu RM10.20
6 tin → RM15.30
4 tin → RM10.20
① Bahagi → 1 unit: RM10.20 ÷ 4 = RM2.55
② Darab → yang diminta: RM2.55 × 6 = RM15.30
① Bahagi → 1 unit: RM10.20 ÷ 4 = RM2.55
② Darab → yang diminta: RM2.55 × 6 = RM15.30
带仙的价钱 = harga dengan sen
价钱有仙时,方法一样:先除再乘。RM10.20 ÷ 4,可以想成 1 020 仙 ÷ 4 = 255 仙,就是 RM2.55;再用 RM2.55 × 6 = RM15.30。算小数的时候,每一步都要把小数点对齐,答案才不会差十倍或一百倍。
例子:3 包饼干 RM4.50,1 包 RM1.50,5 包 RM7.50。
注意:除完以后用乘法检查一次,一罐的价钱乘回 4 罐,应该回到原来的总价。
prices with sen = harga dengan sen
When the price has sen, the method is the same: divide, then multiply. RM10.20 ÷ 4 can be thought of as 1 020 sen ÷ 4 = 255 sen, which is RM2.55; then RM2.55 × 6 = RM15.30. Keep the decimal points lined up when calculating.
Example: 3 packets of biscuits cost RM4.50, so 1 costs RM1.50 and 5 cost RM7.50.
Watch out: after dividing, check that RM2.55 × 4 gives back RM10.20.
Isi padu dan panjang
Bukan wang sahaja
Isi padu
6 botol → 1 800 mℓ1 botol → 1 800 ÷ 6 = 300 mℓ
4 botol → 300 × 4 = 1 200 mℓ
Panjang
3 m kain → RM271 m → RM27 ÷ 3 = RM9
7 m → RM9 × 7 = RM63
量也可以用单一法 = isi padu dan panjang
单一法不只是算钱。6 瓶果汁共 1 800 毫升,先除以 6 得 1 瓶 300 毫升,再乘 4 得 1 200 毫升。3 米布 RM27,先求 1 米 RM9,再算 7 米 RM63。
例子:5 包糖共 10 公斤,1 包 2 公斤,8 包 16 公斤。
注意:答案的单位要和题目要求的一样。
quantities can use the unitary method too = isi padu dan panjang
The unitary method is not only for money. 6 bottles of juice hold 1 800 mℓ altogether; divide by 6 to get 300 mℓ in 1 bottle, then multiply by 4 for 1 200 mℓ. 3 m of cloth costs RM27, so 1 m is RM9 and 7 m is RM63.
Example: 5 bags of sugar weigh 10 kg, so 1 bag is 2 kg and 8 bags are 16 kg.
Watch out: give the answer in the unit the question asks for.
Sekilas fakta
Denyutan jantung
4 minit → 300 kali · 3 minit → 225 kali
Sekilas fakta
Jantung berdenyut untuk mengepam darah ke seluruh badan. Rasa nadi di pergelangan tanganmu!
Jantung berdenyut untuk mengepam darah ke seluruh badan. Rasa nadi di pergelangan tanganmu!
Jantung Aiman: 4 minit → 300 kali
① Bahagi → 1 unit: 300 ÷ 4 = 75 kali
② Darab → yang diminta: 75 × 3 = 225 kali
① Bahagi → 1 unit: 300 ÷ 4 = 75 kali
② Darab → yang diminta: 75 × 3 = 225 kali
心跳也成比例 = denyutan jantung
心脏一直在跳动,把血液送到全身。如果心跳的速度一样,跳的次数就和时间成比例。Aiman 的心脏 4 分钟跳 300 次,先求 1 分钟跳 75 次,再乘 3,就是 3 分钟跳 225 次。
例子:一个水龙头 2 分钟滴 40 滴,1 分钟滴 20 滴,5 分钟滴 100 滴。
注意:你可以按着手腕数一数自己 1 分钟跳几次。
heartbeats are proportional too = denyutan jantung
The heart beats all the time to pump blood around the body. If it beats at a steady rate, the number of beats is proportional to the time. Aiman's heart beats 300 times in 4 minutes, so it beats 75 times in 1 minute, and 3 × 75 = 225 times in 3 minutes.
Example: a tap that drips 40 drops in 2 minutes drips 20 in 1 minute and 100 in 5 minutes.
Watch out: you can feel your own pulse at the wrist and count how many beats you have in 1 minute.
Cuba
4 buah buku cerita berharga RM12. Berapakah harga 9 buah buku cerita yang sama?
先求一本 = cari harga sebuah
用单一法:第一步,用总价除以已知的本数,求出一本多少钱;第二步,用一本的价钱乘以要买的本数。算完以后,可以想一想答案合不合理:买得比较多,价钱应该比较高。
例子:5 支铅笔 RM10,1 支 RM2,8 支 RM16。
注意:第一步的答案不是最后的答案,还要再乘。
find the price of one first = cari harga sebuah
Use the unitary method: step 1, divide the total price by the number you know to find the price of one; step 2, multiply that by the number you want. Afterwards, check that the answer makes sense: buying more should cost more.
Example: 5 pencils cost RM10, so 1 costs RM2 and 8 cost RM16.
Watch out: the answer to step 1 is not the final answer; you still have to multiply.
Cuba
5 kg beras berharga RM14.50. Berapakah harga 3 kg beras yang sama?
带仙的单一法 = kaedah unitari dengan sen
先求 1 公斤的价钱:用总价除以 5,可以先把令吉换成仙再除。再用 1 公斤的价钱乘以 3。最后把仙换回令吉和仙。
例子:4 公斤糖 RM11.20,1 公斤 RM2.80,2 公斤 RM5.60。
注意:要买的比已知的少,答案应该比原来的总价小。
unitary method with sen = kaedah unitari dengan sen
First find the price of 1 kg: divide the total price by 5; you can change ringgit to sen before dividing. Then multiply the price of 1 kg by 3. Finally change sen back to ringgit and sen.
Example: 4 kg of sugar cost RM11.20, so 1 kg costs RM2.80 and 2 kg cost RM5.60.
Watch out: you want fewer than you know about, so the answer should be smaller than the total you started with.
Cuba
Jisim 8 keping biskut ialah 160 g. Berapakah jisim 15 keping biskut yang sama?
重量的单一法 = kaedah unitari untuk jisim
先用总重量除以片数,求出一片饼干多重;再乘以要的片数。答案用克表示。
例子:6 颗鸡蛋共 300 克,1 颗 50 克,10 颗 500 克。
注意:不要把片数直接和重量相加。
unitary method for mass = kaedah unitari untuk jisim
Divide the total mass by the number of pieces to find the mass of one biscuit, then multiply by the number of pieces wanted. Give the answer in grams.
Example: 6 eggs weigh 300 g, so 1 egg is 50 g and 10 eggs are 500 g.
Watch out: do not add the number of pieces to the mass.
Ringkasan
Syabas!
① bahagi ② darab
Kaedah unitari: bahagi untuk mencari nilai 1 unit, kemudian darab dengan bilangan yang diminta.
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