Unit 30
Darab dan Bahagi
Sekolah membeli 9 kotak pensel warna. Setiap kotak ada 12 batang. Pensel itu diagihkan sama banyak kepada 6 kelas.
Berapakah pensel yang diterima oleh setiap kelas?

乘除混合 = darab dan bahagi
先要知道一共有多少支笔(乘法),再平均分给各班(除法),一个算式里就同时有乘号和除号。这个单元学怎样按次序计算,以及怎样先约简,让数字变小、算得更快。
例子:4 盒 × 每盒 6 个 ÷ 3 组 = 24 ÷ 3 = 8 个。
注意:乘除混合要从左到右计算。
multiplication and division together = darab dan bahagi
First we find how many pencils there are altogether (multiply), then share them among the classes (divide), so one number sentence has both × and ÷. In this unit we learn the order of working and how to simplify first to make the numbers smaller and the work quicker.
Example: 4 boxes × 6 each ÷ 3 groups = 24 ÷ 3 = 8.
Watch out: with × and ÷ together, work from left to right.
Cara 1
Darab dahulu, kemudian bahagi
9 × 12 ÷ 6
Langkah 1
| 1 | |||
| 1 | 2 | ||
| × | 9 | ||
| 1 | 0 | 8 |
Langkah 2
| 1 | 8 | ||
| 6) | 1 | 0 | 8 |
| − | 6 | ||
| 4 | 8 | ||
| − | 4 | 8 | |
| 0 |
从左到右 = dari kiri ke kanan
先算左边的乘法:9 × 12 = 108;再把得数除以 6:108 ÷ 6 = 18。每一步都只是一个普通的乘法或除法。
例子:5 × 8 ÷ 4 = 40 ÷ 4 = 10。
注意:第一步的得数要用在第二步。
from left to right = dari kiri ke kanan
First the multiplication on the left: 9 × 12 = 108. Then divide that answer by 6: 108 ÷ 6 = 18. Each step is an ordinary multiplication or division.
Example: 5 × 8 ÷ 4 = 40 ÷ 4 = 10.
Watch out: use the answer from step 1 in step 2.
Cara 2
Permudahkan dahulu
9 × 12 ÷ 6 = 9 × 126
9 × 12 26 1 = 9 × 2 = 18
先约简 = permudahkan dahulu
乘除混合时,如果某个乘数和除数有公因数,可以先约掉,让数字变小。12 和 6 都可以被 6 整除:12 ÷ 6 = 2,所以 9 × 12 ÷ 6 = 9 × 2 = 18,答案一样。
例子:7 × 15 ÷ 5 = 7 × 3 = 21。
注意:只有乘数和除数之间可以约简。
simplify first = permudahkan dahulu
If one of the numbers being multiplied shares a factor with the divisor, cancel it first to make the numbers smaller. 12 and 6 can both be divided by 6: 12 ÷ 6 = 2, so 9 × 12 ÷ 6 = 9 × 2 = 18, the same answer.
Example: 7 × 15 ÷ 5 = 7 × 3 = 21.
Watch out: only a number being multiplied and the divisor can be simplified together.
Nombor besar
Permudahkan menjimatkan masa
450 × 16 ÷ 24
Cara 1
450 × 16 = 7 200
7 200 ÷ 24 = 300
7 200 ÷ 24 = 300
Cara 2
450 × 16 224 3
= 900 ÷ 3 = 300
= 900 ÷ 3 = 300
约简大数 = permudahkan nombor besar
方法一照次序算,要做 450 × 16 和 7 200 ÷ 24,数字比较大。方法二先看 16 和 24 都能被 8 整除,约成 2 和 3,只要算 450 × 2 = 900,900 ÷ 3 = 300,快很多。
例子:300 × 14 ÷ 21 → 14 和 21 约成 2 和 3 → 600 ÷ 3 = 200。
注意:约简时乘数和除数要除以同一个数。
simplify big numbers = permudahkan nombor besar
Method 1 works in order and needs 450 × 16 and 7 200 ÷ 24, which are big. Method 2 notices that 16 and 24 can both be divided by 8, becoming 2 and 3, so we only need 450 × 2 = 900 and 900 ÷ 3 = 300. Much quicker.
Example: 300 × 14 ÷ 21: 14 and 21 become 2 and 3, so 600 ÷ 3 = 200.
Watch out: divide the multiplier and the divisor by the same number.
Empat digit
Permudahkan dengan 5
35 × 2 184 ÷ 5
| 1 | 5 | 2 | |||
| 2 | 1 | 8 | 4 | ||
| × | 7 | ||||
| 1 | 5 | 2 | 8 | 8 |
先除再乘更方便 = permudahkan dengan 5
35 可以被 5 整除,先约成 7,就不用算 35 × 2 184 这么大的乘法了,只要算 2 184 × 7 = 15 288。
例子:45 × 1 230 ÷ 9 = 5 × 1 230 = 6 150。
注意:约简以后,另一个数 2 184 不变。
simplify with 5 = permudahkan dengan 5
35 can be divided by 5, which gives 7, so we avoid the big multiplication 35 × 2 184 and only need 2 184 × 7 = 15 288.
Example: 45 × 1 230 ÷ 9 = 5 × 1 230 = 6 150.
Watch out: after simplifying, the other number, 2 184, stays the same.
Bahagi dahulu
Bahagi, kemudian darab
16 200 biji telur dibahagi sama banyak kepada 40 gerai. Berapakah telur untuk 7 gerai?
16 200 ÷ 40 × 7
÷ 40
| 4 | 0 | 5 | |||
| 40) | 1 | 6 | 2 | 0 | 0 |
| − | 1 | 6 | 0 | ||
| 2 | 0 | ||||
| − | 0 | ||||
| 2 | 0 | 0 | |||
| − | 2 | 0 | 0 | ||
| 0 |
× 7
| 3 | ||||
| 4 | 0 | 5 | ||
| × | 7 | |||
| 2 | 8 | 3 | 5 |
先除后乘 = bahagi dahulu, kemudian darab
算式是 16 200 ÷ 40 × 7。从左到右先除:16 200 ÷ 40 = 405,这是一个摊位分到的鸡蛋;再乘 7,得到 7 个摊位一共 2 835 个。
例子:600 ÷ 20 × 5 = 30 × 5 = 150。
注意:不能先算 40 × 7 再去除,那样次序错了,答案也会错。
divide first, then multiply = bahagi dahulu, kemudian darab
The number sentence is 16 200 ÷ 40 × 7. Working left to right, divide first: 16 200 ÷ 40 = 405, the eggs for one stall. Then multiply by 7 to get 2 835 eggs for seven stalls.
Example: 600 ÷ 20 × 5 = 30 × 5 = 150.
Watch out: do not work out 40 × 7 first and then divide; the order would be wrong and so would the answer.
Adakah sama?
Dua ayat matematik yang sama nilainya
3 900 ÷ 10 × 24 dan 39 000 ÷ 100 × 24
3 900 ÷ 10 = 390
39 000 ÷ 100 = 390
390 × 24 = 9 360
39 000 ÷ 100 = 390
390 × 24 = 9 360
| 3 | 9 | 0 | ||
| × | 2 | 4 | ||
| 1 | 5 | 6 | 0 | |
| + | 7 | 8 | 0 | 0 |
| 9 | 3 | 6 | 0 |
判断是否相等 = semak sama atau tidak
两个算式的第一步都得 390:3 900 ÷ 10 = 390,39 000 ÷ 100 = 390。后面都乘 24,所以两个算式的值相同,都是 9 360。被除数多一个 0,除数也多一个 0,商不变。
例子:5 000 ÷ 100 × 3 和 500 ÷ 10 × 3 都等于 150。
注意:先把每个算式的第一步算出来,再比较。
check whether they are equal = semak sama atau tidak
The first step of both sentences gives 390: 3 900 ÷ 10 = 390 and 39 000 ÷ 100 = 390. Both then multiply by 24, so they have the same value, 9 360. When the number divided and the divisor each gain one zero, the quotient stays the same.
Example: 5 000 ÷ 100 × 3 and 500 ÷ 10 × 3 both equal 150.
Watch out: work out the first step of each sentence, then compare.
Cuba
14 × 250 ÷ 7 = ?
约简 = permudahkan
乘除混合的算式,可以照次序从左到右算,也可以先约简。先找找看:哪一个乘数能被除数整除?如果有,就先把它们约简,让数字变小,最后只做一次简单的乘法。
例子:18 × 40 ÷ 9 → 18 ÷ 9 = 2,2 × 40 = 80。
注意:约简只能在乘数和除数之间进行;算完第一步的乘法就停下来,也是常见的错误。
simplify = permudahkan
A sentence with × and ÷ can be worked in order from left to right, or simplified first. Look for a number being multiplied that the divisor goes into exactly. If there is one, simplify them first to make the numbers smaller, so only one easy multiplication is left.
Example: 18 × 40 ÷ 9: 18 ÷ 9 = 2, then 2 × 40 = 80.
Watch out: simplify only a number being multiplied with the divisor; stopping after the first multiplication is also a common mistake.
Cuba
9 000 ÷ 300 × 14 = ?
先除后乘 = bahagi dahulu, kemudian darab
算式里除号在前、乘号在后,就从左到右,先做除法,再把得数乘上后面的数。除以几百时,被除数和除数可以各去掉同样多个末尾的 0,再除。
例子:8 000 ÷ 400 × 6 → 80 ÷ 4 = 20,20 × 6 = 120。
注意:只做完第一步就停,或者漏了除法只做乘法,都会得到错误的结果。
divide first = bahagi dahulu, kemudian darab
The ÷ comes before the ×, so work left to right: divide first, then multiply the result by the last number. When dividing by hundreds, remove the same number of end zeros from both numbers before dividing.
Example: 8 000 ÷ 400 × 6: 80 ÷ 4 = 20, then 20 × 6 = 120.
Watch out: stopping after the first step, or skipping the division and only multiplying, both give a wrong result.
Cuba
28 000 ÷ 56 × 100 = ?
除以两位数再乘 100 = bahagi dua digit, kemudian darab 100
从左到右:先把被除数除以两位数,可以想“几个 56 是 280”,再看后面还有几个 0;得出商以后,再乘 100,在后面补两个 0。
例子:9 600 ÷ 32 × 100 → 9 600 ÷ 32 = 300,300 × 100 = 30 000。
注意:乘 100 这一步要补两个 0,漏了这一步,得数就少了两个 0。
divide by two digits, then multiply by 100 = bahagi dua digit, kemudian darab 100
Work left to right: divide by the two-digit number first; think how many 56s make 280, then count the zeros left over. After finding the quotient, multiply by 100 by writing two zeros after it.
Example: 9 600 ÷ 32 × 100: 9 600 ÷ 32 = 300, then 300 × 100 = 30 000.
Watch out: the × 100 step adds two zeros; missing it leaves the result two zeros short.
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