Unit 21
Tambah dan Tolak
Sebuah ladang ada 31 425 anak benih. Pekerja menanam 2 680 lagi, kemudian 5 370 dijual.
Berapakah anak benih sekarang?

加减混合 = tambah dan tolak
一个算式里同时有加号和减号,就是加减混合。故事里先发生的事先算,也就是从左到右一步一步算:先算第一个符号,得数再算第二个符号。
例子:500 + 200 − 100 → 先 500 + 200 = 700,再 700 − 100 = 600。
注意:“增加”用加,“卖出、用掉”用减。
addition and subtraction together = tambah dan tolak
When one number sentence has both + and −, it is a mixed operation. What happens first in the story is worked out first, so we go from left to right: do the first sign, then use that answer for the second sign.
Example: 500 + 200 − 100: first 500 + 200 = 700, then 700 − 100 = 600.
Watch out: planting more means add; selling or using up means subtract.
Cara 1
Kira dari kiri ke kanan
31 425 + 2 680 − 5 370
Langkah 1
| 1 | 1 | ||||
| 3 | 1 | 4 | 2 | 5 | |
| + | 2 | 6 | 8 | 0 | |
| 3 | 4 | 1 | 0 | 5 |
Langkah 2
| 2 | 13 | 10 | 10 | ||
| 3 | 4 | 1 | 0 | 5 | |
| − | 5 | 3 | 7 | 0 | |
| 2 | 8 | 7 | 3 | 5 |
从左到右 = dari kiri ke kanan
第一步先算左边的加法:31 425 + 2 680 = 34 105;第二步用这个得数做减法:34 105 − 5 370 = 28 735。每一步都用竖式,小心进位和退位。
例子:12 000 + 3 000 − 5 000 = 15 000 − 5 000 = 10 000。
注意:第一步的答案要写下来,第二步才不会用错数。
from left to right = dari kiri ke kanan
Step 1, the addition on the left: 31 425 + 2 680 = 34 105. Step 2, subtract from that answer: 34 105 − 5 370 = 28 735. Use a column calculation for each step and watch the carrying and regrouping.
Example: 12 000 + 3 000 − 5 000 = 15 000 − 5 000 = 10 000.
Watch out: write down the answer to step 1 so you use the right number in step 2.
Cara 2
Tukar susunan bersama simbolnya
31 425 − 5 370 + 2 680
Tolak dahulu
| 2 | 11 | 3 | 12 | ||
| 3 | 1 | 4 | 2 | 5 | |
| − | 5 | 3 | 7 | 0 | |
| 2 | 6 | 0 | 5 | 5 |
Kemudian tambah
| 1 | |||||
| 2 | 6 | 0 | 5 | 5 | |
| + | 2 | 6 | 8 | 0 | |
| 2 | 8 | 7 | 3 | 5 |
带着符号换次序 = tukar susunan bersama simbol
可以把“− 5 370”和“+ 2 680”换位置,但符号要跟着它的数走:减的还是减,加的还是加。先减后加,答案一样是 28 735。
例子:900 + 50 − 400 = 900 − 400 + 50 = 550。
注意:只换数字、不换符号,答案就错了。
move each number with its sign = tukar susunan bersama simbol
You may swap − 5 370 and + 2 680, but each sign must move with its number: what is subtracted is still subtracted, and what is added is still added. Subtracting first gives the same answer, 28 735.
Example: 900 + 50 − 400 = 900 − 400 + 50 = 550.
Watch out: swapping the numbers without their signs gives a wrong answer.
Cari kesilapan
Kiraan manakah betul?
52 040 − 3 815 + 960
Kiraan 1 ✔
52 040 − 3 815 = 48 225
48 225 + 960 = 49 185
48 225 + 960 = 49 185
Kiraan 2 ✘
52 040 − 960 = 51 080
51 080 + 3 815 = 54 895
51 080 + 3 815 = 54 895
找错误 = cari kesilapan
算式是 52 040 − 3 815 + 960。第二种算法把两个数换了位置,却没有把符号一起带过去:本来要加的 960 被减掉,本来要减的 3 815 反而被加上,所以错了。从左到右算,或者换位置时让符号跟着数走,才对。
例子:100 − 20 + 5 = 85;如果写成 100 − 5 + 20 = 115,就是只换了数字、没换符号。
注意:每个数前面的符号是它自己的,换位置时要一起搬。
find the mistake = cari kesilapan
The sentence is 52 040 − 3 815 + 960. The second working swaps the two numbers but leaves the signs behind: the 960 that should be added is subtracted, and the 3 815 that should be subtracted is added. Work from left to right, or move each sign with its number.
Example: 100 − 20 + 5 = 85; writing 100 − 5 + 20 = 115 swaps the numbers without their signs.
Watch out: the sign in front of a number belongs to it and must move with it.
Nombor yang tidak diketahui
□ + 6 238 − 1 450 = 20 000
Kerja ke belakang.
Tambah balik 1 450
| 2 | 0 | 0 | 0 | 0 | |
| + | 1 | 4 | 5 | 0 | |
| 2 | 1 | 4 | 5 | 0 |
Tolak balik 6 238
| 1 | 11 | 4 | 10 | ||
| 2 | 1 | 4 | 5 | 0 | |
| − | 6 | 2 | 3 | 8 | |
| 1 | 5 | 2 | 1 | 2 |
□ = 15 212 · Semak: 15 212 + 6 238 − 1 450 = 20 000 ✔
倒过来算 = kerja ke belakang
先用小数字想:□ + 3 − 2 = 6,□ 是多少?倒回去:6 + 2 = 8,8 − 3 = 5,所以 □ = 5;检查 5 + 3 − 2 = 6。大数也是一样。未知数在最前面时,从答案倒着推:最后一步是减 1 450,倒回去就加 1 450,得 21 450;前一步是加 6 238,倒回去就减 6 238,得 15 212。
例子:□ + 30 − 10 = 50 → 50 + 10 = 60,60 − 30 = 30。
注意:倒推时加变减、减变加,次序也要倒过来。
work backwards = kerja ke belakang
Think small first: □ + 3 − 2 = 6; going back, 6 + 2 = 8 and 8 − 3 = 5, so □ = 5, and 5 + 3 − 2 = 6 checks. Big numbers work the same way. When the unknown is at the start, work back from the answer. The last step subtracts 1 450, so undo it by adding 1 450 to get 21 450. The step before adds 6 238, so undo it by subtracting 6 238 to get 15 212.
Example: □ + 30 − 10 = 50: 50 + 10 = 60, then 60 − 30 = 30.
Watch out: when working backwards, adding becomes subtracting and the order is reversed too.
Cuba
18 300 − 4 275 + 6 040 = ?
先减后加 = tolak dahulu, kemudian tambah
这是一个有减号又有加号的算式。要从左到右一步一步算:先做左边的符号(减),把得数写下来;再用这个得数做右边的符号(加)。每一步都用竖式,小心借位和进位。
例子:5 000 − 1 200 + 2 400 → 先 5 000 − 1 200 = 3 800,再 3 800 + 2 400 = 6 200。
注意:不能先把减号后面的两个数加起来再一起减,那样会把应该加的数也减掉。
subtract first, then add = tolak dahulu, kemudian tambah
This sentence has a minus and a plus. Work from left to right: do the subtraction first and write down the answer, then add to that answer. Use columns and watch the regrouping.
Example: 5 000 − 1 200 + 2 400: first 3 800, then 3 800 + 2 400 = 6 200.
Watch out: do not add the last two numbers first and take them both away, or the number that should be added gets subtracted.
Anu
□ + 2 560 − 3 845 = 7 715. Apakah nombor dalam □?
倒推 = kerja ke belakang
未知数在最前面,后面先加再减,得到结果。可以先用小数字想:□ + 3 − 2 = 6,倒回去 6 + 2 = 8,8 − 3 = 5。做法就是从结果开始倒着走:最后一步是减,倒回去就加;前一步是加,倒回去就减。最后把答案放回原式检查。
例子:□ + 400 − 150 = 1 000 → 1 000 + 150 = 1 150,1 150 − 400 = 750;检查 750 + 400 − 150 = 1 000。
注意:倒推时次序要反过来,从最后一步开始;加变减、减变加。
work backwards = kerja ke belakang
The unknown is at the start; something is added, then something is taken away. Think small: □ + 3 − 2 = 6, and going back 6 + 2 = 8, 8 − 3 = 5. Start from the result and undo each step from the last one: undo a subtraction by adding and an addition by subtracting. Check in the sentence.
Example: □ + 400 − 150 = 1 000: 1 000 + 150 = 1 150, 1 150 − 400 = 750; check 750 + 400 − 150 = 1 000.
Watch out: undo the steps in reverse order, starting from the last one.
Ringkasan
Syabas!
kiri → kanan
Kira tambah dan tolak dari kiri ke kanan. Jika tukar susunan, simbol mesti ikut nombornya.
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