Unit 15
Akal Pintar
Di makmal sains, Cikgu Ravi menulis teka-teki ini pada papan putih:
4 ℓ 300 mℓ − K mℓ + 1 ℓ 250 mℓ = 3 ℓ 980 mℓ
Apakah nilai K?
求未知数 = cari nilai yang tidak diketahui
算式里有一个方格或字母，表示一个还不知道的容量。先把所有容量都化成毫升，数字就容易比较。然后想一想：这个未知数是被加上去的，还是被减掉的？被减掉的，可以用“已知的总和减去结果”求出来；被加上去的，就用“结果减去其他已知数”。求出来以后，一定要放回算式里检查。
例子：2 ℓ − Y mℓ = 1 ℓ 400 mℓ → 2 000 − 1 400 = 600，所以 Y = 600。
注意：不要忘了把升化成毫升，一升等于一千毫升。
finding the unknown = cari nilai yang tidak diketahui
A box or letter in the number sentence stands for a volume we do not know yet. Change every volume into millilitres first so the numbers are easy to compare. Then ask: is the unknown added or taken away? If it is taken away, find it as the known total minus the result; if it is added, find it as the result minus the other known amounts. Always put your value back into the sentence to check.
Example: 2 ℓ − Y mℓ = 1 ℓ 400 mℓ → 2 000 − 1 400 = 600, so Y = 600.
Watch out: remember to change litres into millilitres, 1 ℓ = 1 000 mℓ.
Cara 1
Gabungkan nilai yang diketahui
4 300 − K + 1 250 = 3 980
4 ℓ 300 mℓ = 4 300 mℓ · 1 ℓ 250 mℓ = 1 250 mℓ · 3 ℓ 980 mℓ = 3 980 mℓ
4 300 + 1 250
| 4 | 3 | 0 | 0 | |
| + | 1 | 2 | 5 | 0 |
| 5 | 5 | 5 | 0 |
K = 5 550 − 3 980
| 4 | 14 | 15 | ||
| 5 | 5 | 5 | 0 | |
| − | 3 | 9 | 8 | 0 |
| 1 | 5 | 7 | 0 |
5 550 − K = 3 980 → K = 1 570
合并已知数 = gabung nilai yang diketahui
先把三个容量都化成毫升：四千三百、一千二百五十、三千九百八十。K 是被减掉的，而一千二百五十是加上去的，所以四千三百和一千二百五十可以先合起来，一共五千五百五十。算式变成“五千五百五十减 K 等于三千九百八十”，被减掉的 K 就等于五千五百五十减三千九百八十，得一千五百七十。
例子：3 000 − N + 500 = 2 800 → 3 500 − N = 2 800 → N = 700。
注意：只有被减掉的是 K 时，才可以这样合并；合并的是加上去的数。
join the known amounts = gabung nilai yang diketahui
Change the three volumes into millilitres: 4 300, 1 250 and 3 980. K is taken away while 1 250 is added, so 4 300 and 1 250 can be joined first: 5 550. The sentence becomes 5 550 − K = 3 980, and the amount taken away is K = 5 550 − 3 980 = 1 570.
Example: 3 000 − N + 500 = 2 800 → 3 500 − N = 2 800 → N = 700.
Watch out: you join the amount that is added; the unknown is the one being taken away.
Cara 2
Kira ke belakang
… + 1 250 = 3 980
4 300− K
→?+ 1 250
→3 980
→?+ 1 250
→3 980
Kira ke belakang ←
3 980− 1 250
→2 730
→2 730
3 980 − 1 250
| 3 | 9 | 8 | 0 | |
| − | 1 | 2 | 5 | 0 |
| 2 | 7 | 3 | 0 |
4 300 − 2 730
| 3 | 12 | 10 | ||
| 4 | 3 | 0 | 0 | |
| − | 2 | 7 | 3 | 0 |
| 1 | 5 | 7 | 0 |
K = 1 570
倒推 = kira ke belakang
从算式的最后一步往回想：加上一千二百五十以后变成三千九百八十，那么加之前就是三千九百八十减一千二百五十，等于两千七百三十。再往回一步：四千三百减去 K 以后剩两千七百三十，所以 K 等于四千三百减两千七百三十，也是一千五百七十。两种方法得到同一个数，更有把握。
例子：5 000 − W + 200 = 4 500 → 4 500 − 200 = 4 300 → W = 5 000 − 4 300 = 700。
注意：倒推时运算要相反：原来加的，往回要减。
work backwards = kira ke belakang
Start from the last step: after adding 1 250 the volume is 3 980, so before adding it was 3 980 − 1 250 = 2 730. One more step back: 4 300 − K leaves 2 730, so K = 4 300 − 2 730, which is 1 570 again. Two methods giving the same number makes us more sure.
Example: 5 000 − W + 200 = 4 500 → 4 500 − 200 = 4 300 → W = 5 000 − 4 300 = 700.
Watch out: when working backwards, use the opposite operation: what was added must be subtracted.
Semak
Masukkan semula nilai K
4 ℓ 300 mℓ − 1 570 mℓ + 1 250 mℓ
4 300 − 1 570
| 3 | 12 | 10 | ||
| 4 | 3 | 0 | 0 | |
| − | 1 | 5 | 7 | 0 |
| 2 | 7 | 3 | 0 |
2 730 + 1 250
| 2 | 7 | 3 | 0 | |
| + | 1 | 2 | 5 | 0 |
| 3 | 9 | 8 | 0 |
3 980 mℓ = 3 ℓ 980 mℓ ✔
K = 1 570
K = 1 570
代入检查 = semak dengan menggantikan nilai
把求出的数放回原来的算式，从左到右重新算一次：四千三百减一千五百七十，剩两千七百三十；再加一千二百五十，得三千九百八十毫升，也就是三升九百八十毫升，和题目的结果一样，说明求出的数是对的。如果算出来不一样，就要回头找错。
例子：检查 W = 700：5 000 − 700 + 200 = 4 500 ✔。
注意：检查时要按原来的次序算，不能先加后减。
check by putting the value back = semak dengan menggantikan nilai
Put the value you found back into the sentence and work it out again from left to right: 4 300 − 1 570 = 2 730, then 2 730 + 1 250 = 3 980 mℓ, which is 3 ℓ 980 mℓ, the same as the result in the puzzle, so the value is right. If the result is different, go back and find the mistake.
Example: check W = 700: 5 000 − 700 + 200 = 4 500 ✔.
Watch out: when checking, follow the order in the number sentence; do not add before subtracting.
Cuba
P mℓ + 2 ℓ 600 mℓ − 900 mℓ = 5 ℓ 45 mℓ
P = ?
未知数在最前面 = nilai tidak diketahui di hadapan
把所有容量化成毫升。未知数 P 在最前面，后面先加再减，所以可以倒推：从结果开始，先把被减掉的加回去，再把被加上的减回去，剩下的就是 P。求出后放回算式检查。
例子：Q + 1 000 − 300 = 2 400 → 2 400 + 300 = 2 700 → 2 700 − 1 000 = 1 700，Q = 1 700。
注意：5 ℓ 45 mℓ 化成毫升时，四十五要放在十位和个位，百位是零。
unknown at the front = nilai tidak diketahui di hadapan
Change every volume into millilitres. The unknown P comes first, followed by an addition and then a subtraction, so work backwards: start from the result, add back what was taken away, then take away what was added. What is left is P. Then substitute P into the sentence to make sure.
Example: Q + 1 000 − 300 = 2 400 → 2 400 + 300 = 2 700 → 2 700 − 1 000 = 1 700, Q = 1 700.
Watch out: 5 ℓ 45 mℓ in millilitres keeps 45 in the tens and ones, with a zero in the hundreds.
Cuba
8 ℓ − 2 ℓ 750 mℓ + W mℓ = 6 ℓ 100 mℓ
W = ?
未知数是加数 = nilai tidak diketahui ditambah
这次未知数 W 是被加上去的。先把 W 前面能算的部分算出来：八升减两升七百五十毫升，化成毫升再减。算式就变成“某数加 W 等于结果”，W 就等于结果减去这个数。最后代入检查。
例子：4 ℓ − 1 ℓ 500 mℓ + V = 3 ℓ 200 mℓ → 2 500 + V = 3 200 → V = 700。
注意：从八千减的时候要连续借位，每一位都要检查。
the unknown is added = nilai tidak diketahui ditambah
This time the unknown W is added. First work out the part before W: 8 ℓ − 2 ℓ 750 mℓ, changed into millilitres. The sentence becomes some number + W = result, so W is the result minus that number. Check it by working the sentence through again.
Example: 4 ℓ − 1 ℓ 500 mℓ + V = 3 ℓ 200 mℓ → 2 500 + V = 3 200 → V = 700.
Watch out: subtracting from 8 000 needs borrowing across several places; check each one.
Ringkasan
Syabas!
Tukar → gabung atau kira ke belakang → semak
Tukar semua isi padu kepada mℓ, cari nilai yang tidak diketahui, kemudian masukkan semula untuk menyemak.
Latihan tambahan →