Akal Pintar

用总距离减 = jumlah tolak bahagian 从 M 到 K 的整条路，是 M 到 H 和 H 到 K 两段合起来的，所以 M 到 H = 总距离 − H 到 K。米栏二百零五不够减八百七十，借 1 km（= 1 000 m）：13 km 1 205 m − 5 km 870 m，得八千米三百三十五米。再化成米，和 Farid 说的数一样，说明他是对的。 例子：9 km 150 m − 3 km 600 m = 8 km 1 150 m − 3 km 600 m = 5 km 550 m。 注意：借了 1 km 以后，要把 1 000 m 加到原来的米数上。

total minus the known part = jumlah tolak bahagian The whole trail from M to K is made of M to H plus H to K, so M to H = total − H to K. In the metres column 205 is not enough to take away 870, so borrow 1 km (= 1 000 m): 13 km 1 205 m − 5 km 870 m = 8 km 335 m. In metres this matches Farid's number, so he is right. Example: 9 km 150 m − 3 km 600 m = 8 km 1 150 m − 3 km 600 m = 5 km 550 m. Watch out: after borrowing 1 km, add the 1 000 m to the metres already there.

先化成米 = tukar kepada m dahulu 也可以一开始就把两个距离都化成米：14 km 205 m = 14 205 m，5 km 870 m = 5 870 m。再列竖式相减，哪一位不够减，就向前一位借。得到的米数和方法一一样，所以两种方法都能说明说法正确。 例子：6 km 40 m − 1 km 500 m = 6 040 m − 1 500 m = 4 540 m。 注意：只有两位数米的距离，化成米时百位要写零。

change to metres first = tukar kepada m dahulu You may change both distances into metres at the start: 14 km 205 m = 14 205 m and 5 km 870 m = 5 870 m. Subtract in a column, borrowing from the next place whenever a digit is not enough. The number of metres matches Way 1, so either way shows the claim is true. Example: 6 km 40 m − 1 km 500 m = 6 040 m − 1 500 m = 4 540 m. Watch out: when a distance has two-digit metres, write 0 in the hundreds place.

用加法检查 = semak dengan menambah 减法可以用加法检查：已知的一段加上算出来的一段，要刚好等于总距离。八百七十米加三百三十五米超过一千米，拿出 1 000 m 换成 1 km，米栏剩二百零五；五加八再加一是十四千米，和总距离一样，说明前面没有算错。 例子：2 km 650 m + 1 km 480 m = 3 km 1 130 m = 4 km 130 m。 注意：米栏满一千时要进 1 km，米栏只留下多出来的部分。

check by adding = semak dengan menambah Subtraction can be checked with addition: the known part plus the part you found must equal the whole distance. 870 m + 335 m is more than 1 000 m, so 1 000 m become 1 km and 205 m stay; 5 + 8 + 1 = 14 km, the same as the total, so the working has no mistake. Example: 2 km 650 m + 1 km 480 m = 3 km 1 130 m = 4 km 130 m. Watch out: when the metres reach 1 000, carry 1 km and keep only the extra metres.

排列证明步骤 = susun langkah bukti 证明要按顺序写：第一步写出算式，用总距离减去已知的一段；第二步写出用千米和米表示的结果；第三步把结果化成米，和题目给的数对照。卡片里有些是错的做法，要看清楚是加还是减，数值是不是合理。 例子：证明 5 km 中另一段是 1 600 m：5 km − 3 km 400 m → 1 km 600 m → 1 600 m。 注意：证明的每一步都要能从上一步推出来。

arranging the proof = susun langkah bukti A proof goes in order: first write the calculation, the total distance minus the known part; next write the result in kilometres and metres; last change it into metres and compare it with the given number. Some cards show a wrong method, so look carefully at whether they add or subtract and whether the value makes sense. Example: to prove the other part of 5 km is 1 600 m: 5 km − 3 km 400 m → 1 km 600 m → 1 600 m. Watch out: each step of a proof must follow from the step before it.

四个点的线段图 = rajah empat titik 如果线段上有四个点，中间那一段的两边都有已知距离。总距离要先后减去两段已知的距离（连减），也可以先把两段已知距离加起来，再用总距离去减。每一步米不够减都要借一千米。 例子：总长 9 km，两边分别 2 km 100 m 和 3 km 500 m，中间 = 9 km − 5 km 600 m = 3 km 400 m。 注意：两段已知距离都要减掉，只减一段就会算错。

four points on a line = rajah empat titik With four points on the line, the middle part has known parts on both sides. Subtract both known parts from the total, one after the other, or add the two known parts first and subtract that sum from the total. Borrow 1 000 m whenever the metres are not enough. Example: total 9 km, outer parts 2 km 100 m and 3 km 500 m, middle = 9 km − 5 km 600 m = 3 km 400 m. Watch out: both known parts must be taken away, not just one.

选出能证明的算式 = pilih ayat bukti 先看图，想清楚要证明的那一段和总距离、其他各段有什么关系，再决定应该怎样列式。然后逐个验算：把等号左边算出来，化成和右边一样的单位，看两边是否相等。算式要既符合图上的关系，又真正成立，才能当作证明。 例子：三点图上总长 9 km 100 m，一段 3 km 750 m，要证明另一段是 5 350 m：9 km 100 m − 3 km 750 m = 8 km 1 100 m − 3 km 750 m = 5 km 350 m = 5 350 m，两边相等，式子成立。 注意：算式成立不等于它在证明这一段，还要对照图上的距离。

choosing the proof = pilih ayat bukti First look at the diagram and work out how the part to be proved is related to the total and to the other parts, and decide how the calculation should be set up. Then test each sentence: work out the left side, change it into the same unit as the right side, and see whether both sides are equal. Only a sentence that matches the diagram and is also true counts as a proof. Example: on a three-point diagram the total is 9 km 100 m and one part is 3 km 750 m; to prove the other part is 5 350 m: 9 km 100 m − 3 km 750 m = 8 km 1 100 m − 3 km 750 m = 5 km 350 m = 5 350 m, both sides are equal, so the sentence is true. Watch out: a true sentence is not always a proof of that part; compare its numbers with the distances on the diagram.