Unit 19
Selesaikan Masalah
Untuk menyelesaikan masalah pecahan, perpuluhan dan peratus, ikut empat langkah.
① Diberi
maklumat yang ada
② Dicari
apa yang ditanya
③ Cara
ayat matematik dan rajah
④ Semak
guna operasi songsang
selesaikan masalah = 解决问题／solve problems
解应用题分四步：Diberi 写已知的数，Dicari 写要找什么，Cara 列算式、画图，Semak 用相反的运算检查。
例子：减法算完后，把答案和减数加起来，看是否等于原来的数。
注意：最后要用完整的句子回答，并写上单位。
selesaikan masalah = solve problems
Solve a word problem in four steps: Diberi lists the numbers you know, Dicari says what you must find, Cara writes the number sentence and a drawing, and Semak checks with the opposite operation. Writing each step clearly prevents mistakes.
Example: after subtracting, add the answer to the number you took away and see whether you get the starting number.
Watch out: finish with a full sentence and the unit.
Masalah 1 · langkah ① dan ②
Diberi dan dicari
Puan Kavitha membeli 12 kg kacang tanah dan 310 kg kacang hijau. Berapakah jumlah jisim kacang yang dibelinya?
| Diberi | 12 kg kacang tanah 310 kg kacang hijau |
|---|---|
| Dicari | jumlah jisim kacang |
| Cara | 12 kg + 310 kg = ? |
已知和要找 = diberi dan dicari
先把题目里的两个重量抄下来，这是 Diberi。题目问一共多重，这是 Dicari。看到 jumlah，就知道要列加法算式。
例子：“糖和盐各有多重，总重多少？” → 已知两个重量，要找总重。
注意：Dicari 要写清楚找的是什么，不只是写一个问号。
diberi dan dicari = what is given and what to find
Copy the two masses from the problem; that is Diberi. The problem asks for the total mass; that is Dicari. The word jumlah tells us to write an addition sentence.
Example: 'sugar 1/4 kg, salt 1/8 kg, what is the total mass?' → two masses are given and the total is wanted.
Watch out: under Dicari, write what you are finding in words, not just a question mark.
Masalah 1 · langkah ③ dan ④
Lukis rajah, kemudian semak
Semak: 810 − 310 = 510 = 12 ✔
Jumlah jisim kacang ialah 45 kg.
Jumlah jisim kacang ialah 45 kg.
画图和检查 = lukis rajah dan semak
画两条一样长的纸条：一条分成 2 份，涂 1 份；一条分成 10 份，涂 5 份，可以看出 1/2 = 5/10。再涂上 3 份，一共 8/10，约分成 4/5 kg。最后用减法检查。
例子：1/5 + 1/10 → 2/10 + 1/10 = 3/10。
注意：8/10 还能约分，答案要写最简分数。
lukis rajah dan semak = draw a diagram and check
Draw two equal strips: one cut into 2 parts with 1 shaded, one cut into 10 parts with 5 shaded, which shows 1/2 = 5/10. Shade 3 more parts to get 8/10, then simplify to 4/5 kg. Finally, check by subtracting.
Example: 1/5 + 1/10 → 2/10 + 1/10 = 3/10.
Watch out: 8/10 can still be simplified, so give the answer in simplest form.
Cuba langkah ②
Kedai roti menggunakan 35 kg mentega pada hari Isnin dan 110 kg pada hari Selasa. Berapakah jisim mentega yang digunakan semuanya? Apakah yang dicari?
找出要找的 = kenal pasti yang dicari
Dicari 就是题目最后一句问的东西。semuanya 是“全部合起来”的意思，想一想题目要的是一天的量，还是两天加在一起的量。
例子：“两天一共跑了多远？” → 要找总距离。
注意：星期一用的 3/5 kg 已经给了，不是要找的东西。
kenal pasti yang dicari = identify what to find
Dicari is what the last sentence of the problem asks for. Semuanya means all together, so decide whether the question wants one day's amount or the two days put together.
Example: 'how far did she run over the two days?' → find the total distance.
Watch out: the 3/5 kg used on Monday is already given, so it is not what we are looking for.
Masalah 2 · tolak pecahan
Lompat ke belakang
Akuarium berisi air 56 penuh. Ayah mengeluarkan air sehingga tinggal 13 penuh. Berapa bahagian air yang dikeluarkan?
56 − 13 = ?
13 = 26
0
16
26
36
46
56
66
56 → 46 → 36 → 26 : 3 lompatan = 36
数线倒着跳 = lompat ke belakang
先把 1/3 换成 2/6，两个分数都是六分之几才好比较。在数线上从 5/6 往回跳到 2/6，一共跳了 3 格，所以放掉的水是 3/6。
例子：7/8 − 1/4 → 1/4 = 2/8，从 7/8 往回跳到 2/8，跳 5 格 → 5/8。
注意：这里是从 5/6 跳到剩下的 2/6，不是往回跳 2 格。
lompat ke belakang = jump backwards
First change 1/3 into 2/6 so that both fractions are in sixths. On the number line, start at 5/6 and jump back to 2/6. That is 3 jumps, so the water taken out is 3/6.
Example: 7/8 − 1/4 → 1/4 = 2/8, jump back from 7/8 to 2/8, 5 jumps → 5/8.
Watch out: here we jump from 5/6 down to the 2/6 that is left; we do not jump back only 2 steps.
Masalah 2 · langkah ③ dan ④
Permudahkan dan semak
Permudahkan: 3 ÷ 36 ÷ 3 = 12
Semak: 12 + 13 = 36 + 26 = 56 ✔
Semak: 12 + 13 = 36 + 26 = 56 ✔
Ayah mengeluarkan 12 air akuarium.
约分和检查 = permudahkan dan semak
3/6 的分子和分母都能被 3 整除，所以 3/6 = 1/2。用加法检查：把答案 1/2 和剩下的 1/3 加起来，得 5/6，正好是原来的水，答案就对了。
例子：4/8 约分 → 分子分母都除以 4 → 1/2。
注意：分子分母要除以同一个数，只除分子会变成另一个分数。
permudahkan dan semak = simplify and check
Both 3 and 6 can be divided by 3, so 3/6 = 1/2. Check by adding: the answer 1/2 plus the 1/3 left gives 5/6, exactly the water at the start, so the answer is right.
Example: simplify 4/8 → divide top and bottom by 4 → 1/2.
Watch out: divide the numerator and the denominator by the same number; dividing only one of them changes the fraction.
Cuba kira
Mira ada 710 m pita pelekat. Dia menggunakan 12 m untuk membalut kotak. Berapakah panjang pita yang tinggal?
先换分母再减 = samakan penyebut dahulu
二分之一要先换成十分之几：分子分母都乘 5，得十分之五。相减以后再约分。用加法检查：答案加二分之一应该等于原来的长度。
例子：9/10 − 3/5 → 9/10 − 6/10 = 3/10。
注意：分子减分子、分母减分母会得到 6/8，这是错的。
samakan penyebut dahulu = make the denominators the same first
Change 1/2 into tenths: multiply top and bottom by 5 to get 5/10. Then subtract the tenths and simplify. Check by adding: the answer plus 1/2 should make 7/10.
Example: 9/10 − 3/5 → 9/10 − 6/10 = 3/10.
Watch out: taking numerator from numerator and denominator from denominator gives 6/8, which is wrong.
Masalah 3 · beza perpuluhan
Beza isi padu air
Jun Hao minum 0.7 ℓ air. Kavin minum 0.26 ℓ air. Berapakah beza isi padu air yang mereka minum?
0.7 = 70 petak
| 6 | 10 | |||
| 0 | . | 7 | 0 | |
| − | 0 | . | 2 | 6 |
| 0 | . | 4 | 4 |
Beza isi padu air ialah 0.44 ℓ.
小数退位减 = tolak dengan mengumpul semula
零点七写成零点七零，就是百格图里涂了七十格。百分位零减六不够，从十分位借一：十分位七变六，百分位变十，相差 0.44 ℓ。
例子：0.50 − 0.18 = 0.32。
注意：借了以后十分位要少 1，不要还是用 7 去减。
tolak dengan mengumpul semula = subtracting with regrouping
Write 0.7 as 0.70, which is 70 shaded squares in the hundred grid. In the hundredths, 0 take away 6 cannot be done, so regroup 1 tenth: the tenths 7 become 6 and the hundredths become 10. The difference is 0.44 ℓ.
Example: 0.5 − 0.18 → 0.50 − 0.18 = 0.32.
Watch out: after regrouping, the tenths digit is one less; do not subtract from 7.
Masalah 4 · tambah perpuluhan
Lebih berat daripada
Anak kucing berjisim 0.46 kg. Arnab 0.27 kg lebih berat daripada anak kucing itu. Berapakah jisim arnab?
| 1 | ||||
| 0 | . | 4 | 6 | |
| + | 0 | . | 2 | 7 |
| 0 | . | 7 | 3 |
Semak
| 6 | 13 | |||
| 0 | . | 7 | 3 | |
| − | 0 | . | 2 | 7 |
| 0 | . | 4 | 6 |
比……重 = lebih berat daripada
兔子比小猫重，就是小猫的重量再加多出的部分，条形图上兔子那一条比较长。百分位六加七等于十三，写三进一；十分位四加二加一等于七。
例子：0.25 m 再长 0.17 m → 0.42 m。
注意：用减法检查，答案减去多出的部分要回到小猫的重量。
lebih berat daripada = heavier than
The rabbit is 0.27 kg heavier than the kitten, so it weighs the kitten's mass plus 0.27 kg; its bar is the longer one. 0.46 + 0.27: hundredths 6 + 7 = 13, write 3 and carry 1; tenths 4 + 2 + 1 = 7, giving 0.73 kg.
Example: 0.25 m and then 0.17 m longer → 0.42 m.
Watch out: check by subtracting; 0.73 − 0.27 should give back 0.46.
Cuba kira
Sebiji epal berjisim 0.24 kg. Sebiji limau berjisim 0.09 kg. Berapakah beza jisim kedua-dua buah itu?
两位小数求差 = beza dua perpuluhan
求差用减法。百分位四减九不够，向十分位借一：十分位二变一，百分位变十四，再逐位相减。
例子：0.32 − 0.07 = 0.25。
注意：不能用九减四来代替四减九，那样会得到错误答案。
beza dua perpuluhan = difference of two decimals
A difference means subtract: 0.24 − 0.09. In the hundredths, 4 take away 9 cannot be done, so regroup from the tenths: the tenths 2 become 1 and the hundredths become 14. Now subtract each place.
Example: 0.32 − 0.07 = 0.25.
Watch out: do not swap to 9 − 4 in the hundredths; that mistake gives 0.25.
Masalah 5 · peratus
Catat dalam jadual
Ada 100 ekor ikan dalam kolam. 38 ekor ialah ikan emas. Yang lain ialah ikan puyu. Nyatakan peratus ikan puyu.
| Ikan | Bilangan |
|---|---|
| Ikan emas | 38 |
| Ikan puyu | 62 |
| Jumlah | 100 |
100 − 38 = 62
62100 = 62%
列表求百分比 = jadual untuk peratus
先把已知的金鱼数和总数填进表格，再用减法找出另一种鱼：100 − 38 = 62 条。100 条里有 62 条，就是 62/100 = 62%。
例子：100 个学生里 27 个戴眼镜 → 不戴的有 73 个，占 73%。
注意：题目问的是另一种鱼，不要直接写 38%。
jadual untuk peratus = a table for percent
Put the known number of goldfish and the total into a table, then subtract to find the other kind: 100 − 38 = 62 fish. 62 out of 100 is 62/100 = 62%.
Example: 27 of 100 pupils wear glasses → 73 do not, which is 73%.
Watch out: the question asks about the other kind of fish, so the answer is not 38%.
Cuba tukar
Di sebuah dusun, 40% daripada pokok ialah pokok pisang. Nyatakan 40% dalam perpuluhan.
百分比化小数 = peratus kepada perpuluhan
百分之四十就是一百分之四十，也就是四十个百分之一。百格图涂四十格，数一数是几整行，每一行是一个十分之一。小数末尾的零可以去掉。
例子：90% = 0.9；15% = 0.15。
注意：两位数的百分比不会变成百分位上的一个数字，十分位和百分位要分清。
peratus kepada perpuluhan = percent to decimal
40% means 40/100, forty hundredths. Shade 40 squares in a hundred grid and count the full rows; each row is one tenth. A zero at the end of a decimal can be dropped.
Example: 90% = 90/100 = 0.9, and 15% = 0.15.
Watch out: a two-digit percent fills the tenths place too, so keep the tenths and hundredths places apart.
Ringkasan
Syabas!
Diberi · Dicari · Cara · Semak
Tulis maklumat, kenal pasti soalan, kira dengan rajah atau bentuk lazim, kemudian semak dengan operasi songsang.
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