Unit 21
Maju Minda
Maju Minda
Ulang kaji semua kemahiran dalam bab Pecahan, Perpuluhan dan Peratus.
Jawab setiap soalan. Jika salah, baca petunjuk dan cuba lagi.
综合复习 = Maju Minda
这是第二章的总复习，题目包括：假分数和带分数互换、分数加减、求一个数量的几分之几、小数的加减乘除、分数和百分比互换、物件的百分比以及应用题。每题答错会有提示，可以再试一次。
例子：一道题可能要先通分再相加，也可能要先约分再化成百分比。
注意：做应用题时，记得用四个步骤并写上单位。
chapter review = Maju Minda
This is the review for Chapter 2. The questions cover improper fractions and mixed numbers, adding and subtracting fractions, a fraction of a quantity, the four operations with decimals, fractions and percentages, percentages of objects and word problems. A wrong answer shows a hint so you can try again.
Example: one question may need a common denominator before adding; another may need simplifying before changing to a percentage.
Watch out: in word problems, use the four steps and write the unit.
Pecahan tak wajar
257 dalam nombor bercampur ialah …
假分数化带分数 = pecahan tak wajar ke nombor bercampur
用分子除以分母：商是带分数的整数部分，余数是新的分子，分母保持不变。算好以后用“整数 × 分母 + 分子”倒回去，看是不是原来的分子。
例子：26/5 → 26 ÷ 5 = 5 余 1 → 5又1/5；检查 5 × 5 + 1 = 26。
注意：商和余数的位置不要放反；余数一定比分母小。
improper fraction to mixed number = pecahan tak wajar ke nombor bercampur
Divide the numerator by the denominator: the quotient is the whole number part, the remainder is the new numerator and the denominator stays the same. Check by working back: whole × denominator + numerator.
Example: 26/5: 26 ÷ 5 = 5 remainder 1, so 5 1/5; check 5 × 5 + 1 = 26.
Watch out: do not swap the quotient and the remainder, and the remainder must be smaller than the denominator.
Nombor bercampur
Tukar 427 kepada pecahan tak wajar.
带分数化假分数 = nombor bercampur ke pecahan tak wajar
每个整数 1 里有“分母”那么多份。整数乘分母，求出整数部分一共几份，再加上分子的份数，分母不变。
例子：2又3/4 → 2 × 4 + 3 = 11 → 11/4。
注意：不能把整数、分子和分母三个数直接相加；乘的时候要用整数乘分母，不是乘分子。
mixed number to improper fraction = nombor bercampur ke pecahan tak wajar
Each whole contains as many parts as the denominator. Multiply the whole number by the denominator to count the parts in the wholes, add the numerator, and keep the denominator.
Example: 2 3/4: 2 × 4 + 3 = 11, so 11/4.
Watch out: do not just add the three numbers, and multiply the whole number by the denominator, not by the numerator.
Tambah pecahan
29 + 59 + 19 = ?
同分母连加 = tambah penyebut sama
几个分数的分母一样，表示每份一样大，只要把所有的分子（份数）加起来，分母照抄。最后看能不能约简或化成带分数。
例子：1/7 + 2/7 + 3/7 = 6/7。
注意：三个分数都要加进去，不要漏掉一个；分母不能相加。
adding with the same denominator = tambah penyebut sama
When the denominators match, the parts are the same size, so add all the numerators and copy the denominator. Then see whether it simplifies or becomes a mixed number.
Example: 1/7 + 2/7 + 3/7 = 6/7.
Watch out: include all three fractions, and never add the denominators.
Penyebut berbeza
110 + 25 = ?
异分母相加 = tambah penyebut berbeza
如果一个分母是另一个分母的倍数，就用较大的分母做公分母，只要把另一个分数换过去（分子分母乘同一个数）。相加以后记得约到最简形式。
例子：1/4 + 3/8 = 2/8 + 3/8 = 5/8。
注意：换分母时分子也要乘；分子加分子、分母加分母是错的。
adding with different denominators = tambah penyebut berbeza
If one denominator is a multiple of the other, use the bigger one as the common denominator and change only the other fraction (multiply top and bottom by the same number). Simplify after adding.
Example: 1/4 + 3/8 = 2/8 + 3/8 = 5/8.
Watch out: multiply the numerator when you change the denominator, and never add tops and bottoms separately.
Tolak pecahan
5 − 238 = ?
整数减带分数 = nombor bulat tolak nombor bercampur
整数没有分数部分，先从整数借 1，写成“几又八分之八”，然后整数减整数、分数减分数。用加法检查：答案加被减数要等于原来的整数。
例子：4 − 1又2/5 = 3又5/5 − 1又2/5 = 2又3/5。
注意：借了 1 之后整数部分要少 1；分数部分也要真的相减，不能照抄。
a whole number minus a mixed number = nombor bulat tolak nombor bercampur
The whole number has no fraction part, so borrow 1 and write it as eighths over eighths, then subtract wholes and fractions. Check by adding the answer to the number taken away.
Example: 4 − 1 2/5 = 3 5/5 − 1 2/5 = 2 3/5.
Watch out: after borrowing, the whole number is 1 less, and the fraction part must really be subtracted, not copied.
Tambah dan tolak
712 − 16 + 13 = ?
加减混合 = tambah dan tolak
先找一个三个分母都适用的公分母，把所有分数换过去；然后按从左到右的次序先减后加；最后约简。
例子：5/6 − 1/3 + 1/6 = 5/6 − 2/6 + 1/6 = 4/6 = 2/3。
注意：做完第一步不要停，后面的加法也要做；答案要写最简形式。
adding and subtracting = tambah dan tolak
Find a common denominator for all three fractions and change them; then work from left to right, subtracting and then adding; finally simplify.
Example: 5/6 − 1/3 + 1/6 = 5/6 − 2/6 + 1/6 = 4/6 = 2/3.
Watch out: do not stop after the first step, and give the answer in simplest form.
Pecahan daripada kuantiti
58 daripada 72 = ?
求几分之几 = pecahan daripada kuantiti
先用分母把总数平均分，求出一份；再用分子决定要几份，把一份乘分子。也可以写成“分数 × 总数”，先约简再乘。
例子：3/4 daripada 20 → 20 ÷ 4 = 5，5 × 3 = 15。
注意：一份不是答案，还要乘分子；分子乘总数却不除，答案会太大。
a fraction of a quantity = pecahan daripada kuantiti
Use the denominator to share the total equally and find one part; the numerator says how many parts, so multiply one part by it. Or write fraction × total and simplify before multiplying.
Example: 3/4 of 20: 20 ÷ 4 = 5 and 5 × 3 = 15.
Watch out: one part is not the answer, and multiplying without dividing gives far too much.
Tambah perpuluhan
16.07 + 3.9 + 0.458 = ?
小数连加 = tambah perpuluhan berturut-turut
三个数的小数位数不同，先补 0 让它们都有三位小数；小数点对成一直线，从千分位加起，每列满十就进位。
例子：2.5 + 1.25 + 0.125 = 2.500 + 1.250 + 0.125 = 3.875。
注意：按数位对齐，不是按最右边的数字对齐；进位的 1 要加到左边一列。
adding decimals = tambah perpuluhan berturut-turut
The three numbers have different decimal places, so fill zeros to give each three places. Put the points in a line, add from the thousandths and carry whenever a column makes ten.
Example: 2.5 + 1.25 + 0.125 = 2.500 + 1.250 + 0.125 = 3.875.
Watch out: line up by place value, not by the last digit, and add each carried 1 to the next column.
Tolak perpuluhan
30 − 12.64 = ?
整数减小数 = nombor bulat tolak perpuluhan
整数后面补上小数点和 0，和减数的小数位数一样。右边都是 0 不够减，要从左边一路借过来，中间的 0 借位后变成 9。每一位借走 1 以后都要少 1。
例子：20 − 4.75 = 20.00 − 4.75 = 15.25。
注意：借位以后要记得左边那一位少 1，否则整数部分会多出 1。
a whole number minus a decimal = nombor bulat tolak perpuluhan
Give the whole number a point and zeros to match the other number. The zeros on the right are too small, so borrow all the way from the left; the middle zeros become 9, and every place that lends 1 goes down by 1.
Example: 20 − 4.75 = 20.00 − 4.75 = 15.25.
Watch out: after borrowing, the place on the left is 1 less, or the whole number part comes out 1 too big.
Darab perpuluhan
3.086 × 7 = ?
小数乘整数 = darab perpuluhan dengan nombor bulat
先不看小数点，当作整数相乘，每一位都注意进位；原来的小数有几位小数，积就从右边数几位点上小数点。用估算检查：约三乘七。
例子：1.205 × 4 → 1 205 × 4 = 4 820 → 4.820 = 4.82。
注意：小数位数要和原来一样多；中间有 0 的数，乘的时候也要算进位。
a decimal times a whole number = darab perpuluhan dengan nombor bulat
Ignore the point and multiply as whole numbers, watching every carry. The product has as many decimal places as the decimal, counted from the right. Estimate to check: about 3 × 7.
Example: 1.205 × 4: 1205 × 4 = 4820, so 4.820 = 4.82.
Watch out: keep the same number of decimal places, and carries still count across a zero digit.
Bahagi perpuluhan
17.34 ÷ 6 = ?
小数除以整数 = bahagi perpuluhan
用长除法从左边除起。每一步的余数，要和下一位合起来继续除；到了小数点，就在商里对齐点上小数点。最后用“商 × 除数”检查。
例子：8.52 ÷ 4 → 8 ÷ 4 = 2，点小数点，5 ÷ 4 = 1 余 1，12 ÷ 4 = 3 → 2.13。
注意：余数不能丢掉，要带到下一位；商的小数点不能移位。
dividing a decimal = bahagi perpuluhan
Use long division from the left. Each remainder joins the next digit before you divide again; when you reach the point, put the point in the quotient directly above it. Check by multiplying the quotient by the divisor.
Example: 8.52 ÷ 4: 8 ÷ 4 = 2, put in the point, 5 ÷ 4 = 1 r 1, 12 ÷ 4 = 3, giving 2.13.
Watch out: carry every remainder to the next place, and do not shift the point in the quotient.
Pecahan → peratus
1325 = ?%
分数化百分比 = pecahan ke peratus
方法一：把分母变成一百，分子乘同一个数，新的分子就是百分之几。方法二：分数 × 100%，先约简再乘。
例子：7/25 → 7 × 4 = 28 → 28/100 = 28%；或 7/25 × 100% = 7 × 4% = 28%。
注意：分子不能照抄；分子和分母相加也没有意义。
fraction to percent = pecahan ke peratus
Method 1: make the denominator 100 and multiply the numerator by the same number; the new numerator is the percentage. Method 2: fraction × 100%, simplifying before multiplying.
Example: 7/25: 7 × 4 = 28, so 28/100 = 28%; or 7/25 × 100% = 7 × 4% = 28%.
Watch out: do not copy the numerator, and adding the numerator and denominator means nothing.
Peratus → pecahan
32% dalam bentuk termudah ialah …
百分比化最简分数 = peratus ke pecahan termudah
百分比写成一百分之几，再找分子和分母的公因数，同时除以同一个数，一直约到不能再约。
例子：15% = 15/100 = 3/20；44% = 44/100 = 11/25。
注意：分母要用一百，不是十；约分时只除分子或只除分母，分数大小就变了。
percent to simplest fraction = peratus ke pecahan termudah
Write the percentage over 100, then find a common factor of the top and bottom and divide both by it, until you cannot simplify any more.
Example: 15% = 15/100 = 3/20; 44% = 44/100 = 11/25.
Watch out: the denominator is 100, not 10, and dividing only the top or only the bottom changes the fraction.
Peratusan objek
Ada 50 biji telur. 7 biji pecah. Berapa peratus telur tidak pecah?
物件百分比 = peratusan objek
题目问的是“没有破”的鸡蛋。先用全部减去破的，求出没破的个数；再写成“没破的个数 / 全部个数”，化成分母一百。也可以先求破了的百分比，再用百分之一百减去它。
例子：50 个里面 9 个坏了 → 好的 41 个 → 41/50 = 82/100 = 82%。
注意：看清楚题目问哪一部分；求出的个数还不是百分比。
percentage of objects = peratusan objek
The question asks about the eggs that are NOT broken. Subtract to find how many, write that number over the total, and change to hundredths. Or find the broken percentage and take it from 100%.
Example: 9 of 50 are bad, so 41 are good: 41/50 = 82/100 = 82%.
Watch out: check which part is asked about, and a count is not yet a percentage.
Bahagi dengan 100
48.3 ÷ 100 = ?
除以 10、100、1 000 = bahagi dengan 10, 100, 1 000
除以 10、100、1 000 时，数字的次序不变，小数点往左移，移的位数等于 1 后面 0 的个数。数字不够时在前面补 0，个位也要写 0。
例子：36.4 ÷ 100 = 0.364；52 ÷ 1 000 = 0.052。
注意：除法让数变小，所以小数点往左；往右移是乘法。
dividing by 10, 100 or 1 000 = bahagi dengan 10, 100, 1 000
The digits keep their order and the point moves left, as many places as there are zeros. If you run out of digits, write zeros in front, including a 0 in the ones.
Example: 36.4 ÷ 100 = 0.364; 52 ÷ 1 000 = 0.052.
Watch out: division makes the number smaller, so the point moves left; moving right is multiplication.
Anu
□ − 2.46 = 5.8. □ = ?
求被减数 = cari nombor asal
方框是原来的数，减去一个数以后剩下另一个数。所以原来的数 = 剩下的 + 减去的，要用加法。补 0 对齐小数点再加，最后代回去用减法检查。
例子：□ − 1.35 = 4.7 → 4.70 + 1.35 = 6.05；检查 6.05 − 1.35 = 4.7。
注意：求被减数用加法，不是把两个已知数相减；相加时进位别漏。
find the starting number = cari nombor asal
The box is the starting number; after taking a number away, the other number is left. So starting number = what is left + what was taken away, which needs addition. Line up with zeros, add, then check by subtracting.
Example: □ − 1.35 = 4.7: 4.70 + 1.35 = 6.05; check 6.05 − 1.35 = 4.7.
Watch out: find the starting number by adding, not by subtracting the two known numbers, and do not miss a carry.
Adakah melebihi?
Aqil membeli 3 botol minyak. Setiap botol berisi 1.85 ℓ. Adakah jumlah minyak melebihi 5.5 ℓ?
判断是否超过 = adakah melebihi
先算出总量：几瓶一样多用乘法。再把总量和题目给的数比较：补 0 让两个小数的小数位数一样，从最高位开始一位一位比，最先出现不同数字的那一位决定谁比较大。
例子：4 瓶，每瓶 1.3 ℓ → 5.2 ℓ；5.2 和 5.25 比 → 5.20 < 5.25，所以没有超过。
注意：不能只看小数的位数多少来判断大小；“瓶数”是乘数，不是加数。
does it exceed = adakah melebihi
First find the total: equal bottles means multiply. Then compare the total with the amount in the question: fill zeros so both have the same decimal places and compare place by place from the left; the first different digit decides.
Example: 4 bottles of 1.3 ℓ make 5.2 ℓ; compare 5.20 with 5.25: 5.20 is smaller, so it does not exceed.
Watch out: the number of digits does not decide which decimal is bigger, and the number of bottles is a multiplier.
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