Unit 4
Tambah Pecahan
Hari Sukan: Irfan berlari 310 km, kemudian berjalan 410 km.
Berapakah jarak yang dilalui semuanya?
分数加法 = tambah pecahan
把两段路程合起来，要用加法。这个单元学怎样把分数、带分数和整数加起来，包括分母相同和分母不同的情况，最后把答案写成最简形式或带分数。
例子：1/5 + 2/5 = 3/5。
注意：分数相加以前，先看分母是否相同。
adding fractions = tambah pecahan
To put two distances together we add. In this unit we add fractions, mixed numbers and whole numbers, with the same or different denominators, and write the answer in simplest form or as a mixed number.
Example: 1/5 + 2/5 = 3/5.
Watch out: before adding, check whether the denominators are the same.
Penyebut sama
Tambah pengangka sahaja
310 + 410
同分母相加 = penyebut sama
分母相同，表示每一份一样大，只要数一数一共有几份：3 份 + 4 份 = 7 份，每份还是 1/10，所以答案是 7/10。分母保持不变。
例子：2/9 + 5/9 = 7/9。
注意：分母不能相加。
same denominators = penyebut sama
The same denominator means every part is the same size, so just count the parts: 3 parts + 4 parts = 7 parts, and each part is still 1/10, so the answer is 7/10. The denominator stays the same.
Example: 2/9 + 5/9 = 7/9.
Watch out: never add the denominators.
Cari kesilapan
Adakah 310 + 410 = 720?
✘ Salah
310 + 410 = 720
penyebut ditambah✔ Betul
310 + 410 = 710
找错 = cari kesilapan
把分母也加起来得到 7/20，这是错的。检查一下：7/20 比原来的 4/10（= 8/20）还小，加了以后反而变小，不合理。分母表示每份的大小，相加时不会改变。
例子：1/4 + 1/4 = 2/4，不是 2/8。
注意：用“答案要变大”来检查。
find the mistake = cari kesilapan
Adding the denominators as well gives 7/20, which is wrong. Check: 7/20 is even smaller than 4/10 (which is 8/20), so adding made it smaller, which cannot be right. The denominator shows the size of each part and does not change when adding.
Example: 1/4 + 1/4 = 2/4, not 2/8.
Watch out: use the idea that a sum must get bigger to check.
Tiga pecahan
Jawapan pecahan tak wajar → nombor bercampur
27 + 37 + 47
0
27
57
1
127
2
27 + 37 + 47 = 97 = 127
三个分数 = tiga pecahan
分母都是 7，分子直接相加：2 + 3 + 4 = 9，得 9/7。9/7 是假分数，要化成带分数：9 ÷ 7 = 1 余 2，所以是 1又2/7。在数线上跳三次也会停在 9/7。
例子：3/5 + 4/5 + 1/5 = 8/5 = 1又3/5。
注意：答案是假分数时，要换成带分数。
three fractions = tiga pecahan
All the denominators are 7, so add the numerators: 2 + 3 + 4 = 9, giving 9/7. 9/7 is improper, so change it to a mixed number: 9 ÷ 7 = 1 remainder 2, which is 1 2/7. Jumping three times on the number line also lands on 9/7.
Example: 3/5 + 4/5 + 1/5 = 8/5 = 1 3/5.
Watch out: change an improper answer into a mixed number.
Nombor bulat dan pecahan
Tambah nombor bulat, kemudian pecahan
125 + 4 + 45
= (1 + 4) + (25 + 45)
= 5 + 65
= 5 + 115 = 615
= 5 + 65
= 5 + 115 = 615
整数和分数分开加 = tambah nombor bulat dan pecahan berasingan
把整数部分加在一起：1 + 4 = 5；分数部分加在一起：2/5 + 4/5 = 6/5 = 1又1/5。最后把两部分合起来：5 + 1又1/5 = 6又1/5。
例子：2又1/3 + 1 + 1/3 = 3又2/3。
注意：分数部分满 1 的，要进到整数部分。
add the whole numbers and fractions separately = tambah berasingan
Add the whole numbers: 1 + 4 = 5. Add the fractions: 2/5 + 4/5 = 6/5 = 1 1/5. Put them together: 5 + 1 1/5 = 6 1/5.
Example: 2 1/3 + 1 + 1/3 = 3 2/3.
Watch out: if the fractions make 1 or more, carry it into the whole number.
Tiga nombor bercampur
Jawapan dalam bentuk termudah
316 + 146 + 256
= 6 + 106 = 6 + 146
= 746 = 723
= 746 = 723
4 ÷ 2 = 2, 6 ÷ 2 = 3 → bentuk termudah
最简形式 = bentuk termudah
分数的分子和分母如果都能被同一个数整除，就要约简到不能再约为止，这叫最简形式。4/6 的分子分母都能被 2 整除，得 2/3，所以 7又4/6 要写成 7又2/3。
例子：6/8 = 3/4；5/10 = 1/2。
注意：答案一般都要写成最简形式。
simplest form = bentuk termudah
If the numerator and denominator can both be divided by the same number, divide them until you cannot any more; this is the simplest form. 4/6 can be divided by 2 to give 2/3, so 7 4/6 should be written 7 2/3.
Example: 6/8 = 3/4; 5/10 = 1/2.
Watch out: answers should normally be in simplest form.
Pecahan yang tidak diketahui
35 + □ = 125
Tukar kepada pecahan tak wajar
35 + □ = 75
□ = 75 − 35 = 45
□ = 75 − 35 = 45
求缺的分数 = cari pecahan yang hilang
先把 1又2/5 换成假分数 7/5，这样两边的分母都是 5。3 份加几份等于 7 份？7 − 3 = 4，所以缺的是 4/5。检查：3/5 + 4/5 = 7/5 = 1又2/5。
例子：1/4 + □ = 1又1/4 → 5/4 − 1/4 = 4/4 = 1。
注意：求加法里缺的数，用减法。
find the missing fraction = cari pecahan yang hilang
Change 1 2/5 to 7/5 so both sides have fifths. 3 parts plus how many make 7 parts? 7 − 3 = 4, so the missing fraction is 4/5. Check: 3/5 + 4/5 = 7/5 = 1 2/5.
Example: 1/4 + □ = 1 1/4, so 5/4 − 1/4 = 4/4 = 1.
Watch out: to find a missing number in addition, subtract.
Penyebut berbeza
Tukar kepada pecahan setara
14 + 23
等值分数 = pecahan setara
分母不同时，每份大小不一样，不能直接加。先把它们换成分母相同的等值分数：1/4 = 3/12（分子分母都乘 3），2/3 = 8/12（都乘 4）。然后 3/12 + 8/12 = 11/12。
例子：1/2 + 1/3 = 3/6 + 2/6 = 5/6。
注意：分子和分母要乘同一个数。
equivalent fractions = pecahan setara
With different denominators the parts are different sizes, so we cannot add straight away. Change them into equivalent fractions with the same denominator: 1/4 = 3/12 (multiply top and bottom by 3) and 2/3 = 8/12 (multiply by 4). Then 3/12 + 8/12 = 11/12.
Example: 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
Watch out: multiply the numerator and denominator by the same number.
Penyebut sama yang paling kecil
Gunakan sifir
56 + 34
Sifir
| 6 | 4 |
|---|---|
| 6 | 4 |
| 12 | 8 |
| 18 | 12 |
Kira
1012 + 912
= 1912
= 1712
= 1912
= 1712
最小公分母 = penyebut sama yang paling kecil
先把两个分母的倍数分别写出来：六的倍数有六、十二、十八，四的倍数有四、八、十二。两边第一个共同出现的数是十二，它就是最小公分母。把两个分数都换成十二分之几，再相加，最后化成带分数 1又7/12。
例子：1/6 + 1/9：6、12、18 与 9、18 → 3/18 + 2/18 = 5/18。
注意：用最小的公分母，数字比较小，也比较容易约简。
the smallest common denominator = penyebut sama yang paling kecil
Write out the multiples of both denominators: 6, 12, 18 and 4, 8, 12. The first one they share, 12, is the smallest common denominator. 5/6 = 10/12 and 3/4 = 9/12, which add to 19/12 = 1 7/12.
Example: 1/6 + 1/9: 6, 12, 18 and 9, 18, so 3/18 + 2/18 = 5/18.
Watch out: the smallest common denominator keeps the numbers small and easy to simplify.
Cara lain
Darab silang penyebut
14 + 56
Darab silang: 4 × 6 = 24
624 + 2024
= 2624 = 1224
= 1112
= 2624 = 1224
= 1112
Sifir: 12
312 + 1012
= 1312
= 1112
= 1312
= 1112
交叉相乘求公分母 = darab silang
另一个找公分母的方法是把两个分母相乘：4 × 6 = 24，一定是两个分母的公倍数。1/4 = 6/24，5/6 = 20/24，相加得 26/24 = 1又2/24，再约简成 1又1/12。用倍数表找到的最小公分母 12，也得到同样的答案，而且数字比较小。
例子：1/2 + 1/3：2 × 3 = 6 → 3/6 + 2/6 = 5/6。
注意：两个分母相乘得到的不一定是最小公分母，所以最后一定要检查能不能约简。
cross multiply the denominators = darab silang
Another way to find a common denominator is to multiply the two denominators: 4 × 6 = 24 is always a common multiple. 1/4 = 6/24 and 5/6 = 20/24, which add to 26/24 = 1 2/24, simplified to 1 1/12. Using multiples to find the smallest common denominator, 12, gives the same answer with smaller numbers.
Example: 1/2 + 1/3: 2 × 3 = 6, so 3/6 + 2/6 = 5/6.
Watch out: the product of the denominators is not always the smallest one, so always check whether the answer can be simplified.
Nombor bercampur, penyebut berbeza
Tambah nombor bulat dan pecahan
238 + 156
= 3 + 924 + 2024
= 3 + 2924 = 3 + 1524
= 4524
= 3 + 2924 = 3 + 1524
= 4524
带分数、分母不同 = nombor bercampur, penyebut berbeza
整数部分先加：2 + 1 = 3。分数部分找最小公分母：8 的倍数 8、16、24，6 的倍数 6、12、18、24，所以用 24。3/8 = 9/24，5/6 = 20/24，相加 29/24 = 1又5/24。合起来 4又5/24。
例子：1又1/2 + 2又1/3 = 3 + 3/6 + 2/6 = 3又5/6。
注意：分数部分满 1 要进位。
mixed numbers with different denominators = nombor bercampur, penyebut berbeza
Add the whole numbers first: 2 + 1 = 3. For the fractions, find the smallest common denominator: multiples of 8 are 8, 16, 24 and of 6 are 6, 12, 18, 24, so use 24. 3/8 = 9/24 and 5/6 = 20/24, which add to 29/24 = 1 5/24. Together: 4 5/24.
Example: 1 1/2 + 2 1/3 = 3 + 3/6 + 2/6 = 3 5/6.
Watch out: if the fractions make 1 or more, carry it.
Cari kesilapan
112 + 225 = 3710?
Semak pecahan setara
✘ Salah
25 → 210
pengangka tidak didarab✔ Betul
25 = 410
× 2 atas dan bawah1510 + 2410 = 3910
找等值分数的错 = cari kesilapan pecahan setara
这位同学把 2/5 换成十分之几时，只把分母乘 2，分子没有乘，写成 2/10，结果答案变小了。等值分数的分子和分母必须乘同一个数：2/5 = (2 × 2)/(5 × 2) = 4/10。改正后 5/10 + 4/10 = 9/10，答案是 3又9/10。
例子：3/4 换成八分之几：分子分母都乘 2，得 6/8，不是 3/8。
注意：换好以后问自己：新分数和原来的分数一样大吗？
find the equivalent fraction mistake = cari kesilapan pecahan setara
This pupil changed 2/5 into tenths by multiplying only the denominator by 2, writing 2/10, so the answer became too small. For an equivalent fraction the numerator and denominator are multiplied by the same number: 2/5 = (2 × 2)/(5 × 2) = 4/10. After correcting, 5/10 + 4/10 = 9/10, so the answer is 3 9/10.
Example: 3/4 in eighths: multiply both by 2 to get 6/8, not 3/8.
Watch out: after changing, ask yourself whether the new fraction is the same size as before.
Bentuk termudah
Semak jawapan akhir
1110 + 225
= 1110 + 2410 = 3510
= 312
= 312
5 ÷ 5 = 1, 10 ÷ 5 = 2
最后检查最简形式 = semak bentuk termudah
算完以后要看分数部分还能不能约简。5/10 的分子分母都能被 5 整除，得 1/2，所以答案写成 3又1/2，不写 3又5/10。两种写法大小一样，但最简形式比较清楚。
例子：2又4/8 = 2又1/2。
注意：约简时要用同一个数去除分子和分母。
check for simplest form = semak bentuk termudah
After calculating, see whether the fraction part can be simplified. In 5/10 both numbers can be divided by 5 to give 1/2, so write 3 1/2, not 3 5/10. Both are the same size, but the simplest form is clearer.
Example: 2 4/8 = 2 1/2.
Watch out: divide the numerator and the denominator by the same number.
Tiga penyebut berbeza
Cari penyebut sama bagi 2, 5 dan 10
12 + 25 + 310
= 510 + 410 + 310
= 1210 = 1210 = 115
= 1210 = 1210 = 115
三个不同分母 = tiga penyebut berbeza
找一个三个分母都能整除的最小数：2、5、10 的倍数里，10 最先同时出现，所以都换成十分之几：5/10 + 4/10 + 3/10 = 12/10 = 1又2/10 = 1又1/5。
例子：1/2 + 1/4 + 1/8 = 4/8 + 2/8 + 1/8 = 7/8。
注意：其中一个分母本身就是公分母时，那个分数不用变。
three different denominators = tiga penyebut berbeza
Find the smallest number that 2, 5 and 10 all divide into; 10 is the first shared multiple, so change everything into tenths: 5/10 + 4/10 + 3/10 = 12/10 = 1 2/10 = 1 1/5.
Example: 1/2 + 1/4 + 1/8 = 4/8 + 2/8 + 1/8 = 7/8.
Watch out: if one denominator is already the common denominator, that fraction stays the same.
Semak cepat
59 + 79 = ?
同分母加法与约简 = tambah dan permudahkan
分母相同，只把分子相加，分母不变。如果得到假分数，就用除法化成带分数；最后看分数部分的分子和分母能不能被同一个数整除，约到最简形式。
例子：4/6 + 5/6 = 9/6 = 1又3/6 = 1又1/2。
注意：分母相同时不能把分母也加起来；化成带分数时，整数部分只能是商。
add and simplify = tambah dan permudahkan
When the denominators match, add only the numerators and keep the denominator. If the result is improper, divide to make a mixed number, then see whether the fraction part can be simplified.
Example: 4/6 + 5/6 = 9/6 = 1 3/6 = 1 1/2.
Watch out: do not add the denominators, and the whole number part is only the quotient of the division.
Penyebut berbeza
23 + 34 = ?
异分母相加 = tambah penyebut berbeza
两个分母不同，先写出两个分母的倍数，找最先相同的数做公分母；把两个分数都换成这个分母（分子和分母乘同一个数），再把分子相加，最后化成带分数。
例子：1/3 + 1/4 = 4/12 + 3/12 = 7/12。
注意：分子加分子、分母加分母是错误的做法，得到的数甚至比其中一个分数还小。
adding with different denominators = tambah penyebut berbeza
The denominators are different, so list their multiples and choose the first shared one as the common denominator. Change both fractions to it, add the numerators, then change the result into a mixed number.
Example: 1/3 + 1/4 = 4/12 + 3/12 = 7/12.
Watch out: adding tops and bottoms separately is wrong; it can even give less than one of the fractions.
Nombor bercampur
134 + 216 = ?
带分数相加 = tambah nombor bercampur
带分数相加可以分两部分：整数加整数；分数加分数（分母不同就先找最小公分母）。分数部分的和如果满 1，就要进位到整数；不满 1 就直接合起来。
例子：2又1/4 + 1又1/2 = 3 + 1/4 + 2/4 = 3又3/4。
注意：分数部分不能分子加分子、分母加分母；也要检查分数和是否已经满 1。
adding mixed numbers = tambah nombor bercampur
Split the work into two parts: add the whole numbers, then add the fractions (finding the smallest common denominator if they differ). If the fractions make 1 or more, carry 1 into the whole number; if not, just put the parts together.
Example: 2 1/4 + 1 1/2 = 3 + 1/4 + 2/4 = 3 3/4.
Watch out: never add tops and bottoms separately, and check whether the fraction sum reaches 1.
Ringkasan
Syabas!
+
Penyebut sama: tambah pengangka. Penyebut berbeza: tukar kepada pecahan setara dahulu. Permudahkan jawapan akhir.
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