Unit 9
Tolak Pecahan
Ada 57 kek lapis di atas meja. Ibu memberi 27 kek itu kepada jiran.
Berapakah bahagian kek yang tinggal? Mari kita tolak pecahan.
tolak pecahan = 分数减法
从一个分数里拿走一部分，或比较两个分数相差多少，都用分数减法。这一课先学分母相同的减法，再学分母不同的减法，答案要写成最简分数。
例子：瓶里有 6/7 瓶水，喝了 1/7 瓶，剩下 5/7 瓶。
注意：减法的分母也不会改变。
tolak pecahan = subtracting fractions
Taking part of a fraction away, or finding how far apart two fractions are, both use subtraction. In this unit we first subtract with the same denominator, then with different denominators, and answers go in simplest form.
Example: a bottle holds 6/7 of water; drink 1/7 and 5/7 is left.
Watch out: in subtraction, too, the denominator stays the same.
Penyebut sama
Tolak pengangka sahaja
57 − 27 = ?
57 − 27 = 5 − 27 = 37
Bahagian kek yang tinggal ialah 37.
penyebut sama = 分母相同
分母相同时，每一份一样大，只要用分子相减，分母照写。5 份拿走 2 份，剩 3 份，每份是七分之一，所以剩 3/7。
例子：6/10 − 1/10 = 5/10 = 1/2。
注意：分母说明每一份有多大，减法只减分子，分母不可以跟着相减。
penyebut sama = same denominator
With the same denominator every part is the same size, so subtract the numerators and keep the denominator. Five parts take away two parts leaves three parts, and each part is one seventh, so 3/7 is left.
Example: 6/10 − 1/10 = 5/10 = 1/2.
Watch out: the denominator tells the size of each part, so only the numerators are subtracted, never the denominators.
Bentuk termudah
Permudahkan jawapan
710 − 110 = ?
→
710 − 110 = 610 = 6 ÷ 210 ÷ 2 = 35
约成最简 = permudahkan jawapan
先用分子相减：7 − 1 = 6，得 6/10。6 和 10 都能被 2 整除，分子分母同时除以 2，得到最简分数 3/5。
例子：5/8 − 3/8 = 2/8，同时除以 2 得 1/4。
注意：减完一定要检查能不能约分，6/10 还不是最简。
permudahkan jawapan = simplify the answer
First subtract the numerators: 7 − 1 = 6, giving 6/10. Both 6 and 10 can be divided by 2, so divide the top and the bottom by 2 to get the simplest form, 3/5.
Example: 5/8 − 3/8 = 2/8; divide both by 2 to get 1/4.
Watch out: always check whether the answer can be simplified; 6/10 is not yet in simplest form.
Cuba kira
89 − 59 = ? (bentuk termudah)
89
59
相减后约分 = tolak, kemudian permudahkan
分母相同，只把分子相减，分母照写。得到的分数再找一个能同时整除分子和分母的数，一起除，写成最简分数。
例子：9/10 − 5/10 = 4/10，分子分母都除以 2，得 2/5。
注意：13/9 是把分子相加了，减法要用减号。
tolak, kemudian permudahkan = subtract, then simplify
The denominators match, so subtract only the numerators and keep the denominator. Then find a number that divides both the numerator and the denominator, and divide both to write the simplest form.
Example: 9/10 − 5/10 = 4/10; divide both by 2 to get 2/5.
Watch out: 13/9 comes from adding the numerators; this is a subtraction.
Garis nombor
Cari beza
Berapakah beza 37 dengan 67?
0
17
27
37
47
57
67
77
67 → 57 → 47 → 37 : undur 3 lompatan
67 − 37 = 37
求差 = cari beza
“相差多少”就是用大的分数减小的分数。在数线上从 6/7 出发，往回跳 3 格，每格七分之一，停在 3/7。用分子算也一样：6 − 3 = 3。
例子：4/10 和 9/10 相差 9/10 − 4/10 = 5/10 = 1/2。
注意：要用大的减小的，顺序不可倒过来。
cari beza = find the difference
The difference between two fractions means the bigger one minus the smaller one. On the number line, start at 6/7 and jump back 3 steps of one seventh each, landing on 3/7. The numerators give the same result: 6 − 3 = 3.
Example: the difference between 4/10 and 9/10 is 9/10 − 4/10 = 5/10 = 1/2.
Watch out: always take the smaller fraction from the bigger one, never the other way round.
Penyebut tak sama
Lihat carta pecahan
12 − 38 = ?
12
48
38
18
12 − 38 = 48 − 38 = 18
分数图 = carta pecahan
分母不同，不能直接减。看分数图：1/2 的长条和 4/8 一样长，所以 1/2 = 4/8。分母相同以后，4/8 − 3/8 = 1/8。
例子：3/4 − 5/8：3/4 = 6/8，6/8 − 5/8 = 1/8。
注意：不可以写成 (1 − 3)/(2 − 8)，分子分母分开乱减是错的。
carta pecahan = fraction chart
The denominators are different, so we cannot subtract straight away. On the fraction chart, the 1/2 bar is as long as 4/8, so 1/2 = 4/8. With matching denominators, 4/8 − 3/8 = 1/8.
Example: 3/4 − 5/8: 3/4 = 6/8, and 6/8 − 5/8 = 1/8.
Watch out: do not subtract the tops and the bottoms separately; that is not how fractions work.
Pecahan setara
Darab untuk samakan penyebut
910 − 25 = ?
910 − 25 = 910 − 2 × 25 × 2
= 910 − 410 = 510
= 5 ÷ 510 ÷ 5 = 12
乘法求等值分数 = darab untuk pecahan setara
五乘二等于十，所以把 2/5 的分子和分母都乘 2，变成 4/10，分母就相同了。再只减分子，得到 5/10，再把分子分母同时除以 5，约成 1/2。
例子：1/3 − 1/9，先把 1/3 的分子分母都乘 3 换成 3/9，再减得 2/9。
注意：分子也要乘 2，2/5 不会变成 2/10。
darab untuk pecahan setara = multiply to get an equivalent fraction
Since 5 × 2 = 10, multiply the top and bottom of 2/5 by 2 to get 4/10, which matches 9/10. Then 9/10 − 4/10 = 5/10, and dividing both by 5 gives 1/2.
Example: 1/3 − 1/9: multiply the top and bottom of 1/3 by 3 to get 3/9, and 3/9 − 1/9 = 2/9.
Watch out: multiply the numerator by 2 as well; 2/5 does not become 2/10.
Bincangkan
Bolehkah kita tolak 23 daripada 49?
能不能减 = boleh tolak atau tidak
“从 A 减去 B”时，B 不可以比 A 大。分母不同时，先把两个分数换成相同的分母再比较大小：哪个分子大，哪个分数就大。
例子：从 3/8 减去 1/2 可以吗？1/2 = 4/8，4/8 比 3/8 大，所以不能减。
注意：只看分子 2 和 4 来比较会上当，要先换分母。
boleh tolak atau tidak = can we subtract or not
When we take B from A, B must not be bigger than A. If the denominators differ, change both fractions to the same denominator before comparing; the bigger numerator then shows the bigger fraction.
Example: can we take 1/2 from 3/8? 1/2 = 4/8, which is bigger than 3/8, so we cannot.
Watch out: comparing only the numerators 2 and 4 is a trap; change the denominators first.
Pecahan yang hilang
Tambah semula atau tolak
? − 37 = 17 · 89 − ? = 59
Cari nombor pertama
? − 37 = 17
17 + 37 = 47 → ? = 47
17 + 37 = 47 → ? = 47
Cari nombor kedua
89 − ? = 59
8 − 3 = 5 → 39 → ? = 13
8 − 3 = 5 → 39 → ? = 13
求被减数和减数 = cari nombor yang hilang
□ 在最前面时，把剩下的和拿走的加回去：1/7 + 3/7 = 4/7。□ 在减号后面时，想 8 减几等于 5，得 3，所以是 3/9 = 1/3。
例子：□ − 1/8 = 2/8 → 2/8 + 1/8 = 3/8。
注意：□ 在前面要用加法，□ 在后面才用减法。
cari nombor yang hilang = find the missing number
When the box comes first, add the two parts back together: 1/7 + 3/7 = 4/7. When the box comes after the minus sign, ask 8 minus what makes 5; it is 3, so 3/9 = 1/3.
Example: □ − 1/8 = 2/8 → 2/8 + 1/8 = 3/8.
Watch out: a box at the front needs adding back; a box after the minus sign needs subtracting.
Cari kesilapan
Lina menulis:
58 − 14 = 5 − 18 − 4 = 44 = 1
Apakah jawapan yang betul?
找错 = cari kesilapan
Lina 把分子减分子、分母也减分母，这是不对的。正确做法：先把分母换成一样，再只减分子，分母不动。也可以估一估：答案不可能比 5/8 还大。
例子：9/10 − 1/5：1/5 = 2/10，9/10 − 2/10 = 7/10。
注意：4/8 是没有换分母就直接 5 − 1 的结果。
cari kesilapan = find the mistake
Lina subtracted the numerators and also the denominators, which is wrong. The right way is to make the denominators the same first, then subtract only the numerators. Estimating helps too: the answer cannot be bigger than 5/8.
Example: 9/10 − 1/5: 1/5 = 2/10, and 9/10 − 2/10 = 7/10.
Watch out: 4/8 is what you get by doing 5 − 1 without changing the denominator.
Padankan
Beza dalam bentuk termudah
配对 = padankan
每一题先看分母：相同就直接减分子；不同就把分母较小的分数换成等值分数。减好以后看能不能约分，约到最简再找配对。
例子：9/10 − 7/10 = 2/10 = 1/5。
注意：减完的分数如果还没约到最简，就找不到配对的卡。
padankan = match
For each one, look at the denominators first: if they match, subtract the numerators; if not, change the fraction with the smaller denominator into an equivalent fraction. After subtracting, simplify, then find the matching card.
Example: 9/10 − 7/10 = 2/10 = 1/5.
Watch out: if a result is not yet in simplest form, you will not find a card that matches it.
Ringkasan
Syabas!
Samakan penyebut → tolak pengangka → permudahkan
Jika penyebut sama, tolak pengangka sahaja. Jika penyebut tidak sama, cari pecahan setara dahulu. Tulis jawapan dalam bentuk termudah.
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