Tolak Pecahan

同分母相减 = penyebut sama 分母相同，每份一样大，只要把分子相减：五份减一份剩四份，分母仍是六，得 1又4/6。四和六都能被二整除，约简成 1又2/3，这就是最简形式。 例子：2又7/8 − 3/8 = 2又4/8 = 2又1/2。 注意：分母保持不变，答案要约简。

same denominators = penyebut sama With the same denominator the parts are the same size, so subtract the numerators: 5 parts − 1 part = 4 parts, with the denominator 6, giving 1 4/6. Both 4 and 6 divide by 2, so it simplifies to 1 2/3. Example: 2 7/8 − 3/8 = 2 4/8 = 2 1/2. Watch out: keep the denominator and simplify the answer.

找错 = cari kesilapan 把分母也相减，九减九得零，变成分母是零的分数，这是没有意义的，因为分母表示把整体分成几份，不能是零。正确做法是分母保持九，只减分子，得九分之三，再约成三分之一。 例子：6/7 − 2/7 = 4/7。 注意：加法和减法都不能改变分母。

find the mistake = cari kesilapan Subtracting the denominators as well gives 9 − 9 = 0, and a denominator of 0 has no meaning, because the denominator tells how many parts the whole is cut into. The correct way keeps 9 and subtracts only the numerators: 3/9, which simplifies to 1/3. Example: 6/7 − 2/7 = 4/7. Watch out: adding and subtracting never change the denominator.

从 1 减 = tolak daripada 1 1 可以写成分母相同的分数：要减八分之几，就把 1 写成八分之八。八份减三份剩五份，所以答案是八分之五。在数线上从 1 往左数三格，也停在八分之五。 例子：1 − 2/5 = 5/5 − 2/5 = 3/5。 注意：1 要换成和另一个分数一样的分母。

subtract from 1 = tolak daripada 1 1 can be written as a fraction with the same denominator: to take away eighths, write 1 as 8/8. 8 parts − 3 parts = 5 parts, so 5/8. On the number line, count 3 steps back from 1 and you also land on 5/8. Example: 1 − 2/5 = 5/5 − 2/5 = 3/5. Watch out: write 1 with the same denominator as the other fraction.

整数减带分数 = nombor bulat tolak nombor bercampur 方法一：从 5 借出 1，写成 4又3/3，这样分数部分就够减：4又3/3 − 2又2/3 = 2又1/3。方法二：把两个数都换成假分数：5 = 15/3，2又2/3 = 8/3，15/3 − 8/3 = 7/3 = 2又1/3。 例子：4 − 1又1/4 = 3又4/4 − 1又1/4 = 2又3/4。 注意：借出的 1 要换成分母相同的分数。

whole number minus a mixed number = nombor bulat tolak nombor bercampur Method 1: borrow 1 from 5 and write 4 3/3, so the fraction part can be subtracted: 4 3/3 − 2 2/3 = 2 1/3. Method 2: change both into improper fractions: 5 = 15/3 and 2 2/3 = 8/3, and 15/3 − 8/3 = 7/3 = 2 1/3. Example: 4 − 1 1/4 = 3 4/4 − 1 1/4 = 2 3/4. Watch out: the borrowed 1 must be written with the same denominator.

连减 = tolak berturut-turut 方法一（借 1）：7又1/5 的分数部分不够减 3/5，借 1 写成 6又6/5，减后得 6又3/5；再减 3又4/5 时又不够减，再借 1 写成 5又8/5，减后得 2又4/5。方法二（假分数）：7又1/5 = 36/5，3又4/5 = 19/5，分子连减 36 − 3 − 19 = 14，得 14/5 = 2又4/5。两种方法答案相同。 例子：3又1/4 − 1/4 − 1又3/4 = 13/4 − 1/4 − 7/4 = 5/4 = 1又1/4。 注意：从左到右连续减，不要漏掉任何一个数。

subtract twice = tolak berturut-turut Method 1 (borrow 1): 1/5 is less than 3/5, so write 7 1/5 as 6 6/5 and subtract to get 6 3/5; 3/5 is less than 4/5, so borrow again, 5 8/5 − 3 4/5 = 2 4/5. Method 2 (improper fractions): 7 1/5 = 36/5 and 3 4/5 = 19/5, and 36 − 3 − 19 = 14, giving 14/5 = 2 4/5. Both methods agree. Example: 3 1/4 − 1/4 − 1 3/4 = 13/4 − 1/4 − 7/4 = 5/4 = 1 1/4. Watch out: subtract from left to right and do not miss any number.

异分母带分数相减 = penyebut berbeza 先减整数：4 − 2 = 2。分数部分分母不同，用倍数表找最小公分母（也就是两个分母的最小公倍数，马来文叫 GSTK，gandaan sepunya terkecil）：四的倍数四、八、十二，六的倍数六、十二，所以是十二。四分之三换成十二分之九，六分之一换成十二分之二，相减得十二分之七。答案 2又7/12。 例子：3又1/2 − 1又1/3 = 2 + 3/6 − 2/6 = 2又1/6。 注意：换分母时，分子也要乘同一个数。

different denominators = penyebut berbeza Subtract the whole numbers first: 4 − 2 = 2. The fractions have different denominators, so use the times tables to find the smallest common denominator, 12. This is the lowest common multiple, called GSTK (gandaan sepunya terkecil) in Malay. 3/4 = 9/12 and 1/6 = 2/12, and 9/12 − 2/12 = 7/12. The answer is 2 7/12. Example: 3 1/2 − 1 1/3 = 2 + 3/6 − 2/6 = 2 1/6. Watch out: when changing the denominator, multiply the numerator by the same number.

减法中的未知数 = anu dalam tolak 要求被减去的数，用原来的数减去剩下的数。先把两个带分数都换成七分之几：2又3/7 是十七份，1又5/7 是十二份。十七份减十二份等于五份，所以缺的是七分之五。放回去检查：2又3/7 − 5/7 = 1又5/7，对了。 例子：2 − □ = 1又1/4 → □ = 3/4。 注意：先统一成假分数，比较不容易算错。

the unknown in subtraction = anu dalam tolak To find the number taken away, subtract what is left from the starting number. Change both mixed numbers into sevenths: 2 3/7 is 17 sevenths and 1 5/7 is 12 sevenths. 17 − 12 = 5, so the missing number is 5/7. Check: 2 3/7 − 5/7 = 1 5/7. Example: 2 − □ = 1 1/4, so □ = 3/4. Watch out: using improper fractions makes mistakes less likely.

三个不同分母 = tiga penyebut berbeza 三、四、六的最小公分母是十二，把三个分数都换成十二分之几。第一步从左减：5又4/12 − 3/12 = 5又1/12。第二步分数部分十二分之一不够减十二分之十，要借一：写成 4又13/12，再减得 3又3/12，约简成 3又1/4。方法二是全部换成假分数：64/12 − 3/12 − 22/12 = 39/12 = 3又1/4，答案一样。 例子：2又1/2 − 1/4 − 1/8 = 2又4/8 − 2/8 − 1/8 = 2又1/8。 注意：分数不够减时，从整数借 1。

three different denominators = tiga penyebut berbeza The smallest common denominator of 3, 4 and 6 is 12, so change all three into twelfths. Step 1, from the left: 5 4/12 − 3/12 = 5 1/12. Step 2: 1/12 is less than 10/12, so borrow 1 and write 4 13/12, then subtract to get 3 3/12, which simplifies to 3 1/4. Method 2 uses improper fractions: 64/12 − 3/12 − 22/12 = 39/12 = 3 1/4, the same answer. Example: 2 1/2 − 1/4 − 1/8 = 2 4/8 − 2/8 − 1/8 = 2 1/8. Watch out: when the fraction is too small, borrow 1 from the whole number.

整数连减两个分数 = nombor bulat tolak dua pecahan 第一步：8 − 3又2/5，从 8 借 1 写成 7又5/5，减后得 4又3/5。第二步：五和四的最小公分母是二十，4又3/5 换成 4又12/20，四分之三换成二十分之十五。十二不够减十五，再借一，变成 3又32/20，减后得 3又17/20。 例子：5 − 1又1/2 − 1/3 = 3又1/2 − 1/3 = 3又1/6。 注意：每一步都检查分数够不够减。

a whole number minus two fractions = nombor bulat tolak dua pecahan Step 1: 8 − 3 2/5; borrow 1 from 8 to write 7 5/5, leaving 4 3/5. Step 2: the smallest common denominator of 5 and 4 is 20, so 4 3/5 = 4 12/20 and 3/4 = 15/20. 12 is less than 15, so borrow again to get 3 32/20, and subtract to get 3 17/20. Example: 5 − 1 1/2 − 1/3 = 3 1/2 − 1/3 = 3 1/6. Watch out: at each step check whether the fraction is big enough to subtract from.

同分母相减再约简 = tolak dan permudahkan 分母相同时，只把分子相减，分母保持不变；减完以后，找一个能同时整除分子和分母的数，把分数约到最简形式。题目要求最简形式。 例子：9/12 − 3/12 = 6/12 = 1/2。 注意：分母不能相减，分母变成零的分数是没有意义的。

subtract and simplify = tolak dan permudahkan When the denominators are the same, subtract only the numerators and keep the denominator. Then find a number that divides both the numerator and the denominator and simplify. The question asks for simplest form. Example: 9/12 − 3/12 = 6/12 = 1/2. Watch out: never subtract the denominators; a fraction with a denominator of zero has no meaning.

借 1 = pinjam 1 整数没有分数部分，不能直接减带分数。从整数借出 1，写成“几又八分之八”，然后整数减整数、分数减分数。最后用加法检查：答案加上被减的数，要等于原来的整数。 例子：2 − 1/6 = 1又6/6 − 1/6 = 1又5/6。 注意：借了 1 以后，整数部分要少 1；整数部分也要记得相减。

borrow 1 = pinjam 1 A whole number has no fraction part, so borrow 1 and write it as eighths over eighths. Then subtract whole from whole and fraction from fraction. Check by adding the answer to the number taken away; you should get the whole number back. Example: 2 − 1/6 = 1 6/6 − 1/6 = 1 5/6. Watch out: after borrowing, the whole number is 1 smaller, and remember to subtract the whole numbers too.

异分母并借位 = penyebut berbeza dan pinjam 先找两个分母的最小公分母，把两个分数部分都换成同一个分母。然后比较：前面的分数部分如果比后面的小，就要从整数借 1，再减。 例子：2又1/4 − 1又1/2 = 2又1/4 − 1又2/4 = 1又5/4 − 1又2/4 = 3/4。 注意：不够减时，不可以把两个分数部分倒过来减，要借 1。

different denominators with borrowing = penyebut berbeza dan pinjam Find the smallest common denominator and change both fraction parts to it. Then compare them: if the first fraction part is smaller, borrow 1 from the whole number before subtracting. Example: 2 1/4 − 1 1/2 = 2 1/4 − 1 2/4 = 1 5/4 − 1 2/4 = 3/4. Watch out: when the first fraction is too small, do not swap the fractions round; borrow 1 instead.