Tolak Perpuluhan

竖式减法 = tolak bentuk lazim 小数点对齐以后，从十分位减起：三不够减八，要向个位借一，一个一等于十个零点一，所以变成十三减八得五；个位五借走一变四，四减四得零；十位一。答案 10.5 公斤。 例子：7.2 − 3.6 = 3.6。 注意：借位以后，那一位要少一。

column subtraction = tolak bentuk lazim With the points lined up, start at the tenths: 3 is less than 8, so borrow 1 from the ones; one whole is ten tenths, so it becomes 13 − 8 = 5. The ones digit 5 becomes 4, and 4 − 4 = 0; the tens digit is 1. The answer is 10.5 kg. Example: 7.2 − 3.6 = 3.6. Watch out: after borrowing, that place is 1 less.

数线往回跳 = lompat ke belakang 减一点五可以分成两步：先减一，从九点二跳到八点二；再减零点五，往回跳五小格，从八点二到七点七。减法在数线上就是往左边走。 例子：6.3 − 1.4 → 6.3 − 1 = 5.3，再 − 0.4 = 4.9。 注意：跨过整数八的时候，八点零的前一格是七点九。

jump backwards on the number line = lompat ke belakang Taking away 1.5 can be done in two steps: take 1 to go from 9.2 to 8.2, then take 0.5 by jumping back 5 small steps to 7.7. Subtraction moves to the left on the number line. Example: 6.3 − 1.4: 6.3 − 1 = 5.3, then − 0.4 = 4.9. Watch out: when passing 8, the step before 8.0 is 7.9.

补 0 再减 = tulis sifar dahulu 被减数 2.5 只有一位小数，减数 0.36 有两位。先在 2.5 后面补 0 写成 2.50，百分位才有数可以减。零不够减六，向十分位借一，得十减六等于四；十分位五借走一变四，四减三得一。答案 2.14。 例子：4.2 − 1.15 = 4.20 − 1.15 = 3.05。 注意：不补 0 很容易把 6 直接写下来，这是错的。

write a zero first = tulis sifar dahulu 2.5 has one decimal place and 0.36 has two. Write 2.5 as 2.50 so the hundredths place has a digit. 0 is less than 6, so borrow from the tenths: 10 − 6 = 4; the tenths 5 becomes 4, and 4 − 3 = 1. The answer is 2.14. Example: 4.2 − 1.15 = 4.20 − 1.15 = 3.05. Watch out: without the zero it is easy to copy the 6 down, which is wrong.

找错 = cari kesilapan 整数 2 是两个一，它的小数点在 2 的后面，所以 2 要写在个位 6 的下面，而不是写在最右边。错误的写法把 2 当成 0.002 来减，得到 6.252。正确答案是 4.254。 例子：3.75 − 1 = 2.75。 注意：整数减小数或小数减整数，都要先对齐小数点。

find the mistake = cari kesilapan The whole number 2 means two ones; its decimal point is after the 2, so the 2 goes under the ones digit 6, not at the far right. The wrong working treats 2 as 0.002 and gets 6.252. The correct answer is 4.254. Example: 3.75 − 1 = 2.75. Watch out: always line up the decimal points first.

整数连减 = nombor bulat tolak berturut-turut 先把八写成 8.00，减 0.75 得 7.25；再把 7.25 写成 7.250，减 3.108 得 4.142。每一步都补零、对齐小数点，从右边减起。 例子：5 − 0.5 − 1.25 = 4.5 − 1.25 = 3.25。 注意：整数后面补零时，要补到和另一个数一样多的小数位。

a whole number minus two decimals = nombor bulat tolak berturut-turut Write 8 as 8.00 and take away 0.75 to get 7.25; then write 7.25 as 7.250 and take away 3.108 to get 4.142. At each step fill in zeros, line up the points and subtract from the right. Example: 5 − 0.5 − 1.25 = 4.5 − 1.25 = 3.25. Watch out: add enough zeros to match the other number's decimal places.

小数连减 = tolak perpuluhan berturut-turut 按从左到右的次序：先把四十三点六写成四十三点六零，减去十五点二七，得二十八点三三；再补零写成二十八点三三零，减去零点八五三，得二十七点四七七。也可以先把两个要减的数加起来，再从原来的数一次减掉，答案一样。 例子：10.5 − 2.25 − 3.1 = 5.15。 注意：连续借位时，每一位都要记得少一。

subtract two decimals in a row = tolak perpuluhan berturut-turut From left to right: 43.60 − 15.27 = 28.33, then 28.330 − 0.853 = 27.477. You can also add the two numbers taken away first: 15.27 + 0.853 = 16.123, then 43.6 − 16.123 gives the same answer. Example: 10.5 − 2.25 − 3.1 = 5.15. Watch out: when borrowing across several places, each place goes down by 1.

求减数 = cari nombor yang ditolak 原来的数是二十三点五，减去某个数以后剩八点六四。被减去的数等于原来的数减去剩下的数，先补零写成二十三点五零，再减八点六四，得十四点八六。最后用原来的数减去十四点八六检查，刚好剩八点六四。 例子：9 − □ = 4.5 → □ = 4.5。 注意：被减去的数要用减法求，不是加法。

find the number taken away = cari nombor yang ditolak The starting number is 23.5 and 8.64 is left, so the number taken away is 23.50 − 8.64 = 14.86. Check: 23.50 − 14.86 = 8.64. Example: 9 − □ = 4.5, so □ = 4.5. Watch out: the number taken away is found by subtracting, not adding.

补 0 与借位 = sifar dan kumpul semula 两个数的小数位数不同，先在较短的数后面补 0，让小数点和每一位都对齐；从百分位开始减，不够减就向左边一位借 1（借来的 1 等于右边一位的 10）。 例子：6.04 − 1.7 = 6.04 − 1.70 → 十分位 0 不够减 7，借 1 得 10 − 7 = 3，个位 6 − 1 − 1 = 4 → 4.34。 注意：一位小数的数字在十分位，要写在十分位下面，不能对着百分位写。

zeros and borrowing = sifar dan kumpul semula The numbers have different numbers of decimal places, so put a zero after the shorter one to line up every place. Subtract from the hundredths, borrowing 1 from the place on the left when a digit is too small (that 1 is worth 10 in the place on the right). Example: 6.04 − 1.7 = 6.04 − 1.70: tenths 0 is less than 7, so borrow, 10 − 7 = 3; ones 6 − 1 − 1 = 4, giving 4.34. Watch out: the digit of a one-place decimal belongs in the tenths, not under the hundredths.

从整数减 = tolak daripada nombor bulat 整数后面补上小数点和三个 0，和减数的小数位数一样。右边几位都是 0，不够减，要从个位开始一路借过来：中间几位借了又被借走，都变成 9，最右边一位变成 10。 例子：5 − 1.25 = 5.00 − 1.25：借位后变成 4、9、10 → 3.75。 注意：小数部分也要减，不能只把整数部分相减；借位后中间的 0 会变成 9。

subtract from a whole number = tolak daripada nombor bulat Give the whole number a decimal point and three zeros to match the other number. The zeros on the right are too small, so borrow all the way from the ones: the middle places become 9 and the last place becomes 10. Example: 5 − 1.25 = 5.00 − 1.25: after borrowing the digits are 4, 9, 10, giving 3.75. Watch out: subtract the decimal part too, not just the whole numbers; after borrowing, the middle zeros become 9.