Tolak Lagi

竖式退位 = mengumpul semula dalam bentuk lazim 个位 2 不够减 7，向十位借 1：12−7=5，十位 5 变 4；十位 4−2=2；百位 3 不够减 8，向千位借 1：13−8=5，千位 6 变 5；千位 5−1=4。答案 4 525。红色小字是借过以后的新数字（5、13、4、12），原来的数字画上斜线。 例子：4 731 − 1 516 = 3 215。 注意：每一位都要先看够不够减，再决定要不要借。

regrouping in columns = mengumpul semula dalam bentuk lazim Ones: 2 is less than 7, so borrow from the tens: 12−7=5, tens 5 becomes 4. Tens 4−2=2. Hundreds: 3 is less than 8, so borrow from the thousands: 13−8=5, thousands 6 becomes 5. Thousands 5−1=4. The answer is 4 525. The small red numbers (5, 13, 4, 12) are the new values after borrowing, and the old digits are crossed out. Example: 4 731 − 1 516 = 3 215. Watch out: check each place first to see whether you need to borrow.

连续从零退位 = kumpul semula melalui sifar 6 000 的个位、十位、百位都是 0，个位要借，但十位和百位没有东西可借，只好一直借到千位。千位 6 变 5，百位得到 10；百位再借 1 给十位，剩 9；十位得到 10，再借 1 给个位，剩 9；个位得到 10。所以上面变成 5、9、9、10。再逐位减：10−5=5，9−7=2，9−4=5，5−2=3，答案 3 525。 例子：4 000 − 1 368 → 3、9、9、10 → 2 632。 注意：中间的 0 借到 10 以后又借出 1，所以是 9，不是 10。

borrowing across zeros = kumpul semula melalui sifar 6 000 has 0 ones, tens and hundreds. The ones need to borrow, but the tens and hundreds have nothing, so you borrow all the way from the thousands. Thousands 6 becomes 5 and the hundreds get 10; the hundreds lend 1 to the tens and keep 9; the tens get 10, lend 1 to the ones and keep 9; the ones get 10. The top row becomes 5, 9, 9, 10. Then subtract: 10−5=5, 9−7=2, 9−4=5, 5−2=3, so the answer is 3 525. Example: 4 000 − 1 368 → 3, 9, 9, 10 → 2 632. Watch out: a middle 0 becomes 10 and then lends 1, so it ends up as 9, not 10.

两个数都减 1 = kedua-dua nombor tolak 1 从 7 000 这样的整千减，可以把两个数都减 1：7 000 变 6 999，2 364 变 2 363。两个数一起变小 1，它们的相差不会改变。6 999 − 2 363 每一位都够减，不用退位，答案 4 636。另一种想法：先算 6 999 − 2 364 = 4 635，再把 1 加回来，也是 4 636。 例子：5 000 − 1 238 → 4 999 − 1 237 = 3 762。 注意：两个数都要减 1；只把 7 000 变成 6 999 而不改减数，答案会少 1。

take 1 from both numbers = kedua-dua nombor tolak 1 When subtracting from a round thousand like 7 000, take 1 from both numbers: 7 000 becomes 6 999 and 2 364 becomes 2 363. Making both numbers 1 smaller does not change the difference. 6 999 − 2 363 needs no borrowing, so the answer is 4 636. Another way: 6 999 − 2 364 = 4 635, then add the 1 back to get 4 636. Example: 5 000 − 1 238 → 4 999 − 1 237 = 3 762. Watch out: take 1 from both numbers; changing only 7 000 to 6 999 makes the answer 1 too small.

算盘退位减 = tolak dengan kawan besar 算盘上某一档不够减时，要向左边一档“拿 1”，也就是拿走 10，再把多拿的部分拨回来。十位只有 3，要减 5：拿走 1 个百（等于减 10 个十），5 的大朋友数是 5，所以十位拨上 5，10 − 5 = 5，刚好减了 5。个位是 0，要减 8：拿走 1 个十，8 的大朋友数是 2，个位拨上 2。答案 5 172。 例子：3 210 − 6 → 个位 0 不够减 6 → 拿走 1 个十，拨上 4 → 3 204。 注意：拨上的是“大朋友数”，不是要减的数；拨上 8 就会多出 6。

subtracting with a big friend = tolak dengan kawan besar When a rod does not have enough to take away, take 1 from the rod on the left, which is taking away 10, then put back the extra. The tens rod has only 3 and we take away 5: take 1 hundred (10 tens); the big friend of 5 is 5, so push up 5 tens; 10 − 5 = 5, exactly the 5 we wanted to take. The ones rod is 0 and we take away 8: take 1 ten; the big friend of 8 is 2, so push up 2 ones. The answer is 5 172. Example: 3 210 − 6 → 0 is not enough → take 1 ten, push up 4 → 3 204. Watch out: push up the big friend, not the number you are taking away; pushing up 8 would leave 6 too many.

用大朋友数减 = tolak dengan kawan besar 个位只有 1，不够减 7，不能直接拨去 7 颗珠子。所以向十位拿 1（减 10），再拨上 7 的大朋友数 3：个位 1 + 3 = 4，十位 7 变 6。算盘显示 4 364，和 4 371 − 7 = 4 364 一样。 例子：2 362 − 9 → 个位 2 不够 → 拿 1 个十，拨上 1 → 2 353。 注意：拿了 1 个十以后拨上 7，就等于只减了 3，答案会错。

take away with a big friend = tolak dengan kawan besar The ones rod has only 1, which is not enough to take away 7, so you cannot just remove 7 beads. Take 1 from the tens (take away 10), then push up the big friend of 7, which is 3: the ones become 1 + 3 = 4 and the tens 7 become 6. The abacus shows 4 364, the same as 4 371 − 7 = 4 364. Example: 2 362 − 9 → 2 is not enough → take 1 ten, push up 1 → 2 353. Watch out: taking 1 ten and pushing up 7 only takes away 3, so the answer would be wrong.

求减数 = cari nombor yang ditolak 减掉的数就是 2 870 和 3 500 之间的距离。在数线上从小的数往上跳：+30 到 2 900，+100 到 3 000，+500 到 3 500。30 + 100 + 500 = 630。 例子：1 000 − ? = 850 → 850 跳到 1 000 是 150。 注意：检查 3 500 − 630 = 2 870。

find the number taken away = cari nombor yang ditolak The number taken away is the distance between 2 870 and 3 500. Jump up from the smaller number: +30 to 2 900, +100 to 3 000, +500 to 3 500. 30 + 100 + 500 = 630. Example: 1 000 − ? = 850 → from 850 to 1 000 is 150. Watch out: check that 3 500 − 630 = 2 870.

三次退位 = tiga kali mengumpul semula 个位 3 不够减 6：借 1 → 13−6=7；十位变 0，不够减 4：借 1 → 10−4=6；百位变 1，不够减 7：借 1 → 11−7=4；千位变 4，4−1=3。答案 3 467。 例子：4 102 − 1 356 = 2 746。 注意：4 533 是把下面的数减上面的数，这是常见错误。

regrouping three times = tiga kali mengumpul semula Ones 3 < 6: borrow → 13−6=7; tens is now 0, less than 4: borrow → 10−4=6; hundreds is now 1, less than 7: borrow → 11−7=4; thousands is now 4, 4−1=3. The answer is 3 467. Example: 4 102 − 1 356 = 2 746. Watch out: 4 533 comes from taking the top digit from the bottom digit, a common mistake.

简便退位 = cara mudah tolak dari sifar 8 000 = 7 999 + 1。先算 7 999 − 3 452 = 4 547（不用借），再加 1 = 4 548。 例子：3 000 − 1 111 → 2 999 − 1 111 = 1 888，加 1 = 1 889。 注意：用 4 548 + 3 452 = 8 000 检查。

shortcut from zeros = cara mudah tolak dari sifar 8 000 = 7 999 + 1. Work out 7 999 − 3 452 = 4 547 (no borrowing), then add 1 = 4 548. Example: 3 000 − 1 111 → 2 999 − 1 111 = 1 888, plus 1 = 1 889. Watch out: check with 4 548 + 3 452 = 8 000.

找错 = cari kesilapan Danial 在个位做了 1−0，在十位做了 7−2，这是把下面减上面，错了。正确：个位 0 不够减 1，借 → 10−1=9；十位 2 变 1，不够减 7，借 → 11−7=4；百位 8 变 7，7−4=3；千位 5−2=3。答案 3 349。 例子：620 − 145 = 475。 注意：永远是上面减下面，不够就借。

find the mistake = cari kesilapan Danial did 1−0 in the ones and 7−2 in the tens, taking the top from the bottom. Correctly: ones 0 < 1, borrow → 10−1=9; tens 2 becomes 1, less than 7, borrow → 11−7=4; hundreds 8 becomes 7, 7−4=3; thousands 5−2=3. The answer is 3 349. Example: 620 − 145 = 475. Watch out: always top minus bottom; borrow when it is not enough.