Darab

交换位置 = tukar tertib 看点阵：横着看有 3 行，每行 23 个点，是 3 × 23；竖着看有 23 列，每列 3 个点，是 23 × 3。点的数目没有变，都是 69。所以两个数相乘，交换位置，积不变。计算时可以选比较方便的写法，例如把大的数写在上面做竖式。 例子：5 × 12 = 12 × 5 = 60。 注意：只有乘法（和加法）可以这样交换，减法和除法不行。

change the order = tukar tertib Look at the dots: across there are 3 rows of 23, which is 3 × 23; down there are 23 columns of 3, which is 23 × 3. The number of dots does not change: 69 either way. So swapping the two numbers in a multiplication gives the same answer, and we may pick the easier way, such as putting the bigger number on top in the column. Example: 5 × 12 = 12 × 5 = 60. Watch out: this works for multiplication (and addition), but not for subtraction or division.

阵列 = tatasusunan；行 = baris；每行 = setiap baris 实验台用同样大小的圆点排成整齐行列。第一组按钮改变行数，第二组改变每一行的圆点数，画面会同时写出乘法算式。按“交换次序”后，行和列互换，但圆点总数不变。 例子：2 行、每行 3 个，一共有 2 × 3 = 6 个；转过来是 3 × 2，还是 6。 注意：算式前一个数表示行数，后一个数表示每行几个。

array = tatasusunan; rows = baris; in each row = setiap baris The lab arranges equal dots in neat rows and columns. One pair of buttons changes the number of rows and another changes the dots in each row, while the multiplication sentence updates. Press change order to turn the array; its rows and columns swap, but the total number of dots stays the same. Example: 2 rows of 3 give 2 × 3 = 6; turned around, 3 × 2 is still 6. Watch out: the first number tells the rows and the second tells how many are in each row.

保持不变 = kekal；交换次序 = tukar tertib 题目要你比较阵列转动前后，哪一项保持不变。回想实验台：转动会让行数和每行个数交换位置，但并没有增加或拿走任何圆点。请把三个选项分别与这个观察比较。 例子：先画一个 2 行 4 列的阵列，再把纸转过来，数一数圆点。 注意：行数和每行个数可以改变，所以要找的是不会改变的量。

stays the same = kekal; change order = tukar tertib The question asks which quantity stays unchanged when an array is turned. Recall that turning the lab array swapped the number of rows with the number in each row, but no dots were added or removed. Compare each option with that observation. Example: draw a 2 by 4 array, turn the paper, and count all the dots again. Watch out: both the number of rows and the number in each row can change, so look for the quantity that cannot change.

竖式乘法 = darab dalam bentuk lazim 把乘数 2 写在个位下面。从个位开始，用 2 去乘上面每一个数字：2×4=8，2×1=2，2×3=6。每一位的积都小于 10，直接写下来，所以 2 × 314 = 628。也可以用加法检查：314 + 314 = 628。 例子：3 × 132 = 396。 注意：每一个数字都要乘，不要漏掉十位或百位。

column multiplication = darab dalam bentuk lazim Write the 2 under the ones. Starting from the ones, multiply every digit on top by 2: 2×4=8, 2×1=2, 2×3=6. Each product is under 10, so write it down: 2 × 314 = 628. Check by adding: 314 + 314 = 628. Example: 3 × 132 = 396. Watch out: multiply every digit; do not skip the tens or hundreds.

乘 10、100、1 000 = darab 10, 100, 1 000 一个数乘 10，每个数字都往左移一位，个位补一个 0；乘 100 补两个 0；乘 1 000 补三个 0。 例子：7 × 10 = 70，7 × 100 = 700，7 × 1 000 = 7 000，36 × 10 = 360。 注意：乘 10 要补 1 个 0，乘 100 要补 2 个 0，数清楚 0 的个数，不要多补或少补。

multiply by 10, 100, 1 000 = darab 10, 100, 1 000 Multiplying by 10 moves every digit one place to the left and puts a 0 in the ones; by 100 add two zeros; by 1 000 add three zeros. Example: 7 × 10 = 70, 7 × 100 = 700, 7 × 1 000 = 7 000, 36 × 10 = 360. Watch out: count the zeros carefully: one for 10, two for 100, three for 1 000.

约数检查 = anggar untuk menyemak 4 012 约等于 4 000，2 × 4 000 = 8 000。准确答案 2 × 4 012 = 8 024，和 8 000 很接近，所以合理。如果算出来是 80 024 或 824，一看约数就知道错了。 例子：3 × 2 103 → 约 3 × 2 000 = 6 000，准确答案 6 309。 注意：约数只用来检查。

estimate to check = anggar untuk menyemak 4 012 is about 4 000, and 2 × 4 000 = 8 000. The exact answer 2 × 4 012 = 8 024 is close, so it is reasonable. An answer like 80 024 or 824 would clearly be wrong. Example: 3 × 2 103 → about 3 × 2 000 = 6 000; exact answer 6 309. Watch out: the estimate is only for checking.

每一位都乘 = darab setiap digit 个位 3×2=6，十位 3×3=9，百位 3×1=3，所以答案 396。135 是把 3 加上去，不是乘。 例子：2 × 243 = 486。 注意：乘法不是加法，每一位都要乘。

multiply every digit = darab setiap digit Ones 3×2=6, tens 3×3=9, hundreds 3×1=3, so the answer is 396. 135 comes from adding 3, not multiplying. Example: 2 × 243 = 486. Watch out: multiplying is not adding; multiply every place.

乘 100 = darab 100 乘 100 要在后面补两个 0：45 → 4 500。450 只补了一个 0（那是乘 10），45 000 补了三个 0（那是乘 1 000）。乘 100 之后，原来的个位数字会移到百位。 例子：23 × 100 = 2 300。 注意：数清楚 100 有两个 0。

multiply by 100 = darab 100 Multiplying by 100 adds two zeros: 45 → 4 500. 450 has only one zero (that is × 10), and 45 000 has three (that is × 1 000). Example: 23 × 100 = 2 300. Watch out: 100 has two zeros.

求缺数 = cari nombor yang hilang 40 变成 4 000，后面多了两个 0（40 → 400 → 4 000）。多两个 0 就是乘 100，所以 40 × 100 = 4 000。先比较两个数，数一数多了几个 0，就知道是乘 10、100 还是 1 000。 例子：30 × ? = 300 → 10。 注意：4 000 一共有三个 0，但 40 本来已经有一个 0，只多了两个。

find the missing number = cari nombor yang hilang 40 becomes 4 000, which has two more zeros (40 → 400 → 4 000). Two more zeros means × 100, so 40 × 100 = 4 000. Example: 30 × ? = 300 → 10. Watch out: 4 000 has three zeros, but 40 already had one, so only two were added.