Multiplication tables of 2, 5, 10

1Summary 重點摘要

×2 = doubles; ×5 ends in 50; ×10 add 0.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Step 1: Multiply = repeated additionMultiplication is a quick way of adding the same number again and again; this is its most basic meaning. Why learn it? Because a long chain of equal addends can be written in one line. 3 × 2 means 3 groups of 2, which is 2 + 2 + 2 = 6, so 3 × 2 = 6. Take care that 3 × 2 and 2 × 3 tell slightly different stories, 3 groups of 2 versus 2 groups of 3; the results agree, but when reading a problem, follow the order as given.
2. Step 2: Table of 2The table of 2 adds 2 each time: 2, 4, 6, 8, 10, 12, exactly the even numbers, which is its clearest feature. Why all even? Because adding 2 always lands on an even number. For example, 2 × 6 means 6 groups of 2; starting from 2 and adding 2 six times gives 2 × 6 = 12. Take care not to read 2 × 6 as 2 + 6; the table skips along six times, it does not add just once.
3. Step 3: Table of 5The table of 5 adds 5 each time: 5, 10, 15, 20, 25, 30, and every product ends in 5 or 0, a feature that lets you check yourself. For example, 5 × 4 means 4 groups of 5, and 5 + 5 + 5 + 5 = 20, so 5 × 4 = 20, ending in 0, just as the feature promises. The usual error is reciting answers like 5 × 4 = 24 with the wrong final digit; one glance at that digit exposes the slip, so the ending is the safety rope of the table.
4. Step 4: Table of 10The table of 10 is the easiest: to multiply by 10, write the number and add a 0. Why does this work? Any number of tens always gives a 0 in the ones place. For example, 10 × 3 = 30, 10 × 7 = 70 and 10 × 10 = 100. Take care to append the 0 at the end, not to place it inside the digits; 10 × 10 is 100, not 110, so write the number first and attach the 0 last, never reversing the order.
5. Step 5: Either order, same productSwapping the order of two numbers does not change the product, an important rule that saves half the memorising. Why is the product unchanged? 2 × 5 is 5 groups of 2 and 5 × 2 is 2 groups of 5, yet both total 10, only grouped differently. So if you know 2 × 8 = 16, you also know 8 × 2 = 16, and half the table follows free. Take care that the rule holds for multiplication and addition only; subtraction and division give different results once the order is swapped.
6. Step 6: Use multiplication to countMany everyday problems need multiplication to find a total, and every case with equal groups fits it. Example: with 4 boxes and 5 pens in each box, addition needs 5 + 5 + 5 + 5, while multiplication needs only 4 × 5 = 20, so there are 20 pens, quickly and without missing any. Take care to confirm the groups really are equal before writing the sentence; if one box holds a pen more and another a pen fewer, work the odd boxes separately and add them on.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• Multiplication is repeated addition.
• Table of 2: 2, 4, 6, 8...
• Table of 5 ends in 5 or 0.
• Times 10: add a 0.
• Swapping the order keeps the product.