Multiplication tables of 7, 8

1Summary 重點摘要

×7, ×8 tables. 7×8=56.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Part 1: The 7 times tableThe 7 times table: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, adding 7 each time. Learn the common ones by heart: 7 × 6 = 42, 7 × 8 = 56 and 7 × 9 = 63. The 7 table has few patterns; its ones digits 7, 4, 1, 8, 5, 2, 9, 6, 3, 0 are all different, so read and practise it often. A common mistake is to remember 7 × 8 as 54, the most frequent slip of all. To memorise, read the whole table once a day, then cover the answers and recite line by line; alternating reading and reciting fixes the whole table in about a week.
2. Part 2: The 8 times tableThe 8 times table: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, adding 8 each time. Common facts include 8 × 5 = 40 and 8 × 7 = 56. Each step of adding 8 really means one more group of 8: 8 is one 8, 16 is two 8s, 24 is three 8s. A common mistake is to lose the order halfway, jumping from 32 straight to 56. Write out where each product comes from to check: 8 × 4 = 32, 8 × 5 = 40, adding 8 step by step, and any slip shows at once. The ones digits of the 8 table cycle through 8, 6, 4, 2, 0, and this even-number pattern helps with checking.
3. Part 3: Eights by doublingEight is two doubled three times: 2 doubled is 4, and 4 doubled is 8. So 8 times a number can be found by doubling that number three times. For 8 × 6: double 6 once to get 12, twice to get 24, three times to get 48. So 8 × 6 = 48. Try 8 × 7: 7 to 14 to 28 to 56. This method is very handy for rescuing yourself when a fact is forgotten. A common mistake is to stop after two doublings and take 8 × 6 as 24, which is really 4 × 6. Remember to complete all three doublings, write down the result after each, and check step by step.
4. Part 4: The famous 7×8The famous fact 7 × 8 = 56 is the one most often remembered wrongly, and some people mix it up with 54. Use the chain 5, 6, 7, 8 to remember: read it out, and the two middle numbers 6 and 7 multiply while the two end numbers 5 and 6 form the answer 56, so 56 = 7 × 8. Write it a few times and the mistake disappears. A common error is being swayed by 7 × 7 = 49 and working out 7 × 8 as 49 + 5; in fact what follows 49 is one more 7, and 49 + 7 = 56. Before a test, copy 7 × 8 = 56 out three times on its own, and this mark will not be lost again.
5. Part 5: Build from facts you knowIf you forget 7 × 9, do not worry. You know 7 × 8 = 56, so add one more 7: 56 + 7 = 63. So 7 × 9 = 63. A times table adds the same number each step, so a fact you know leads to the next one; the other way, 7 × 7 is 56 − 7 = 49. The method works for the 8 table too: forgetting 8 × 6, take 8 × 7 = 56 and subtract 8 to get 48. A common mistake is to reverse the direction, subtracting 7 for 7 × 9 and getting 49. One step forward makes the product bigger, so add; one step back makes it smaller, so subtract. Think out the direction before writing.
6. Part 6: Everyday useSeven and eight appear in daily life. A week has 7 days, so 8 weeks make 7 × 8 = 56 days; a spider has 8 legs, so 5 spiders have 8 × 5 = 40 legs; a workbook line holds 7 characters, so 9 lines hold 7 × 9 = 63 characters. Times tables give these answers at once. A common mistake is to write the factors in an order that does not match the wording, putting '5 spiders with 8 legs each' as 5 × 8; in multiplication the result is the same, but following the meaning keeps the working clear. Think first of 'how many groups of what', then write the sentence.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• The 7 times table adds 7 each time: 7 to 70
• The 8 times table adds 8 each time: 8 to 80
• 8×n doubles n three times
• 7×8 = 56 is the key fact — never 54
• Knowing 7×8 gives you 8×7 free