Multiplication tables of 5, 6

1Summary 重點摘要

×5, ×6 tables. 5×7=35, 6×8=48.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Part 1: The 5 times table is easyThe 5 times table is easy to count: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, adding 5 each time, and every answer ends in 0 or 5, which makes this the simplest table to learn. For example 5×6 = 30 and 5×9 = 45, the final digits plain to see, so slips are easy to spot. Take care that 5×5 = 25 ends in 5, not 0; do not assume that two fives multiplied make the product end in 0. Watching the final digit while reciting greatly cuts the chance of a slip.
2. Part 2: Halve the tensSince 5 is half of 10, the table of 5 can be found by working the table of 10 first and halving, which avoids blind memorising. Example: for 5×8, first work out 10×8 = 80, then take half: 80 ÷ 2 = 40, so 5×8 = 40. Why does it work? Groups of 5 total exactly half of groups of 10, so the totals halve as well. Take care that the halving must come out exact; happily every product of 10 ends in 0, so the half is always a whole number and the method is always safe.
3. Part 3: The 6 times tableThe 6 times table starts at 6 and adds 6 each time: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60. To work out 6×7, count to the 7th number: 42, and 6×8 is 48. Reading it aloud with claps a few times makes it familiar, and rhythm helps the memory. Take care that any product you forget can be rebuilt by adding 6 to the one before; for example, forgetting 6×7, take 6×6 = 36 and add 6 to reach 42. Practise this rescue method until it is smooth.
4. Part 4: Six is double threeSix is double three, so the 6 times table can be found by doubling the 3 times table, growing a new table from an old one. Example: for 6×4, first 3×4 = 12, then double it: 12 + 12 = 24, so 6×4 = 24. Why does it work? A group of 6 is exactly two groups of 3, so the total doubles as well. Remember, 6 times a number is 3 times it, doubled. Take care to double accurately: 12 doubled is 24, not 22 or 26.
5. Part 5: Shared answersThe 5 and 6 times tables share some answers, products that appear in both tables. 5×6 = 30 and 6×5 = 30: swapping the order gives the same answer, so 30 appears in both tables. But 6×6 = 36 belongs only to the 6 times table, because 36 is not a multiple of 5. Take care that a number must be a multiple of both 5 and 6 to appear in both tables, like 60, which is 5×12 and also 6×10; the final digit and the divisibility rules help you judge.
6. Part 6: Everyday useTimes tables serve daily life wherever equal groups are counted. Example: six bags with 5 oranges each hold 6×5 = 30 oranges in all; a hall with 7 rows of 6 seats has 6×7 = 42 seats. Knowing the tables well gives the answer at once, with no need to count group by group. Take care to confirm how many groups there are and how many in each group before writing the sentence; either number may come first, since the product is unchanged, but the count of groups and the size of each group must not be mixed up.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• The 5 times table adds 5 each time; answers end in 0 or 5
• 5×n = half of 10×n
• The 6 times table adds 6 each time; 6×n doubles 3×n
• 5×6 = 6×5 = 30 appears in both tables
• Boxes × per-box means multiply