Don’t stop here
Once your times-table facts are becoming reliable, do not stop at the table itself. Start using them inside harder calculations. The same methods now let you multiply much larger numbers mentally.
A useful point to move on: when you are getting roughly 90% of your times-table practice correct, start mixing in harder mental multiplication as well. Keep practising any weaker facts, but do not wait for absolute perfection before using what you know.
The old methods work on bigger numbers
The strategies from the earlier lessons were not just times-table tricks. They are general ways of thinking about multiplication.
23 × 10 + 23 × 4
230 + 92
= 322
20 × 17 − 2 × 17
340 − 34
= 306
24 × 8 = 192
double 192
= 384
This is why the groundwork matters
In a calculation such as 23 × 14, the hard-looking problem breaks into smaller multiplication facts. If 23 × 4 is easy to build from 20 × 4 and 3 × 4, the whole calculation becomes manageable.
More challenging practice keeps calling on the basic facts, but now you must also decide which fact or strategy will help.
The groundwork becomes cemented while your calculations become more fluid.
Practice: two-digit multiplication
Try these mentally. There is no single required method: look for a convenient route.
- 21 × 13
- 24 × 12
- 18 × 16
- 27 × 14
- 32 × 18
Show some possible routes
21 × 13 = 21 × 10 + 21 × 3 = 210 + 63 = 273
24 × 12 = 24 × 10 + 24 × 2 = 240 + 48 = 288
18 × 16 = 20 × 16 − 2 × 16 = 320 − 32 = 288
27 × 14 = 27 × 10 + 27 × 4 = 270 + 108 = 378
32 × 18 = 32 × 20 − 32 × 2 = 640 − 64 = 576
A few shortcuts worth knowing
These are not rules you need for every problem. They are useful patterns to notice when the numbers happen to fit.
Shortcut 1: multiplying by 11
Multiplying by 11 means multiplying by 10 and then adding the original number:
34 × 11 = 340 + 34 = 374
For a two-digit number, there is also a compact pattern. Add the two digits and place the sum between them:
34 × 11 → 3 (3 + 4) 4 → 374
If the middle sum is 10 or more, carry as usual. For example, 57 × 11 = 627.
Practice ×11
23 × 11 41 × 11 62 × 11 78 × 11
Answers
253, 451, 682, 858
Shortcut 2: (n − 1)(n + 1)
If two numbers are one below and one above the same number, there is a useful identity:
(n − 1)(n + 1) = n² − 1
For example:
29 × 31 = 30² − 1 = 900 − 1 = 899
This becomes particularly handy once some common square numbers are familiar.
Practice numbers either side
19 × 21 24 × 26 39 × 41 49 × 51
Answers
399, 624, 1599, 2499
Shortcut 3: multiplying by 25
Since 25 is one quarter of 100, multiplying by 25 can be thought of as multiplying by 100 and dividing by 4.
36 × 25 = 3600 ÷ 4 = 900
Sometimes it is easier to divide first:
48 × 25 = (48 ÷ 4) × 100 = 12 × 100 = 1200
Choose whichever direction makes the arithmetic easiest.
Practice ×25
12 × 25 28 × 25 44 × 25 72 × 25
Answers
300, 700, 1100, 1800
The methods we have built
- Split a multiplication into easier pieces.
- Complete to a friendly number such as 10, 20, 50 or 100, then adjust.
- Double or halve when powers of 2 appear.
- Reuse familiar facts instead of starting every calculation from scratch.
- Notice special structures such as ×11, ×25 and numbers either side of a square.
Fluent multiplication is not just reciting a table. It is recognising useful structure quickly and choosing a good route through a calculation. Keep practising the basic facts — but use them in new and harder ways too.