{"id":26,"date":"2026-09-18T07:28:49","date_gmt":"2026-09-18T07:28:49","guid":{"rendered":"https:\/\/www.bemathmaster.com\/blogs\/?p=26"},"modified":"2026-09-18T07:29:26","modified_gmt":"2026-09-18T07:29:26","slug":"multiplication-tricks-for-faster-calculation-12-useful-methods","status":"publish","type":"post","link":"https:\/\/www.bemathmaster.com\/blogs\/multiplication-tricks-for-faster-calculation-12-useful-methods\/","title":{"rendered":"Multiplication tricks for faster calculation: 12 useful methods"},"content":{"rendered":"

\"multiplication
\nThe best multiplication tricks for faster calculation<\/strong> do not make you calculate the same difficult problem faster. They help you transform the problem into an easier multiplication that gives the same answer<\/strong>.<\/p>\n

For example:<\/p>\n

48 \u00d7 5<\/strong><\/p>\n

may look like a multiplication-table problem, but you can rewrite it mentally as:<\/p>\n

48 \u00d7 10 \u00f7 2<\/strong><\/p>\n

480 \u00f7 2 = 240<\/strong><\/p>\n

So:<\/p>\n

48 \u00d7 5 = 240<\/strong><\/p>\n

That idea\u2014changing a difficult calculation into a friendlier one\u2014is the foundation of useful mental multiplication.<\/p>\n

Educational mathematics resources from The Open University also recommend strategies such as doubling, halving, and transforming multiplication by 5, 9, 11, 20 and 50 into simpler operations.<\/p>\n

This guide covers the multiplication shortcuts worth understanding, why they work, when to use them, and the mistakes that can make a \u201cfast\u201d method slower or less reliable.<\/p>\n

Quick multiplication tricks<\/h2>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Multiplication<\/th>\nMental shortcut<\/th>\n<\/tr>\n
\u00d75<\/td>\n\u00d710, then halve<\/td>\n<\/tr>\n
\u00d79<\/td>\n\u00d710, then subtract the number<\/td>\n<\/tr>\n
\u00d711<\/td>\n\u00d710, then add the number<\/td>\n<\/tr>\n
\u00d715<\/td>\n\u00d710 + half of \u00d710<\/td>\n<\/tr>\n
\u00d720<\/td>\n\u00d72, then \u00d710<\/td>\n<\/tr>\n
\u00d725<\/td>\n\u00d7100, then divide by 4<\/td>\n<\/tr>\n
\u00d750<\/td>\n\u00d7100, then halve<\/td>\n<\/tr>\n
\u00d799<\/td>\n\u00d7100, then subtract the number<\/td>\n<\/tr>\n
\u00d7101<\/td>\n\u00d7100, then add the number<\/td>\n<\/tr>\n
\u00d74<\/td>\nDouble twice<\/td>\n<\/tr>\n
\u00d78<\/td>\nDouble three times<\/td>\n<\/tr>\n
Even-number products<\/td>\nDouble one factor and halve the other<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

The shortcuts above are useful because they are based on ordinary multiplication properties rather than memorized magic.<\/p>\n

1. Multiply by 5: multiply by 10 and halve<\/h2>\n

Multiplying by 5 becomes easier when you recognize:<\/p>\n

5 = 10 \u00f7 2<\/strong><\/p>\n

So:<\/p>\n

number \u00d7 5 = number \u00d7 10 \u00f7 2<\/strong><\/p>\n

Example: 46 \u00d7 5<\/h3>\n

Multiply by 10:<\/p>\n

46 \u00d7 10 = 460<\/strong><\/p>\n

Halve:<\/p>\n

460 \u00f7 2 = 230<\/strong><\/p>\n

Therefore:<\/p>\n

46 \u00d7 5 = 230<\/strong><\/p>\n

Example: 128 \u00d7 5<\/h3>\n

128 \u00d7 10 = 1,280<\/strong><\/p>\n

1,280 \u00f7 2 = 640<\/strong><\/p>\n

Answer:<\/p>\n

640<\/strong><\/p>\n

This is one of the most reusable multiplication tricks because multiplying by 10 and halving are usually easy mental operations.<\/p>\n

2. Multiply by 9: multiply by 10 and subtract once<\/h2>\n

Nine is one less than ten:<\/p>\n

9 = 10 \u2212 1<\/strong><\/p>\n

Therefore:<\/p>\n

number \u00d7 9 = number \u00d7 10 \u2212 number<\/strong><\/p>\n

Example: 47 \u00d7 9<\/h3>\n

First:<\/p>\n

47 \u00d7 10 = 470<\/strong><\/p>\n

Then subtract 47:<\/p>\n

470 \u2212 47 = 423<\/strong><\/p>\n

So:<\/p>\n

47 \u00d7 9 = 423<\/strong><\/p>\n

Example: 83 \u00d7 9<\/h3>\n

830 \u2212 83 = 747<\/strong><\/p>\n

Answer:<\/p>\n

747<\/strong><\/p>\n

This method is particularly useful when the original number is easy to subtract from its multiple of ten.<\/p>\n

3. Multiply by 11: multiply by 10 and add once<\/h2>\n

Eleven is:<\/p>\n

10 + 1<\/strong><\/p>\n

Therefore:<\/p>\n

number \u00d7 11 = number \u00d7 10 + number<\/strong><\/p>\n

Example: 34 \u00d7 11<\/h3>\n

340 + 34 = 374<\/strong><\/p>\n

Example: 72 \u00d7 11<\/h3>\n

720 + 72 = 792<\/strong><\/p>\n

There is also a popular digit shortcut for two-digit numbers.<\/p>\n

For:<\/p>\n

32 \u00d7 11<\/strong><\/p>\n

Keep the outer digits and add them for the middle:<\/p>\n

3 _ 2<\/strong><\/p>\n

3 + 2 = 5<\/strong><\/p>\n

So:<\/p>\n

352<\/strong><\/p>\n

This shortcut works directly when the middle sum stays below 10.<\/p>\n

What if the digits add to 10 or more?<\/h3>\n

Consider:<\/p>\n

68 \u00d7 11<\/strong><\/p>\n

Add the digits:<\/p>\n

6 + 8 = 14<\/strong><\/p>\n

You cannot simply write 6148.<\/p>\n

Carry the 1:<\/p>\n

6 + 1 = 7<\/strong><\/p>\n

Then write 4 and 8:<\/p>\n

748<\/strong><\/p>\n

Check:<\/p>\n

68 \u00d7 11 = 748<\/strong><\/p>\n

For many learners, the \u00d710 + original number<\/strong> method is easier to remember and less error-prone than memorizing separate carry rules.<\/p>\n

4. Multiply by 15 using 10 and 5<\/h2>\n

Because:<\/p>\n

15 = 10 + 5<\/strong><\/p>\n

you can calculate:<\/p>\n

number \u00d7 15 = number \u00d7 10 + number \u00d7 5<\/strong><\/p>\n

And you already know that multiplying by 5 means multiplying by 10 and halving.<\/p>\n

Example: 36 \u00d7 15<\/h3>\n

First find:<\/p>\n

36 \u00d7 10 = 360<\/strong><\/p>\n

Then:<\/p>\n

36 \u00d7 5 = 180<\/strong><\/p>\n

Add:<\/p>\n

360 + 180 = 540<\/strong><\/p>\n

Answer:<\/p>\n

540<\/strong><\/p>\n

Another way to think about it:<\/p>\n

\u00d715 = \u00d710 + half of \u00d710<\/strong><\/p>\n

This can be useful for prices, quantities and percentage-related calculations.<\/p>\n

5. Multiply by 25: multiply by 100 and divide by 4<\/h2>\n

Because:<\/p>\n

25 = 100 \u00f7 4<\/strong><\/p>\n

you can use:<\/p>\n

number \u00d7 25 = number \u00d7 100 \u00f7 4<\/strong><\/p>\n

Example: 32 \u00d7 25<\/h3>\n

32 \u00d7 100 = 3,200<\/strong><\/p>\n

Then:<\/p>\n

3,200 \u00f7 4 = 800<\/strong><\/p>\n

So:<\/p>\n

32 \u00d7 25 = 800<\/strong><\/p>\n

Faster variation<\/h3>\n

When the number is easily divisible by four, divide first:<\/p>\n

32 \u00f7 4 = 8<\/strong><\/p>\n

Then:<\/p>\n

8 \u00d7 100 = 800<\/strong><\/p>\n

Another example:<\/p>\n

76 \u00d7 25<\/strong><\/p>\n

76 \u00f7 4 = 19<\/strong><\/p>\n

19 \u00d7 100 = 1,900<\/strong><\/p>\n

Answer:<\/p>\n

1,900<\/strong><\/p>\n

This is usually much easier than multiplying 76 by 25 directly.<\/p>\n

6. Multiply by 50: multiply by 100 and halve<\/h2>\n

Because:<\/p>\n

50 = 100 \u00f7 2<\/strong><\/p>\n

calculate:<\/p>\n

number \u00d7 50 = number \u00d7 100 \u00f7 2<\/strong><\/p>\n

Example: 38 \u00d7 50<\/h3>\n

38 \u00d7 100 = 3,800<\/strong><\/p>\n

Half:<\/p>\n

1,900<\/strong><\/p>\n

So:<\/p>\n

38 \u00d7 50 = 1,900<\/strong><\/p>\n

You can also halve first:<\/p>\n

38 \u00f7 2 = 19<\/strong><\/p>\n

Then:<\/p>\n

19 \u00d7 100 = 1,900<\/strong><\/p>\n

The Open University includes multiplying by 5 and 50 through multiplication by powers of ten followed by halving among its recommended mental multiplication strategies.<\/p>\n

7. Multiply by 4 or 8 using repeated doubling<\/h2>\n

Multiplication by powers of two can often be handled through doubling.<\/p>\n

Multiply by 4<\/h3>\n

Double twice.<\/p>\n

For:<\/p>\n

37 \u00d7 4<\/strong><\/p>\n

First double:<\/p>\n

37 \u00d7 2 = 74<\/strong><\/p>\n

Double again:<\/p>\n

74 \u00d7 2 = 148<\/strong><\/p>\n

Answer:<\/p>\n

148<\/strong><\/p>\n

Multiply by 8<\/h3>\n

Double three times.<\/p>\n

For:<\/p>\n

23 \u00d7 8<\/strong><\/p>\n

23 \u00d7 2 = 46<\/strong><\/p>\n

46 \u00d7 2 = 92<\/strong><\/p>\n

92 \u00d7 2 = 184<\/strong><\/p>\n

Answer:<\/p>\n

184<\/strong><\/p>\n

This method is especially useful when you are comfortable doubling numbers mentally. Doubling and repeated doubling are also established mental multiplication strategies in mathematics teaching resources.<\/p>\n

8. Double one factor and halve the other<\/h2>\n

Sometimes you can simplify a multiplication problem without changing the answer.<\/p>\n

Consider:<\/p>\n

16 \u00d7 35<\/strong><\/p>\n

Halve 16:<\/p>\n

8<\/strong><\/p>\n

Double 35:<\/p>\n

70<\/strong><\/p>\n

Now:<\/p>\n

8 \u00d7 70 = 560<\/strong><\/p>\n

Therefore:<\/p>\n

16 \u00d7 35 = 560<\/strong><\/p>\n

You can simplify again:<\/p>\n

8 \u00d7 70<\/strong><\/p>\n

becomes:<\/p>\n

4 \u00d7 140<\/strong><\/p>\n

Still:<\/p>\n

560<\/strong><\/p>\n

Another example<\/h3>\n

25 \u00d7 24<\/strong><\/p>\n

Double 25:<\/p>\n

50 \u00d7 12<\/strong><\/p>\n

Double again:<\/p>\n

100 \u00d7 6<\/strong><\/p>\n

Answer:<\/p>\n

600<\/strong><\/p>\n

Why does this work?<\/p>\n

Because:<\/p>\n

a \u00d7 b = (a \u00f7 2) \u00d7 (2b)<\/strong><\/p>\n

when one factor can be halved conveniently.<\/p>\n

This is not merely a shortcut. It is a flexible way of restructuring multiplication, and doubling-and-halving appears in formal mental-multiplication teaching material.<\/p>\n

9. Break numbers apart using the distributive property<\/h2>\n

This may be the most useful multiplication strategy of all<\/strong> because it works with almost any numbers.<\/p>\n

Suppose you need:<\/p>\n

17 \u00d7 6<\/strong><\/p>\n

Break 17 into:<\/p>\n

10 + 7<\/strong><\/p>\n

Then:<\/p>\n

10 \u00d7 6 = 60<\/strong><\/p>\n

7 \u00d7 6 = 42<\/strong><\/p>\n

Add:<\/p>\n

60 + 42 = 102<\/strong><\/p>\n

Therefore:<\/p>\n

17 \u00d7 6 = 102<\/strong><\/p>\n

Another example: 23 \u00d7 14<\/h3>\n

Break 14 into:<\/p>\n

10 + 4<\/strong><\/p>\n

Then:<\/p>\n

23 \u00d7 10 = 230<\/strong><\/p>\n

23 \u00d7 4 = 92<\/strong><\/p>\n

Add:<\/p>\n

230 + 92 = 322<\/strong><\/p>\n

Answer:<\/p>\n

322<\/strong><\/p>\n

The underlying relationship is:<\/p>\n

a \u00d7 (b + c) = a \u00d7 b + a \u00d7 c<\/strong><\/p>\n

Unlike narrow numerical tricks, decomposition works across a huge range of multiplication problems.<\/p>\n

If you are building mental calculation skills more broadly, Math Master’s Smart Tips & Tricks<\/a> includes additional arithmetic techniques for multiplication, division, addition, subtraction and other topics.<\/p>\n

10. Multiply by 99: multiply by 100 and subtract once<\/h2>\n

Since:<\/p>\n

99 = 100 \u2212 1<\/strong><\/p>\n

you can calculate:<\/p>\n

number \u00d7 99 = number \u00d7 100 \u2212 number<\/strong><\/p>\n

Example: 47 \u00d7 99<\/h3>\n

First:<\/p>\n

47 \u00d7 100 = 4,700<\/strong><\/p>\n

Subtract 47:<\/p>\n

4,700 \u2212 47 = 4,653<\/strong><\/p>\n

Answer:<\/p>\n

4,653<\/strong><\/p>\n

Example: 82 \u00d7 99<\/h3>\n

8,200 \u2212 82 = 8,118<\/strong><\/p>\n

Answer:<\/p>\n

8,118<\/strong><\/p>\n

This is often easier than performing a traditional two-digit multiplication.<\/p>\n

11. Multiply by 101: multiply by 100 and add once<\/h2>\n

The opposite idea works for 101:<\/p>\n

101 = 100 + 1<\/strong><\/p>\n

So:<\/p>\n

number \u00d7 101 = number \u00d7 100 + number<\/strong><\/p>\n

Example: 42 \u00d7 101<\/h3>\n

4,200 + 42 = 4,242<\/strong><\/p>\n

Answer:<\/p>\n

4,242<\/strong><\/p>\n

Example: 73 \u00d7 101<\/h3>\n

7,300 + 73 = 7,373<\/strong><\/p>\n

Answer:<\/p>\n

7,373<\/strong><\/p>\n

These \u00d799 and \u00d7101 methods are examples of a larger strategy:<\/p>\n

Use a nearby round number, then compensate.<\/strong><\/p>\n

12. Multiply numbers close to 100<\/h2>\n

One popular multiplication trick works particularly well when both numbers are close to 100<\/strong>.<\/p>\n

Consider:<\/p>\n

97 \u00d7 96<\/strong><\/p>\n

Both numbers are below 100.<\/p>\n

Their deficits are:<\/p>\n

100 \u2212 97 = 3<\/strong><\/p>\n

100 \u2212 96 = 4<\/strong><\/p>\n

Cross-subtract either deficit:<\/p>\n

97 \u2212 4 = 93<\/strong><\/p>\n

or:<\/p>\n

96 \u2212 3 = 93<\/strong><\/p>\n

Then multiply the deficits:<\/p>\n

3 \u00d7 4 = 12<\/strong><\/p>\n

Combine:<\/p>\n

93 | 12<\/strong><\/p>\n

Answer:<\/p>\n

9,312<\/strong><\/p>\n

So:<\/p>\n

97 \u00d7 96 = 9,312<\/strong><\/p>\n

Why does the trick work?<\/h3>\n

Write:<\/p>\n

97 = 100 \u2212 3<\/strong><\/p>\n

and:<\/p>\n

96 = 100 \u2212 4<\/strong><\/p>\n

Then:<\/p>\n

(100 \u2212 3)(100 \u2212 4)<\/strong><\/p>\n

expands to:<\/p>\n

10,000 \u2212 700 + 12<\/strong><\/p>\n

which is:<\/p>\n

9,312<\/strong><\/p>\n

This method is useful when both numbers are sufficiently close to 100, but it is much less useful for a calculation such as:<\/p>\n

43 \u00d7 27<\/strong><\/p>\n

In that situation, decomposition is usually simpler.<\/p>\n

Current exam-preparation resources commonly feature the near-100 method because it can reduce work for specific two-digit products.<\/p>\n

Bonus trick: square numbers ending in 5<\/h2>\n

Suppose you need:<\/p>\n

35 \u00d7 35<\/strong><\/p>\n

or:<\/p>\n

35\u00b2<\/strong><\/p>\n

Take the number before the 5:<\/p>\n

3<\/strong><\/p>\n

Multiply it by the next number:<\/p>\n

3 \u00d7 4 = 12<\/strong><\/p>\n

Then append:<\/p>\n

25<\/strong><\/p>\n

Answer:<\/p>\n

1,225<\/strong><\/p>\n

So:<\/p>\n

35\u00b2 = 1,225<\/strong><\/p>\n

Another example: 65\u00b2<\/h3>\n

Take 6.<\/p>\n

Multiply by the next integer:<\/p>\n

6 \u00d7 7 = 42<\/strong><\/p>\n

Append 25:<\/p>\n

4,225<\/strong><\/p>\n

Therefore:<\/p>\n

65\u00b2 = 4,225<\/strong><\/p>\n

Why does this work?<\/h3>\n

A number ending in 5 can be written as:<\/p>\n

10n + 5<\/strong><\/p>\n

Squaring it gives:<\/p>\n

(10n + 5)\u00b2<\/strong><\/p>\n

which simplifies to a number formed from:<\/p>\n

n(n + 1)<\/strong> followed by 25<\/strong>.<\/p>\n

This is a useful specialized shortcut, but remember that it works for squaring numbers ending in 5<\/strong>, not for arbitrary multiplication.<\/p>\n

Which multiplication tricks are actually worth learning?<\/h2>\n

You do not need to memorize dozens of tricks.<\/p>\n

Prioritize methods based on how widely you can reuse them.<\/p>\n\n\n\n\n\n\n\n\n\n\n\n
Strategy<\/th>\nUsefulness<\/th>\nBest for<\/th>\n<\/tr>\n
Decomposition<\/td>\nVery high<\/td>\nAlmost any multiplication<\/td>\n<\/tr>\n
Doubling and halving<\/td>\nVery high<\/td>\nEven factors<\/td>\n<\/tr>\n
\u00d710 then adjust<\/td>\nVery high<\/td>\n\u00d79, \u00d711, \u00d799, \u00d7101<\/td>\n<\/tr>\n
\u00d7100 then divide<\/td>\nHigh<\/td>\n\u00d725 and \u00d750<\/td>\n<\/tr>\n
Repeated doubling<\/td>\nHigh<\/td>\n\u00d74 and \u00d78<\/td>\n<\/tr>\n
Numbers near 100<\/td>\nMedium<\/td>\nTwo factors close to 100<\/td>\n<\/tr>\n
Square ending in 5<\/td>\nSpecialized<\/td>\nNumbers such as 25\u00b2, 65\u00b2<\/td>\n<\/tr>\n
Digit-specific tricks<\/td>\nSpecialized<\/td>\nParticular number patterns<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

If you remember only three ideas, make them:<\/p>\n

1. Break numbers apart.<\/strong><\/p>\n

2. Use nearby round numbers.<\/strong><\/p>\n

3. Double and halve when it simplifies the factors.<\/strong><\/p>\n

Those principles generate many of the \u201ctricks\u201d in this article automatically.<\/p>\n

How to choose the fastest multiplication method<\/h2>\n

Before calculating, look at the numbers.<\/p>\n

Is one number close to 10, 100 or 1,000?<\/h3>\n

Use compensation.<\/p>\n

Example:<\/p>\n

39 \u00d7 7<\/strong><\/p>\n

Think:<\/p>\n

40 \u00d7 7 \u2212 7<\/strong><\/p>\n

280 \u2212 7 = 273<\/strong><\/p>\n

Is one factor 5, 25 or 50?<\/h3>\n

Use powers of ten followed by division.<\/p>\n

Is one factor 4 or 8?<\/h3>\n

Try repeated doubling.<\/p>\n

Is one factor even?<\/h3>\n

Consider doubling one side and halving the other.<\/p>\n

Are both numbers close to 100?<\/h3>\n

Consider the near-100 method.<\/p>\n

Are the numbers ordinary and not especially convenient?<\/h3>\n

Use decomposition.<\/p>\n

The fastest mental calculator is not necessarily the person who calculates each step fastest.<\/p>\n

It is often the person who recognizes the easier version of the problem first<\/strong>.<\/p>\n

Worked examples: choosing the right trick<\/h2>\n

48 \u00d7 5<\/h3>\n

Best method:<\/p>\n

\u00d710 then halve<\/strong><\/p>\n

480 \u00f7 2 = 240<\/strong><\/p>\n

68 \u00d7 25<\/h3>\n

Best method:<\/p>\n

divide by 4, then \u00d7100<\/strong><\/p>\n

68 \u00f7 4 = 17<\/strong><\/p>\n

17 \u00d7 100 = 1,700<\/strong><\/p>\n

39 \u00d7 8<\/h3>\n

Possible method:<\/p>\n

Repeated doubling:<\/p>\n

39 \u2192 78 \u2192 156 \u2192 312<\/strong><\/p>\n

Answer:<\/p>\n

312<\/strong><\/p>\n

49 \u00d7 6<\/h3>\n

Best method:<\/p>\n

Use 50:<\/p>\n

50 \u00d7 6 \u2212 6<\/strong><\/p>\n

300 \u2212 6 = 294<\/strong><\/p>\n

18 \u00d7 35<\/h3>\n

Possible method:<\/p>\n

Halve 18 and double 35:<\/p>\n

9 \u00d7 70 = 630<\/strong><\/p>\n

24 \u00d7 17<\/h3>\n

Best general method:<\/p>\n

Decompose 17:<\/p>\n

24 \u00d7 10 = 240<\/strong><\/p>\n

24 \u00d7 7 = 168<\/strong><\/p>\n

240 + 168 = 408<\/strong><\/p>\n

Choosing a strategy is itself part of mental multiplication skill.<\/p>\n

Multiplication tricks for competitive exams<\/h2>\n

Fast multiplication can be useful in aptitude, quantitative reasoning and other timed exams because routine arithmetic can consume time that could otherwise go toward solving the main problem.<\/p>\n

Useful exam techniques include:<\/p>\n