Multiplication · Teknikguide
Mental Multiplication of Large Numbers
Av Robert Hansson, Kung Fu Math
Multiplication tables up to 10 × 10 are the alphabet of mental arithmetic. Larger products are words built from that alphabet. You rarely need to memorise them; you need to know how to break them apart and put them back together.
The techniques below range from the universal, such as splitting a number into tens and ones, to special shortcuts that only work for certain numbers. Learn the universal method first, then add the shortcuts one at a time.
01
Split into parts
Break one factor into tens and ones, multiply each part and add the results. This is the distributive law, and it works for every multiplication. Choose to split the number that gives the easiest parts.
Löst exempel
47 × 6
- → 40 × 6 = 240
- → 7 × 6 = 42
- → 240 + 42 = 282
Svar: 282
Öva: Try 38 × 7, 64 × 9 and 125 × 8.
02
Multiply by 11
For a two-digit number, add its two digits and put the sum in the middle. If the sum is 10 or more, carry 1 to the first digit.
Löst exempel
57 × 11
- → 5 + 7 = 12
- → Put 2 in the middle and carry 1: 5 + 1 = 6
- → 627
Svar: 627
Öva: Try 36 × 11, 82 × 11 and 99 × 11.
03
Multiply by 5 and 25
5 is 10 ÷ 2, so multiply by 10 and halve. 25 is 100 ÷ 4, so multiply by 100 and halve twice. These turn hard products into easy ones.
Löst exempel
84 × 25
- → 84 × 100 = 8 400
- → Half: 4 200
- → Half again: 2 100
Svar: 2 100
Öva: Try 46 × 5, 132 × 5 and 36 × 25.
04
Square numbers ending in 5
Take the tens digit, multiply it by the next number up, and write 25 after it. This works because (10a + 5)² = 100·a(a + 1) + 25.
Löst exempel
75²
- → 7 × 8 = 56
- → Write 25 after it: 5 625
Svar: 5 625
Öva: Try 35², 65² and 105².
05
Difference of squares
When two numbers sit equally far from a round number, use (a + b)(a − b) = a² − b². 48 × 52 is 50² minus 2².
Löst exempel
48 × 52
- → Both are 2 away from 50
- → 50² = 2 500
- → 2² = 4
- → 2 500 − 4 = 2 496
Svar: 2 496
Öva: Try 39 × 41, 97 × 103 and 28 × 32.
06
Two-digit by two-digit
Split one factor and multiply the other by each part. Keep a running total from the largest part. With practice, 34 × 27 takes only two steps.
Löst exempel
34 × 27
- → 34 × 20 = 680
- → 34 × 7 = 238
- → 680 + 238 = 918
Svar: 918
Öva: Try 23 × 46, 58 × 32 and 71 × 19 (use 71 × 20 − 71).
Vanliga misstag
- Forgetting to multiply both parts. In 47 × 6, both 40 and 7 must be multiplied by 6.
- Forgetting the carry in the 11 trick. 57 × 11 is 627, not 5 127.
- Using difference of squares when the numbers are not equally far from the middle.
Sammanfattning
- Split into tens and ones and add the partial products.
- Turn × 5 and × 25 into × 10 or × 100 followed by halving.
- Look for patterns: numbers ending in 5, numbers around a round middle, and × 11.
In i dojon
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