Mental Calculations - Getting the result fast Flashcards
Addition of 5
When adding 5 to a digit greater than 5, it is easier to first subtract 5 and then add 10.
For example,
7 + 5 = 12.
Also 7 - 5 = 2; 2 + 10 = 12.
Subtraction of 5
When subtracting 5 from a number ending with a a digit smaller than 5, it is easier to first add 5 and then subtract 10.
For example,
23 - 5 = 18.
Also 23 + 5 = 28; 28 - 10 = 18.
Division by 5
Similarly, it’s often more convenient instead to multiply first by 2 and then divide by 10.
For example,
1375/5 = 2750/10 = 275.
Multiplication by 5
It’s often more convenient instead of multiplying by 5 to multiply first by 10 and then divide by 2.
For example,
137×5 = 1370/2 = 685.
Division/multiplication by 4
Replace either with a repeated operation by 2.
For example,
124/4 = 62/2 = 31. Also, 124×4 = 248×2 = 496.
Division/multiplication by 25
Use operations with 4 instead.
For example,
37×25 = 3700/4 = 1850/2 = 925.
Division/multiplication by 8
Replace either with a repeated operation by 2.
For example,
124×8 = 248×4 = 496×2 = 992.
Division/multiplication by 125
Use operations with 8 instead.
For example,
37×125 = 37000/8 = 18500/4 = 9250/2 = 4625.
Product of two one-digit numbers greater than 5.
This is a rule that helps remember a big part of the multiplication table. Assume you forgot the product 7×9. Do this. First find the excess of each of the multiples over 5: it’s 2 for 7 (7 - 5 = 2) and 4 for 9 (9 - 5 = 4). Add them up to get 6 = 2 + 4. Now find the complements of these two numbers to 5: it’s 3 for 2 (5 - 2 = 3) and 1 for 4 (5 - 4 = 1). Remember their product 3 = 3×1. Lastly, combine thus obtained two numbers (6 and 3) as 63 = 6×10 + 3.
Product of numbers close to 100.
Say, you have to multiply 94 and 98. Take their differences to 100: 100 - 94 = 6 and 100 - 98 = 2. Note that 94 - 2 = 98 - 6 so that for the next step it is not important which one you use, but you’ll need the result: 92. These will be the first two digits of the product. The last two are just 2×6 = 12. Therefore, 94×98 = 9212.
Multiplying by 11.
To multiply a 2-digit number by 11, take the sum of its digits. If it’s a single digit number, just write it between the two digits. If the sum is 10 or more, do not forget to carry 1 over.
For example, 34×11 = 374 since 3 + 4 = 7. 47×11 = 517 since 4 + 7 = 11.
Faster subtraction.
Subtraction is often faster in two steps instead of one.
For example,
427 - 38 = (427 - 27) - (38 - 27) = 400 - 11 = 389.
A generic advice might be given as “First remove what’s easy, next whatever remains”. Another example:
1049 - 187 = 1000 - (187 - 49) = 900 - 38 = 862.
Faster addition.
Addition is often faster in two steps instead of one.
For example,
487 + 38 = (487 + 13) + (38 - 13) = 500 + 25 = 525.
A generic advice might be given as “First add what’s easy, next whatever remains”. Another example:
1049 + 187 = 1100 + (187 - 51) = 1200 + 36 = 1236.
Faster addition, #2.
It’s often faster to add a digit at a time starting with higher digits. For example,
583 + 645 = 583 + 600 + 40 + 5
= 1183 + 40 + 5
= 1223 + 5
= 1228.
Multipliply, then subtract.
When multiplying by 9, multiply by 10 instead, and then subtract the other number. For example,
23×9 = 230 - 23 = 207.
The same applies to other numbers near those for which multiplication is simplified: 23×51 = 23×50 + 23 = 2300/2 + 23 = 1150 + 23 = 1173.
87×48 = 87×50 - 87×2 = 8700/2 - 160 - 14 = 4350 - 160 - 14 = 4190 - 14 = 4176.