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In school, we always add from the back (Units), but in this trick, we break the numbers and add from the front (Tens).
Step 1: Add the Tens (tens place) parts of both numbers (e.g., 50 from 55 and 80 from 80).
Step 2: Add the remaining Unit (ones place) digits.
Step 3: Combine both results.
Example 1: 55 + 80
Add Tens: From 55 take 50 and the other number is 80.
50 + 80 = 130
Add Units: The remaining digit from 55 is 5.
Combine: 130 + 5 = 135
Answer: 135
Example 2: 67 + 28
Add Tens: 60 + 20 = 80.
Add Units: 7 + 8 = 15.
Combine: 80 + 15 = 95.
Answer: 95
Example 3: 45 + 37
Add Tens: 40 + 30 = 70.
Add Units: 5 + 7 = 12.
Combine: 70 + 12 = 82.
Answer: 82
Example 4: 125 + 46
Add Larger Parts: 120 + 40 = 160.
Remaining Units: 5 + 6 = 11.
Combine: 160 + 11 = 171.
Answer: 171
When adding a number very close to 100 or 200 (like 90, 99, 190, 195), follow these steps:
Step 1: Add it as a round figure (e.g., treat 90 as 100).
Step 2: Subtract the extra amount you added from the final answer.
Example 1: 684 + 90
Round Figure: Treat 90 as 100.
684 + 100 = 784
Subtract Extra: Since we added 100 instead of 90, we added 10 extra. Now subtract 10:
784 - 10 = 774
Answer: 774
Example 2: 456 + 99
Round Figure: Treat 99 as 100.
456 + 100 = 556
Subtract Extra: Adding 100 added 1 extra (since 99 is 1 less than 100).
556 - 1 = 555
Answer: 555
Example 3: 825 + 190
Round Figure: Treat 190 as 200.
825 + 200 = 1025
Subtract Extra: From 190 to 200 we added 10 extra.
1025 - 10 = 1015
Answer: 1015
Example 4: 347 + 48
Round Figure: Treat 48 as 50.
347 + 50 = 397
Subtract Extra: Adding 50 added 2 extra.
397 - 2 = 395
Answer: 395
When adding large numbers, simplify them by following these steps:
Step 1: Add the difficult number as a round figure (e.g., treat 580 as 600).
Step 2: Subtract the extra amount you added from the final answer.
Example 1: 263 + 580
Round Figure: Treat 580 as 600.
263 + 600 = 863
Subtract Extra: From 580 to 600 we added 20 extra, so subtract 20:
863 - 20 = 843
Answer: 843
Example 2: 450 + 295
Round Figure: Treat 295 as 300.
450 + 300 = 750
Subtract Extra: 295 to 300 is a gap of 5, so subtract 5:
750 - 5 = 745
Answer: 745
Example 3: 1240 + 880
Round Figure: Treat 880 as 900.
1240 + 900 = 2140
Subtract Extra: 880 to 900 is a gap of 20, so subtract 20:
2140 - 20 = 2120
Answer: 2120
Example 4: 537 + 398
Round Figure: Treat 398 as 400.
537 + 400 = 937
Subtract Extra: Adding 400 added 2 extra, so subtract 2:
937 - 2 = 935
Answer: 935
When two numbers are reverses of each other, follow these 2 steps:
Step 1: Add the two digits of any one number.
Step 2: Multiply the result by 11.
Example 1: 37 + 73
Add Digits: 3 + 7 = 10
Multiply by 11: 10 x 11 = 110
Answer: 110
Example 2: 45 + 54
Add Digits: 4 + 5 = 9
Multiply by 11: 9 x 11 = 99
Answer: 99
Example 3: 82 + 28
Add Digits: 8 + 2 = 10
Multiply by 11: 10 x 11 = 110
Answer: 110
For a long list of numbers, follow these 3 steps:
Step 1 (Scan): Look for pairs whose last digits sum to 10 (e.g., 8 and 2, 9 and 1, or 7 and 3).
Step 2 (Pairing): Combine pairs that sum to 100.
Step 3 (Final Total): Add all the 100s together.
Example 1: 48 + 59 + 52 + 41
First Pair: 48 and 52 (8 + 2 = 10).
48 + 52 = 100
Second Pair: 59 and 41 (9 + 1 = 10).
59 + 41 = 100
Total: 100 + 100 = 200
Answer: 200
Example 2: 25 + 67 + 75 + 33
First Pair: 25 and 75 (ends with 5 and 5).
25 + 75 = 100
Second Pair: 67 and 33 (ends with 7 and 3).
67 + 33 = 100
Total: 100 + 100 = 200
Answer: 200
Example 3: 14 + 82 + 86 + 18
First Pair: 14 and 86 (ends with 4 and 6).
14 + 86 = 100
Second Pair: 82 and 18 (ends with 2 and 8).
82 + 18 = 100
Total: 100 + 100 = 200
Answer: 200
When subtracting a number close to 100, 200, or 1000, follow these steps:
Step 1: Subtract the round figure instead (e.g., 200 instead of 190).
Step 2: Since you subtracted too much, add back the extra amount.
Example 1: 825 − 190
Round Figure: Treat 190 as 200 and subtract.
825 − 200 = 625
Add Extra: We needed to subtract 190 but we subtracted 200, so we subtracted 10 extra. Add 10 back:
625 + 10 = 635
Answer: 635
Example 2: 543 − 98
Round Figure: Treat 98 as 100.
543 − 100 = 443
Add Extra: Subtracting 100 subtracted 2 extra (since 98 is 2 less than 100).
443 + 2 = 445
Answer: 445
Example 3: 1250 − 890
Round Figure: Treat 890 as 900.
1250 − 900 = 350
Add Extra: 890 to 900 is a difference of 10, so add 10 back:
350 + 10 = 360
Answer: 360
Example 4: 765 − 49
Round Figure: Treat 49 as 50.
765 − 50 = 715
Add Extra: Subtracting 50 subtracted 1 extra, so add 1:
715 + 1 = 716
Answer: 716
When two numbers are reverses of each other (e.g., 96 and 69), follow these 2 steps:
Step 1: Find the difference between the two digits. (Subtract the smaller digit from the larger digit).
Step 2: Multiply the result by 9.
Example 1: 96 − 69
Digit Difference: 9 − 6 = 3
Multiply by 9: 3 x 9 = 27
Answer: 27
Example 2: 82 − 28
Digit Difference: 8 − 2 = 6
Multiply by 9: 6 x 9 = 54
Answer: 54
Example 3: 73 − 37
Digit Difference: 7 − 3 = 4
Multiply by 9: 4 x 9 = 36
Answer: 36
To find the difference between two numbers, treat a round figure (like 100, 400, 600) as a "Bridge" and follow these steps:
Step 1: Find the gap from the smaller number to the Bridge.
Step 2: Find the gap from the Bridge to the larger number.
Step 3: Add both gaps.
Example 1: 627 − 578 (Bridge = 600)
First Gap: From 578 to 600, how much to add?
578 + 22 = 600.
Second Gap: From 600 to 627, how much ahead?
600 + 27 = 627.
Total Gap: Add both:
22 + 27 = 49.
Answer: 49
Example 2: 412 − 385 (Bridge = 400)
First Gap: 385 to 400:
385 + 15 = 400.
Second Gap: 400 to 412:
400 + 12 = 412.
Total Gap: 15 + 12 = 27.
Answer: 27
When subtracting two large numbers, follow these steps:
Step 1 (Big Jump): Add a big number (100, 200, 300) to the smaller number to get close to or slightly past the larger number.
Step 2 (Check): See how far past your actual target you went.
Step 3 (Adjustment): Subtract that extra part from the big jump you took.
Example 1: 815 − 519
Big Jump: Add 300 directly to 519:
519 + 300 = 819
How much over?: We needed 815, but reached 819. We overshot by 4.
Final Answer: Subtract 4 from the 300 we added:
300 − 4 = 296
Answer: 296
Example 2: 450 − 192
Big Jump: Add 300 to 192:
192 + 300 = 492
How much over?: How much is 492 larger than our target (450)?
492 − 450 = 42
Final Answer: Subtract 42 from 300:
300 − 42 = 258
Answer: 258
Example 3: 725 − 395
Big Jump: Add 400 to 395:
395 + 400 = 795
How much over?: How much is 795 larger than target (725)?
795 − 725 = 70
Final Answer: Subtract 70 from 400:
400 − 70 = 330
Answer: 330
When one number is double the other, follow these 3 steps:
Step 1: Identify if one number is double the other (e.g., 15 and 30).
Step 2: Square the smaller number (multiply it by itself).
Step 3: Multiply the result by 2 (double it).
Example 1: 15 × 30
Here 30 is double of 15 (15 x 2 = 30).
Square the smaller number (15):
15 x 15 = 225
Now double 225:
225 x 2 = 450
Answer: 450
Example 2: 12 × 24
Here 24 is double of 12.
Square 12:
12 x 12 = 144
Double 144:
144 x 2 = 288
Answer: 288
Example 3: 25 × 50
Here 50 is double of 25.
Square 25:
25 x 25 = 625
Double 625:
625 x 2 = 1250
Answer: 1250
When multiplying 37 by a multiple of 3 (3, 6, 9, 12... 30, 33), follow these 2 steps:
Step 1: Divide the other number by 3.
Step 2: Multiply the result by 111 (or write the number three times if it's a single digit).
Example 1: 37 x 33
First, divide 33 by 3:
33 / 3 = 11
Now multiply 11 by 111:
11 x 111 = 1221
Answer: 1221
Example 2: 37 x 18
Divide 18 by 3:
18 / 3 = 6
Multiply 6 by 111 (write 6 three times):
6 x 111 = 666
Answer: 666
Example 3: 37 x 27
Divide 27 by 3:
27 / 3 = 9
Multiply 9 by 111:
9 x 111 = 999
Answer: 999
To multiply any number by 15, follow these 3 steps:
Step 1: Add a zero to the number (multiply by 10).
Step 2: Halve the new number.
Step 3: Add both numbers together.
Example 1: 15 x 164
Add a zero to 164:
164 → 1640
Half of 1640:
1640 / 2 = 820
Add them together:
1640 + 820 = 2460
Answer: 2460
Example 2: 15 x 42
Add a zero to 42:
42 → 420
Half of 420:
420 / 2 = 210
Add them:
420 + 210 = 630
Answer: 630
Example 3: 15 x 84
Add a zero to 84:
84 → 840
Half of 840:
840 / 2 = 420
Add them:
840 + 420 = 1260
Answer: 1260
When multiplying two consecutive numbers (e.g., 12‑13, 20‑21), follow these steps:
Step 1: Square the smaller number.
Step 2: Add the same smaller number to the square.
Example 1: 26 x 27
Smaller number is 26. Square it:
26 x 26 = 676
Now add the smaller number (26):
676 + 26 = 702
Answer: 702
Example 2: 12 x 13
Square 12:
12 x 12 = 144
Add 12:
144 + 12 = 156
Answer: 156
Example 3: 15 x 16
Square 15:
15 x 15 = 225
Add 15:
225 + 15 = 240
Answer: 240
When both numbers end with 1, follow these 3 steps:
Step 1 (Last Digit): Always write 1 at the end.
Step 2 (Middle Digit): Add the leading digits. (If the sum is 10 or more, write only the last digit and carry the rest).
Step 3 (First Digit): Multiply the leading digits and add any carry.
Example 1: 61 x 51
Last Digit: Write 1.
Add: 6 + 5 = 11
(We write 1 and carry 1).
Multiply: 6 x 5 = 30
30 + 1 (carry) = 31
Answer: 3111
Example 2: 41 x 31
Last Digit: 1.
Add: 4 + 3 = 7.
Multiply: 4 x 3 = 12.
Answer: 1271
Use this trick when the leading digits are the same and the last digits sum to 10.
Step 1 (Last Two Digits): Multiply the last digits. (Always write 2 digits, e.g., 9 as 09).
Step 2 (First Digits): Multiply the leading digit by its next number (Next Number).
Example 1: 31 x 39
Check: Leading digits are both 3 (Same) and last digits 1 + 9 = 10. Trick works!
Last Digits: 1 x 9 = 9. Write as two digits: 09.
First Digits: The next number after 3 is 4.
3 x 4 = 12.
Answer: 1209
Example 2: 72 x 78
Check: 7 is same and 2 + 8 = 10.
Last Digits: 2 x 8 = 16.
First Digits: Next number after 7 is 8.
7 x 8 = 56.
Answer: 5616
Example 3: 43 x 47
Check: 4 is same and 3 + 7 = 10.
Last Digits: 3 x 7 = 21.
First Digits: Next number after 4 is 5.
4 x 5 = 20.
Answer: 2021
Example 4: 114 x 116 (Large Numbers)
Check: 11 is same and 4 + 6 = 10.
Last Digits: 4 x 6 = 24.
First Digits: Next number after 11 is 12.
11 x 12 = 132.
Answer: 13224
Use this trick when the last digit is the same and the leading digits sum to 10.
Step 1 (Last Two Digits): Square the common last digit. Always write 2 digits.
Step 2 (First Digits): Multiply the leading digits and add the same last digit.
Example 1: 15 x 95
Check: Last digit 5 is same and leading digits 1 + 9 = 10. Trick works!
Last Part: Square the common digit (5):
5 x 5 = 25.
First Part: Multiply leading digits and add the common unit digit:
(1 x 9) + 5 = 9 + 5 = 14.
Answer: 1425
Example 2: 46 x 66
Check: Last digit 6 is same and 4 + 6 = 10.
Last Part: 6 x 6 = 36.
First Part: (4 x 6) + 6 = 24 + 6 = 30.
Answer: 3036
Example 3: 38 x 78
Check: Last digit 8 is same and 3 + 7 = 10.
Last Part: 8 x 8 = 64.
First Part: (3 x 7) + 8 = 21 + 8 = 29.
Answer: 2964
Use this trick when both numbers end with 5 and their difference is exactly 10.
Step 1 (Last Two Digits): This part is always fixed. Always write 75 at the end.
Step 2 (First Part): Choose the larger leading digit. Square it and subtract 1.
Example 1: 75 x 85
Check: Both end with 5 and difference is 10 (85 - 75 = 10).
Last Part: Write 75 at the end.
First Part: Leading digits are 7 and 8. Larger is 8.
Square 8: 8 x 8 = 64
Subtract 1: 64 - 1 = 63
Answer: 6375
Example 2: 45 x 55
Check: Difference 10 and ends with 5.
Last Part: 75.
First Part: Larger digit is 5.
Square 5: 5 x 5 = 25
Subtract 1: 25 - 1 = 24
Answer: 2475
Example 3: 95 x 105
Check: Difference 10 (105 - 95 = 10).
Last Part: 75.
First Part: Leading digits are 9 and 10. Larger is 10.
Square 10: 10 x 10 = 100
Subtract 1: 100 - 1 = 99
Answer: 9975
When multiplying a repeating number by a single digit, follow these 4 steps:
Step 1 (Single Multiply): Multiply just one digit of the repeating number by the single digit.
Step 2 (Boundary): Place the two digits of the answer at the beginning and end, leaving a gap in the middle.
Step 3 (Add): Add those two digits together.
Step 4 (Fill Gap): Fill the middle gap with the sum, repeated one fewer time than the number of digits in the original number.
Example 1: 7777 x 2
Multiply: 7 x 2 = 14.
Boundary: 1 at start, 4 at end: 1 _ _ _ 4.
Add: 1 + 4 = 5.
Fill Gap: 7777 has four digits, so we put 5 in the middle three times.
Result: 15554
Answer: 15554
Example 2: 666 x 4
Multiply: 6 x 4 = 24.
Boundary: 2 _ _ 4.
Add: 2 + 4 = 6.
Fill Gap: 666 has three digits, so put 6 in the middle twice.
Result: 2664
Answer: 2664
Example 3: 33333 x 3
Multiply: 3 x 3 = 09.
Boundary: 0 _ _ _ _ 9.
Add: 0 + 9 = 9.
Fill Gap: Five digits, so put 9 in the middle four times.
Result: 099999 (i.e., 99999)
Answer: 99999
To divide any number by 5, follow these two simple steps:
Step 1: Double the Number
Multiply the given number by 2.
Step 2: Put the Decimal
Move the decimal one place from the right.
Example 1: 18 ÷ 5
18 × 2 = 36 → 3.6 ✅
Example 2: 124 ÷ 5
124 × 2 = 248 → 24.8 ✅
Example 3: 4232 ÷ 5
4232 × 2 = 8464 → 846.4 ✅
To divide any number by 25, follow these two steps:
Step 1: Multiply by 4
Multiply the given number by 4. (Tip: Multiplying by 4 means doubling it twice).
Step 2: Put the Decimal (2 Places)
Move the decimal two places from the right.
Example 1: 12 ÷ 25
Step 1: Multiply 12 by 4.
12 x 4 = 48
Step 2: Move decimal two places (since 25 has two digits).
48 → 0.48
Answer: 0.48
Example 2: 212 ÷ 25
Step 1: 212 x 4 = 848
Step 2: 848 → 8.48
Answer: 8.48
Example 3: 31 ÷ 25
Step 1: 31 x 4 = 124
Step 2: 124 → 1.24
Answer: 1.24
To divide any number by 125, follow these 2 steps:
Step 1: Multiply the number by 8.
Step 2: Move the decimal three places from the right.
Example 1: 11 / 125
First, multiply 11 by 8:
11 x 8 = 88
Now move decimal three places. Since we only have two digits (88), we add a zero first:
088 becomes 0.088
Answer: 0.088
Example 2: 12 / 125
12 x 8 = 96
Add zero: 096 → 0.096
Answer: 0.096
Example 3: 102 / 125
102 x 8 = 816
Move decimal: 816 → 0.816
Answer: 0.816
Example 4: 250 / 125 (Check)
250 x 8 = 2000
Move decimal: 2000 → 2.000 (i.e., 2)
Answer: 2
To divide any number by 50, remember these 2 steps:
Step 1: Multiply the number by 2.
Step 2: Move the decimal two places from the right.
Example 1: 15 / 50
15 x 2 = 30
Move decimal two places: 30 → 0.30 (which is 0.3)
Answer: 0.3
Example 2: 124 / 50
124 x 2 = 248
Move decimal: 248 → 2.48
Answer: 2.48
Example 3: 7 / 50
7 x 2 = 14
Move decimal: 14 → 0.14
Answer: 0.14
To divide any number by 500, follow these 2 steps:
Step 1: Multiply the number by 2.
Step 2: Move the decimal three places from the right.
Example 1: 15 / 500
15 x 2 = 30
Move decimal three places. Since we have only two digits (30), add a zero first:
030 → 0.030 (i.e., 0.03)
Answer: 0.03
Example 2: 124 / 500
124 x 2 = 248
Move decimal three places:
248 → 0.248
Answer: 0.248
Example 3: 7 / 500
7 x 2 = 14
Add two zeros to make three digits: 014 → 0.014
Answer: 0.014
When dividing a single digit number by 9, that digit repeats after the decimal.
Step 1: Write 0.
Step 2: Write the digit repeatedly after the decimal.
Step 3: A bar (line) over the repeating digit indicates it repeats forever.
Example 1: 4 ÷ 9
Step 1: 0.
Step 2: 0.4444...
Step 3: Write as 0.4 (with bar)
Answer: 0.444...
Example 2: 7 ÷ 9
0.777... → 0.7 (bar)
Answer: 0.777...
Example 3: Larger numerator (e.g., 12 ÷ 9)
If the numerator is bigger than 9, use the addition method:
Look at 12: first digit 1, second 2.
Write the first digit as is: 1.
Add the first digit to the second: 1 + 2 = 3.
Repeat this 3 after the decimal.
Answer: 1.333... or 1.3 (bar)
If the numerator is less than 99, follow these 2 steps:
Step 1: Write 0.
Step 2: Write the two digits after the decimal and put a bar over them to indicate repetition.
Example 1: 45 / 99
0. written.
45 repeats: 0.454545...
Written as 0.45 (bar)
Answer: 0.4545...
Example 2: 13 / 99
0.131313... → 0.13 (bar)
Answer: 0.1313...
Example 3: 7 / 99 (Single Digit)
Write 7 as 07.
0.070707... → 0.07 (bar)
Answer: 0.0707...
Special Case: 3-digit numerator (e.g., 145 / 99)
Add the first digit (1) to the remaining two digits (45):
1 + 45 = 46
Place the first digit before the decimal and repeat the new sum after it.
Answer: 1.4646... or 1.46 (bar)
Another example: 254 / 99
First digit (2) + remaining (54) = 56
Answer: 2.5656... or 2.56 (bar)
If the numerator is less than 999, follow these simple steps:
Step 1: Write 0.
Step 2: Write the three digits after the decimal and put a bar over them.
Example 1: 123 / 999
0. written.
123 repeats: 0.123123...
Bar format: 0.123 (bar)
Answer: 0.123123...
Example 2: 45 / 999 (Only 2 digits)
Write 45 as 045.
0.045045... → 0.045 (bar)
Answer: 0.045045...
Example 3: 7 / 999 (Only 1 digit)
Write 7 as 007.
0.007007... → 0.007 (bar)
Answer: 0.007007...
Special Case: 4-digit numerator (e.g., 1234 / 999)
Add the first digit (1) to the remaining three (234):
1 + 234 = 235
Answer: 1.235235... or 1.235 (bar)