Below is an easy and straight-forward approach in proving the sum of natural numbers from 1 to N

Proof of Sum of Natural Numbers From 1 to N

Read More

Shortcut on Finding 15 Percent Of A Number

1. Choose a number.
2. Multiply the number by 3.
3. Divide by two
4. Move the decimal point one (to the left)

Example:

Find 15% of 72

72 x 3 = 216
216 ÷ 2 = 108

10.8 (move the decimal point to the left)

Thus, 15% of 72 = 10.8 Read More

Shortcut on Finding 45 Percent Of A Number

1. Choose a number.
2. Multiply the number by 9
3. Divide by 2.
4. Move the decimal point one place to the left.

Example:

Find 45% of 157.

Solution:

9 x 157 = 1,413
1,413 ÷ 2 = 706.5

70.65 (by moving the decimal point one place to the left)

Thus, 45% of 157 = 70.65 Read More

Shortcut on Squaring A 2-Digit Number Ending In 1:

1. Choose a 2-digit number ending in 1.
2. Subtract 1 from it.
3. Square the difference
4. Add the difference twice to its square(result of step 3).
5. Add 1
   

Example:

Step 1: Choose 41
Step2: 41-1 = 40
Step 3: 40² = 1,600
Step 4: 1,600 + 40 + 40 = 1,680
Step 5: 1,680 + 1 = 1,681

Thus, 41² = 1,681




Read More

Tricks on finding the sum of a sequence from 1 to a selected 1-digit number and back.

1. Choose a 1-digit number.
2. Square it.

Example:

Choose 6. Then, find the sum of 1+2+3+4+5+6+5+4+3+2+1. Instead of adding this manually, just simply take the square of 6.So, the sum is 36.

Thus, 1+2+3+4+5+6+5+4+3+2+1 = 36
Read More

Tricks on finding the sum of a sequence from 1 to a selected 2-digit number.

1. Choose a 2-digit number
2. If the number is odd, multiply it by half the number next to it. If the number is even, multiply half of it by the number next to it.

Example 1:

Find the sum of the sequence: 1,2,3,......., 33, 34

Step 1: The two-digit number number is 34

Step 2: The number next to 34 is 35. Multiply 35 by half of 34 which is 17.

           17 x 35 = 595


Therefore, the sum of the sequence 1,2,3,......., 33, 34 is 595.


Example 2:

Find the sum of the sequence: 1,2,3,.......,10, 11

Step 1: The two-digit number number is 11

Step 2: The number next to 11 is 12. Multiply 11 by half of 12 which is 6.

           11 x 6 = 66

Therefore, the sum of the sequence 1,2,3,.......,10,11 is 66. Read More

Tricks on getting the sum of consecutive numbers inclusive of two numbers.

1. Choose any two counting numbers (or signed numbers)
2. Add the numbers
3. Subtract the smaller number from the larger. Then add one (1) to the difference.
4. Multiply half the sum(in step 2) by the result in step 3.
   OR: Multiply half the result in step 3 by the sum (in step 2).

Example:

Find the sum of all the numbers from 5 to 26.


Step 1: 5 & 26

Step 2: 5 + 26 = 31

Step 3: 26 - 5 = 21
           21 + 1 = 22

Step 4: Multiply half of 22 by 31 :

            11 x 31 = 341

     OR: Multiply half of 31 by 22:

            15.5 X 22 = 341


Therefore, the sum of all the numbers from 5 to 26 is 341. Read More