# Addition Shortcut

**Adding By Group**

Look for combinations that reach to 10-level (10, 20, 30, 40, etc.).

For example:

3 + 4 + 7 + 6 + 3 + 7 → 3 + 7 + 4 + 6 + 3 + 7 → 10 + 10 +10 = 30;

22 + 41 + 5 + 8 + 4 → 22 + 8 + 41 + 4 + 5 → 30 + 50 = 80

Splitting numbers into easy parts, can make them easier to add.

For example:

22 + 41 + 35 + 44 → (20 + 2) + (40 + 1) + (30 + 5) + (40 + 4) → 130 + 12 = 142

**Add and Subtract Method of Simplifying Numbers**

Sometimes it is possible to make an addition simpler by adding and subtracting a number from both numbers that we are adding.

For example:

91 + 79 → (91 + 9) + (79 – 9) → 100 + 70 = 170;

396 + 536 → (396 + 4) + (536 – 4) → 400 + 532 = 932

**Adding By Multiplying**

If a number is repeated often, use multiplication to speed up addition.

For example:

7 + 5 + 7 + 6 + 2 + 7 → 3 × 7 + 5 + 6 + 2 → 21 + 13 = 34;

25 + 20 + 25 + 9 + 25 → 3 × 25 + 29 → 75 + 29 = 75 + 30 – 1 = 104

**Rounding Off Numbers for Addition**

GRE folks will not ask you exact value in most cases. So it is better to round off any numbers to speed up addition.

For instance:

38,323 + 24,625 + 95,321 + 12,456 ≈ 39,000 + 24,000 + 96,000 + 12,000 ≈ 171,000 (exact sum 170,725).

To round off each number to the nearest thousand, add 1 to the thousand digit if the hundred digit is 5 or more; otherwise, let the thousand digit stand as it is.

You add decimal number in similar approach.

543.5 + 235.34 + 356.78 ≈ 544 + 235 + 357 ≈ 500 + 200 + 300 + (44 + 35 + 57) ≈ 1000 + 136 = 1,136 (exact sum 1,135.62).

**Sum of Sequence**

Sum of all numbers from 1, 2, 3, 4, 5, ……. (N – 2), (N – 1), N can be found by the following way:

For example:

Sum of all numbers from 1, 2, 3, 4, ….., 100 can be found by:

Sum= 100 (100 + 1)/2 = 50 × 101 = 5050

Sum of all numbers between two numbers m and n can be found by following way:

Where, Inclusive counting, N = n – m + 1; m= first number, n= last number

For example:

Sum of all numbers between 30 to 39:

Sum= 10 (30 + 39)/2 = 10 × 34.5 = 345;

Where, N= 39 – 30 + 1= 10; m= 30, n= 39