Addition is combining two or more numbers to find their sum or total.

Subtraction is taking away one number from another to find the difference.

In fractions, addition is combining fractions; subtraction is removing one fraction from another.

1. Align place values: Write numbers one under the other so that units align with units, tens with tens, etc.


2. Add from right to left: Start at the units column, then tens, hundreds, etc.


3. Carry if needed: If the sum of a column is ≥ 10, write the last digit in that column and carry the tens part to the next left column.


4. Write down final carried over if there is one at the leftmost column.

Example 1 :
Add 237 + 489

  237
+ 489
------

1. Units: 7 + 9 = 16 → write down 6, carry 1 to tens


2. Tens: 3 + 8 = 11, plus carried 1 = 12 → write down 2, carry 1 to hundreds


3. Hundreds: 2 + 4 = 6, plus carried 1 = 7


4. Result = 726

1. Align place values: Write the larger (or minuend) on top, smaller (subtrahend) below, aligned by place.


2. Subtract right to left: Start from units column, then tens, etc.


3. Borrow if needed: If the top digit is smaller than the bottom digit, borrow 1 from the next left column (making the top of current column + 10), reduce the next column by 1.


4. Continue to leftmost column and write the difference.

Example 2 :
Subtract 154 from 572

  572
− 154
-------

1. Units: 2 − 4 → can’t, borrow 1 ten from tens → tens becomes 6, units becomes 12 → 12 − 4 = 8


2. Tens: now 6 − 5 = 1


3. Hundreds: 5 − 1 = 4


4. Result = 418

1 Fractions — Same Denominator

If fractions have the same denominator, we add or subtract numerators and keep the denominator same.

Example 3: 3/7 + 2/7 = (3 + 2)/7 = 5/7

Example 4: 5/8 − 3/8 = (5 − 3)/8 = 2/8 = 1/4 after simplification.

2 Fractions — Different Denominators

1. Find LCM of denominators to get a common denominator.


2. Convert each fraction to an equivalent fraction with that common denominator.


3. Add or subtract numerators, keep the common denominator.


4. Simplify result (if possible).

Example 5 — Addition: 1/3 + 1/4

1. LCM(3,4) = 12


2. 1/3 = 4/12, 1/4 = 3/12


3. Sum = (4 + 3)/12 = 7/12

Example 6 — Subtraction: 5/6 − 1/4

1. LCM(6,4) = 12


2. 5/6 = 10/12, 1/4 = 3/12


3. Difference = (10 − 3)/12 = 7/12

Examples (Whole Numbers & Fractions)

Whole Numbers

Example A: 345 + 678

1. Units: 5 + 8 = 13, write 3 carry 1


2. Tens: 4 + 7 = 11 + carry 1 = 12, write 2 carry 1


3. Hundreds: 3 + 6 = 9 + carry 1 = 10


4. Answer = 1 023

Example B: 900 − 478

1. Units: 0 − 8 → borrow → becomes 10 − 8 = 2


2. Tens: (borrowed) 9 becomes 8 → 8 − 7 = 1


3. Hundreds: 8 − 4 = 4


4. Answer = 422

Fractions

Example C: 2/5 + 3/5 = 5/5 = 1

Example D: 7/10 − 2/10 = 5/10 = 1/2

Example E: 3/8 + 1/4

1. LCM(8,4)=8


2. 1/4 = 2/8


3. Sum = (3 + 2)/8 = 5/8

Example F: 5/12 − 1/6

1. LCM(12,6)=12
2. 1/6 = 2/12
3. Difference = (5 − 2)/12 = 3/12 = 1/4

Example G: 4/9 + 5/18

1. LCM(9,18)=18


2. 4/9 = 8/18


3. Sum = (8 + 5)/18 = 13/18

Example H: 7/15 − 2/9

1. LCM(15,9)=45


2. 7/15 = 21/45, 2/9 = 10/45


3. Difference = (21 − 10)/45 = 11/45

Common Mistakes

1. Always align place values when adding/subtracting whole numbers.


2. Always work right to left.


3. For fractions, always convert to common denominator before adding/subtracting.


4. Simplify final answer if possible.


5. Watch out for borrowing across several columns.


6. In subtraction, do not subtract larger top from smaller — borrow properly.