A fraction represents a part of a whole.

It is written as a/b, where:

1. a is the numerator (how many parts we have),
2. b is the denominator (how many equal parts the whole is divided into).

Example: 3/4 means “3 of the 4 equal parts.”

Example: 1/2 is one half (one of two equal parts).

The numerator must be ≤ denominator (for proper fraction), or > (for improper). (From EduPadi)

Type	Description	Example
Proper fraction	Numerator is less than denominator	3/5
Improper fraction	Numerator is equal to or greater than denominator	7/4, 5/5
Mixed number	A whole number + a proper fraction	2 3/4
Equivalent fractions	Fractions that have the same value though different form	1/2 = 2/4 = 3/6

1. Equivalent fractions are different fractions that have the same value. You obtain them by multiplying or dividing numerator and denominator by the same nonzero number. (EduPadi)


2. To simplify a fraction, divide numerator and denominator by their greatest common factor (GCF / HCF) until no more division is possible.

Example: Simplify 12/18.

1. GCF(12,18) = 6


2. 12 ÷ 6 = 2 and 18 ÷ 6 = 3

So, 12/18 = 2/3

1. Bring them to a common denominator (often the LCM of their denominators).


2. Convert to equivalent fractions with that denominator.


3. Compare the numerators.

Example: Which is bigger, 3/4 or 5/6?

1. Denominators are 4 and 6 → LCM = 12


2. 3/4 = 9/12


3. 5/6 = 10/12


4. Compare numerators: 9 < 10 → 5/6 is larger.

(a) Addition of Fractions

1. If denominators are the same: add numerators, keep denominator.

   2/5 + 1/5 = (2+1)/5 = 3/5



2. If denominators differ: find LCM (common denominator), convert each to equivalent fraction, then add.

   Example: 1/3 + 1/4

   LCM(3,4) = 12

   1/3 = 4/12, 1/4 = 3/12

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

(b) Subtraction of Fractions

1. If denominators are the same: subtract numerators.

   5/8 − 3/8 = 2/8 = 1/4

2. If denominators differ: convert to common denominator first, then subtract.

   Example: 5/6 − 1/4

   LCM(6,4) = 12

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

   Difference = (10−3)/12 = 7/12

(c) Multiplication of Fractions

Multiply numerators to get new numerator; multiply denominators to get new denominator.

2/3 × 4/5 = (2×4)/(3×5) = 8/15

You can simplify before multiplying (cross-cancel) where possible to make calculation easier.

(d) Division of Fractions

Division of a fraction by another is the same as multiplying by its reciprocal (flip second fraction).

2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6

Examples

1. 3/7 + 2/7 = 5/7


2. 2/5 + 3/10 → LCM of 5,10 = 10 → 2/5 = 4/10 → 4/10 + 3/10 = 7/10


3. 5/6 − 1/3 → 1/3 = 2/6 → 5/6 − 2/6 = 3/6 = 1/2


4. 2/3 × 3/4 = 6/12 = 1/2


5. 5/8 ÷ 3/4 = 5/8 × 4/3 = 20/24 = 5/6

1. Sharing things: dividing a pizza, sharing money, splitting time.


2. Cooking / recipes: use fractional measurements (½ cup, ⅓ teaspoon).


3. Construction / measurement: lengths, parts of rods, cutting wood, tiling.


4. Finance: interest rates, parts of amounts.


5. In school / exam scores: fractional marks.