A fraction shows a part of a whole. It is written as numerator / denominator.

Numerator – the number on top, showing how many parts we have.
Denominator – the number below, showing how many equal parts make one whole.

Example: 3/4 means 3 parts out of 4 equal parts.

People needed to show parts of things that are not whole numbers.

1. Sharing food (½ of a cake)


2. Measuring liquids (¾ litre of milk)


3. Telling time (¼ hour = 15 minutes)


4. Money (½ of ₦100 = ₦50)

Fractions help in mathematics, science, trade and daily life whenever something is not a complete whole.

Rules

1. Same denominator: Add numerators only, keep the denominator, simplify if possible.


2. Different denominators:
   
   
   1. Find the LCM of the denominators (common denominator).
   
   
   2. Convert each fraction to an equivalent fraction with that denominator.
   
   
   3. Add numerators, keep the common denominator.
   
   
   4. Simplify the result.
   
   

Examples – Addition

(A) Same Denominator

1. 1/4 + 2/4 = (1 + 2)/4 = 3/4


2. 3/8 + 1/8 = (3 + 1)/8 = 4/8 = 1/2


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


4. 5/6 + 1/6 = (5 + 1)/6 = 6/6 = 1

(B) Different Denominators

1. 1/2 + 1/3 → LCM(2,3)=6 → 3/6 + 2/6 = 5/6


2. 2/3 + 1/4 → LCM(3,4)=12 → 8/12 + 3/12 = 11/12


3. 3/5 + 1/10 → LCM(5,10)=10 → 6/10 + 1/10 = 7/10


4. 1/3 + 2/9 → LCM(3,9)=9 → 3/9 + 2/9 = 5/9


5. 3/4 + 1/8 → LCM(4,8)=8 → 6/8 + 1/8 = 7/8


6. 5/12 + 1/6 → LCM(12,6)=12 → 5/12 + 2/12 = 7/12


7. 1 1/2 + 2 1/3 → Convert: 1 1/2 = 3/2, 2 1/3 = 7/3 → LCM(2,3)=6 → 9/6 + 14/6 = 23/6 = 3 5/6


8. 1/4 + 1/2 + 1/8 → LCM(4,2,8)=8 → 2/8 + 4/8 + 1/8 = 7/8

Rules

1. Same denominator: Subtract numerators; keep denominator; simplify if possible.


2. Different denominators:
   
   
   1. Find LCM of denominators.
   
   
   2. Change fractions to equivalent fractions with that denominator.
   
   
   3. Subtract numerators, keep the denominator.
   
   
   4. Simplify.
   
   

Examples – Subtraction

(A) Same Denominator

1. 3/4 − 1/4 = (3 − 1)/4 = 2/4 = 1/2


2. 5/6 − 2/6 = (5 − 2)/6 = 3/6 = 1/2


3. 4/5 − 1/5 = (4 − 1)/5 = 3/5


4. 7/8 − 3/8 = (7 − 3)/8 = 4/8 = 1/2

(B) Different Denominators

1. 3/4 − 1/3 → LCM(4,3)=12 → 9/12 − 4/12 = 5/12


2. 5/6 − 1/4 → LCM(6,4)=12 → 10/12 − 3/12 = 7/12


3. 7/10 − 2/5 → 2/5 = 4/10 → 7/10 − 4/10 = 3/10


4. 2 1/3 − 1 1/6 → Convert: 7/3 − 7/6 → LCM(3,6)=6 → 14/6 − 7/6 = 7/6 = 1 1/6


5. 1/2 − 1/3 → LCM(2,3)=6 → 3/6 − 2/6 = 1/6


6. 5/8 − 1/4 → 1/4 = 2/8 → 5/8 − 2/8 = 3/8


7. 3/5 − 4/15 → LCM(5,15)=15 → 9/15 − 4/15 = 5/15 = 1/3


8. 1 − 3/4 → 1 = 4/4 → 4/4 − 3/4 = 1/4

1. Cooking & baking – e.g. ½ cup + ¼ cup of sugar = ¾ cup.


2. Money & trade – adding or subtracting part payments.


3. Time – ¼ hour + ½ hour = ¾ hour.


4. Construction & measurement – measuring lengths in fractions of a metre.


5. Sports & games – adding or taking away points that are fractional.

Tips & Common Mistakes

1. Always simplify your final answer.


2. When subtracting, always change to common denominator first.


3. For mixed numbers: convert to improper fractions or subtract whole numbers separately and then fractions.


4. Check that your answer makes sense (for example: ½ + ¼ should be less than 1, and it is ¾).