Class 6 · Maths

Fractions

4 min readUpdated November 2026

In one line

A fraction shows a part of a whole: the bottom number says how many equal parts, and the top number says how many you have.

Parts of a fraction

3 is the numerator (parts taken); 4 is the denominator (equal parts in all).

Type	Meaning	Example
Proper	Numerator smaller than denominator (less than 1)	2/5, 3/4
Improper	Numerator equal to or bigger than denominator	7/4, 5/5
Mixed	A whole number and a proper fraction	1¾ (same as 7/4)
Like	Same denominator	1/8, 3/8, 5/8
Unlike	Different denominators	1/2, 2/3

Mixed → improper: 2⅓ = (2 × 3 + 1)/3 = 7/3. Improper → mixed: 11/4 = 11 ÷ 4 = 2 remainder 3 = 2¾.

Multiply or divide the top and bottom by the same number to get an equivalent fraction: 1/2 = 2/4 = 3/6 = 50/100.
A fraction is in its simplest form when the top and bottom have no common factor except 1.
To simplify, divide both by their HCF: 18/24 → HCF is 6 → 3/4.

Same denominator: bigger numerator, bigger fraction. 5/9 > 2/9.
Same numerator: smaller denominator, bigger fraction. 1/3 > 1/5 (a pizza cut into 3 gives bigger slices than one cut into 5).
Both different: change them to the same denominator using the LCM. 2/3 vs 3/4 → 8/12 vs 9/12 → 3/4 is bigger.

Like fractionsAdd the tops, keep the bottom. 2/7 + 3/7 = 5/7.

Unlike fractions1/2 + 1/3: LCM of 2 and 3 is 6. 3/6 + 2/6 = 5/6.
3/4 − 1/6: LCM is 12. 9/12 − 2/12 = 7/12.

Adding the bottoms too. 1/2 + 1/3 is not 2/5. Make the denominators the same first.
Thinking a bigger denominator means a bigger fraction. 1/8 is smaller than 1/4.
Forgetting to simplify. Always give the answer in its simplest form.

Numerator / denominator	Parts taken / total equal parts
Proper	Top < bottom · Improper: top ≥ bottom · Mixed: whole + fraction
Equivalent	× or ÷ top and bottom by the same number
Simplest form	Divide both by the HCF
Add / subtract	Make denominators the same (LCM), then add or subtract tops