Schooling · Class 6 · Mathematics · Fractions · Chapter on a page
CBSE Class 6 · Mathematics · NCERT Ganita Prakash
Fractions: chapter on a page
A cut of Shishya's notes for this chapter: the first paragraph of the introduction and the key ideas, formulas and facts, common mistakes and quick revision lists, word for word. Nothing is added or reworded; the worked examples are left out (they are on the chapter page).
About the notes: Written by Shishya's AI on 26 Sept 2026 from the chapter's title and class level, in Shishya's own words — not a copy or summary of the textbook. Read the official chapter for the book's own text, activities and exercises.
This note's current text has no applied fact-check on record.
Mind map
Drawn from the same notes by a fixed rule (no AI): each label is the item's own words — its bold term, its label before a colon, a short formula as written, or its first words.
The mind map as a list
- Key ideas
- A fraction has two parts
- Fractions like 1/2, 1/3, 1/4, 1/5…
- A proper fraction has a numerator…
- A mixed number combines a whole…
- Equivalent fractions look different…
- To compare fractions with the same…
- To add or subtract fractions with…
- Formulas and facts
- Fraction = Numerator / Denominator.…
- Equivalent fractions
- Comparing fractions with the same…
- a/c + b/c = (a + b)/c
- a/c − b/c = (a − b)/c
- Changing improper fraction to mixed…
- Watch out for
- Writing 3/8 as 8/3
- Thinking 1/4 is bigger than 1/2…
- Adding denominators when adding…
- Forgetting to multiply both…
- Writing an improper fraction like…
What this chapter is about
A fraction is a way to show a part of a whole. When you cut a roti into 4 equal pieces and eat 1 piece, you have eaten 1/4 of the roti. The bottom number tells how many equal parts the whole is divided into. The top number tells how many parts you are talking about.
Key ideas
- A fraction has two parts: the numerator (top number) shows how many parts you have; the denominator (bottom number) shows how many equal parts the whole is divided into.
- Fractions like 1/2, 1/3, 1/4, 1/5 where the numerator is 1 are called unit fractions.
- A proper fraction has a numerator smaller than its denominator, like 3/5. An improper fraction has a numerator equal to or greater than its denominator, like 7/4.
- A mixed number combines a whole number and a fraction, like 2 and 1/3.
- Equivalent fractions look different but show the same amount. For example, 1/2 and 2/4 are equivalent because both mean half.
- To compare fractions with the same denominator, look at the numerators. The fraction with the bigger numerator is bigger.
- To add or subtract fractions with the same denominator, keep the denominator and add or subtract the numerators.
Formulas and facts to remember
- Fraction = Numerator / Denominator. The numerator tells how many parts; the denominator tells the total equal parts.
- Equivalent fractions: Multiply or divide both numerator and denominator by the same number. Example: 1/2 = 2/4 = 3/6.
- Comparing fractions with the same denominator: The one with the larger numerator is larger. Example: 5/7 > 3/7.
- Adding fractions with the same denominator: a/c + b/c = (a + b)/c. Example: 2/9 + 4/9 = 6/9.
- Subtracting fractions with the same denominator: a/c − b/c = (a − b)/c. Example: 5/8 − 3/8 = 2/8.
- Changing improper fraction to mixed number: Divide numerator by denominator. The quotient is the whole part; the remainder over the denominator is the fraction part.
Common mistakes
- Writing 3/8 as 8/3 → Remember: the part you are talking about goes on top; the total equal parts go at the bottom.
- Thinking 1/4 is bigger than 1/2 because 4 is bigger than 2 → With the same numerator, a larger denominator means smaller parts; so 1/4 is less than 1/2.
- Adding denominators when adding fractions (2/5 + 1/5 = 3/10) → Keep the denominator the same; add only the numerators: 2/5 + 1/5 = 3/5.
- Forgetting to multiply both numerator and denominator when finding equivalent fractions → Always multiply or divide both by the same number.
- Writing an improper fraction like 9/4 as a mixed number by just putting a line (9/4 = 9 and 4) → Divide: 9 ÷ 4 = 2 remainder 1, so 9/4 = 2 and 1/4.
Quick revision
- Fraction = part / whole (numerator / denominator).
- Unit fraction has 1 on top; proper fraction has numerator less than denominator.
- To get equivalent fractions, multiply or divide top and bottom by the same number.
- Compare fractions with the same denominator by comparing numerators.
- Add or subtract fractions with the same denominator by working only with the numerators.
- Improper fraction to mixed number: divide and write quotient with remainder over denominator.