Schooling · Class 7 · Mathematics · Working with Fractions · Chapter on a page
CBSE Class 7 · Mathematics · NCERT Ganita Prakash
Working with 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 a numerator (top…
- To add or subtract fractions, first…
- To multiply two fractions, multiply…
- To divide by a fraction, multiply by…
- A mixed number like 2 3/4 can be…
- Always simplify your final answer by…
- Multiplication of a fraction by a…
- Formulas and facts
- a/b + c/b = (a + c)/b
- a/b − c/b = (a − c)/b
- Multiplication
- Division
- Reciprocal
- Mixed to improper
- Watch out for
- Adding numerators and denominators…
- Forgetting to convert mixed numbers…
- Inverting the wrong fraction when…
- Not simplifying the final answer
- Thinking multiplication always makes…
What this chapter is about
This chapter helps you become comfortable with fractions in everyday situations. You already know what fractions are from earlier classes. Now you will learn to add, subtract, multiply and divide fractions, including mixed numbers. These skills let you solve problems about sharing food, measuring cloth, mixing ingredients and many other daily tasks.
Key ideas
- A fraction has a numerator (top number) and a denominator (bottom number). The denominator tells how many equal parts make a whole; the numerator tells how many parts we have.
- To add or subtract fractions, first make their denominators the same (find a common denominator), then add or subtract the numerators.
- To multiply two fractions, multiply the numerators together and multiply the denominators together: (a/b) × (c/d) = (a × c) / (b × d).
- To divide by a fraction, multiply by its reciprocal. The reciprocal of c/d is d/c. So (a/b) ÷ (c/d) = (a/b) × (d/c).
- A mixed number like 2 3/4 can be written as an improper fraction: 2 3/4 = (2 × 4 + 3)/4 = 11/4. Convert before multiplying or dividing.
- Always simplify your final answer by dividing numerator and denominator by their highest common factor.
- Multiplication of a fraction by a whole number means repeated addition: 3 × 2/5 = 2/5 + 2/5 + 2/5 = 6/5.
Formulas and facts to remember
- Addition: a/b + c/b = (a + c)/b (same denominator). For different denominators, convert to a common denominator first.
- Subtraction: a/b − c/b = (a − c)/b.
- Multiplication: (a/b) × (c/d) = (a × c) / (b × d).
- Division: (a/b) ÷ (c/d) = (a/b) × (d/c).
- Reciprocal: the reciprocal of n is 1/n; the reciprocal of a/b is b/a.
- Mixed to improper: whole part × denominator + numerator, all over the same denominator.
Common mistakes
- Adding numerators and denominators separately, like 1/4 + 2/3 = 3/7 → Find a common denominator first; add only the numerators.
- Forgetting to convert mixed numbers before multiplying or dividing → Always change 2 3/4 to 11/4 first.
- Inverting the wrong fraction when dividing → Flip only the divisor (the second fraction), not the first.
- Not simplifying the final answer → Divide numerator and denominator by their HCF.
- Thinking multiplication always makes a number larger → Multiplying by a proper fraction gives a smaller result.
Quick revision
- Same denominator: just add or subtract numerators.
- Multiply straight across: top × top, bottom × bottom.
- Divide means multiply by the reciprocal.
- Convert mixed numbers to improper fractions before multiplying or dividing.
- Always simplify your answer.