Schooling · Class 8 · Mathematics · Fractions in Disguise · Chapter on a page
CBSE Class 8 · Mathematics · NCERT Ganita Prakash Part-II
Fractions in Disguise: 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, a decimal, and a…
- To convert a fraction to a decimal…
- To convert a decimal to a…
- To convert a percentage to a…
- A ratio like 4:5 can be thought of…
- Equivalent fractions are fractions…
- When comparing fractions with…
- Formulas and facts
- a/b = a ÷ b
- Decimal to percentage
- Percentage to fraction
- Fraction to percentage
- Finding a percentage of a quantity
- If a ratio is m:n, the first part as…
- Watch out for
- Thinking 1/4 = 0.14
- Writing 0.6 as 6%
- Forgetting to simplify after…
- Confusing ratio parts with the whole
- Comparing fractions by looking only…
What this chapter is about
This chapter explores how fractions appear in different forms — as decimals, percentages, and ratios — and how to recognise and convert between these forms. A fraction like 3/4 can also be written as 0.75 or 75%, and understanding these connections helps you solve real-life problems involving discounts, comparisons, and measurements.
Key ideas
- A fraction, a decimal, and a percentage are three ways of writing the same part of a whole. For example, 1/2 = 0.5 = 50%.
- To convert a fraction to a decimal, divide the numerator by the denominator. For example, 3/8 = 3 ÷ 8 = 0.375.
- To convert a decimal to a percentage, multiply by 100. For example, 0.375 × 100 = 37.5%.
- To convert a percentage to a fraction, write the percentage over 100 and simplify. For example, 40% = 40/100 = 2/5.
- A ratio like 4:5 can be thought of as fractions: the first quantity is 4/9 of the total, the second is 5/9.
- Equivalent fractions are fractions in disguise — they look different but represent the same value. For example, 6/8 = 3/4.
- When comparing fractions with different denominators, convert them to decimals or to fractions with a common denominator.
Formulas and facts to remember
- Fraction to decimal: a/b = a ÷ b
- Decimal to percentage: multiply decimal by 100, then write the % sign
- Percentage to fraction: write percentage over 100, then simplify
- Fraction to percentage: (a/b) × 100 %
- Finding a percentage of a quantity: (percentage/100) × quantity
- If a ratio is m:n, the first part as a fraction of the total is m/(m + n)
Common mistakes
- Thinking 1/4 = 0.14 → Divide properly: 1 ÷ 4 = 0.25, not just placing digits side by side.
- Writing 0.6 as 6% → Remember to multiply by 100: 0.6 × 100 = 60%.
- Forgetting to simplify after converting percentage to fraction → Always reduce 20/100 to 1/5.
- Confusing ratio parts with the whole → In ratio 3:2, there are 5 parts total, not 3 or 2.
- Comparing fractions by looking only at numerators → 3/7 is not greater than 2/5 just because 3 > 2; convert to common denominators or decimals first.
Quick revision
- Fraction to decimal: divide top by bottom.
- Decimal to percentage: multiply by 100 and add %.
- Percentage to fraction: put over 100, then simplify.
- A ratio m:n means first part is m/(m + n) of the total.
- Equivalent fractions are the same value in different disguises.
- Always simplify fractions to their lowest terms for clarity.