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.
At Class 8, you already know basic fraction operations. Now you will see how fractions hide in everyday situations: a 25% discount is really 1/4 off, a ratio of 2:3 is really the fraction 2/5 of one part. Learning to spot these disguises makes you quicker at mental calculations and better at understanding information in newspapers, shops, and data tables.
By the end of this chapter, you should be able to move smoothly between fractions, decimals, and percentages, use them to compare quantities, and apply them in problems about money, mixtures, and data.
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)
Worked examples
Example 1: Converting between forms
Express 5/8 as a decimal and as a percentage.
Step 1: Divide numerator by denominator. 5 ÷ 8 = 0.625
Step 2: Multiply the decimal by 100 to get the percentage. 0.625 × 100 = 62.5%
Answer: 5/8 = 0.625 = 62.5%
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Example 2: Finding a percentage of an amount
A shirt costs ₹600. The shop offers a 15% discount. What is the discount amount?
Step 1: Write the percentage as a fraction or decimal. 15% = 15/100 = 0.15
Step 2: Multiply by the original price. 0.15 × 600 = ₹90
Answer: The discount is ₹90.
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Example 3: Using ratios as fractions
In a class, boys and girls are in the ratio 3:2. What fraction of the class are girls?
Step 1: Add the parts of the ratio. 3 + 2 = 5
Step 2: Girls form 2 parts out of 5 total parts. Fraction of girls = 2/5
Answer: 2/5 of the class are girls.
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.