Percentages and Applications
"Connect fractions, decimals, and percents in shopping, scores, and statistics."
A Today you'll learn
- Understand "per cent" as parts per hundred and convert between fractions, decimals, and percentages.
- Calculate a specified percentage of a quantity in real-life problems.
- Solve practical word problems on discounts, marks, and percentage increases.
B Let's understand
The word "percent" comes from the Latin "per centum", meaning "out of every hundred". The symbol % denotes a denominator of 100. For instance, 25% means 25 out of 100, which equals 1/4 or 0.25. To convert a fraction to a percentage, multiply by 100%. To find the percentage of a given number, convert the percentage into a decimal or fraction and multiply by the quantity. Percentages are commonly used for exam scores, discounts in stores, interest rates, and population statistics.
C See it step by step
- Step 1: Multiply fraction by 100%: (3/5) × 100%.
- Step 2: 100 ÷ 5 = 20.
- Step 3: 3 × 20% = 60%.
- Step 1: Write 15% as 15/100.
- Step 2: Multiply by 800: (15/100) × 800.
- Step 3: Cancel common factors: 15 × 8 = ₹120.
D Your turn
E Ready to practise?
Key idea 1
Percent means "per hundred" and is represented by the % symbol.
To convert a fraction to percentage
To convert a fraction to percentage, multiply by 100%; to convert percentage to fraction, divide by 100.
50% = 1/2
50% = 1/2, 25% = 1/4, 75% = 3/4, 20% = 1/5, 10% = 1/10.
To find x% of Y
To find x% of Y, calculate (x / 100) × Y.
Key idea 5
The entire whole or full total always equals 100%.