A ratio compares quantities in a stated order. A percentage describes a quantity per hundred. Both help with everyday questions about mixtures, marks, prices and sharing. Before calculating, check which amount is the whole and whether the quantities use the same unit.
Keep the order and units
If there are 8 red beads and 12 blue beads, red : blue = 8 : 12 = 2 : 3. Red : all beads is a different ratio, 8 : 20 = 2 : 5. The order of the words determines the order of the numbers.
Convert units before simplifying: 1 metre : 50 centimetres becomes 100 : 50 = 2 : 1, not 1 : 50.
- Divide both parts by a common non-zero factor.
- In a 2 : 3 share, the whole contains 2 + 3 = 5 equal parts.
A percentage is out of 100
To find p% of an amount, multiply the amount by p/100. To express a part as a percentage, calculate part ÷ whole × 100, with a non-zero whole.
A 15% discount reduces the original price by 15%, so the customer pays 85% of the original price. State the base amount when comparing percentage changes.
- 25% = 1/4, 50% = 1/2 and 75% = 3/4.
- A percentage can be greater than 100 when a quantity is larger than the reference whole.
Put it into practice
A worked example
A bag marked ₹800 has a 15% discount. What is the sale price?
- Discount = 15/100 × ₹800 = ₹120.
- Subtract the discount from the original price: ₹800 − ₹120.
Answer: ₹680, assuming no additional charge or tax is added.
Try it yourself
Have a go before revealing the answer.
Share ₹250 in the ratio 2 : 3.
Show answer
Five parts total; each part is ₹50. The shares are ₹100 and ₹150.
Answer: Five parts total; each part is ₹50. The shares are ₹100 and ₹150.
What percentage is 18 out of 60?
Show answer
18/60 × 100 = 30%.
Answer: 18/60 × 100 = 30%.
Watch out for these
- Do not confuse a part-to-part ratio with a part-to-whole fraction.
- Convert units and identify the original amount before finding a percentage change.
Continue with official resources
Match these concept notes to your current textbook and syllabus. They are independent explanations, not official board publications.
