Ratio and Proportion (NCERT Ch. 12)

• Express a comparison between two quantities as a ratio.
• Simplify ratios to their lowest terms.
• Understand proportion — when two ratios are equal.
• Use the unitary method to solve real-life problems.

1. Ratio compares two quantities of the same kind, written as a : b.
2. A ratio is simplified by dividing both terms by their HCF.
3. Two ratios are in proportion if a : b = c : d, i.e. a/b = c/d.
4. Unitary method: first find the value of one unit, then multiply to find the value of the required number of units.

If 5 pens cost ₹75, find the cost of 8 pens using the unitary method.

Cost of 1 pen = 75 / 5 = 15
Cost of 8 pens = 15 x 8 = 120
Answer: ₹120

• Writing a ratio in the wrong order (a:b is not the same as b:a).
• Forgetting to simplify a ratio to lowest terms.
• Skipping the "find 1 unit" step in the unitary method and guessing instead.

• Simplify the ratio 18 : 24.
• Are 2:3 and 8:12 in proportion?

Open the Practice tab for graded questions on Ratio and Proportion (NCERT Ch. 12).