🔵Understanding Ratio
A ratio compares two quantities. If there are 3 apples and 2 oranges, the ratio of apples to oranges is 3 : 2 (read 'three to two').
Order matters: 3 : 2 is not the same as 2 : 3. A ratio can be simplified like a fraction by dividing both parts by a common factor (6 : 4 = 3 : 2).
👀 See a worked example
There are 4 boys and 6 girls. Write the ratio of boys to girls in simplest form.
4 : 6 = 2 : 3 (divide both by 2).
Simplify the ratio 10 : 5.
Divide both by 5 → 2 : 1.
🤖 Vidi's Key Points
- A ratio compares two quantities, written a : b.
- Order matters: 3 : 2 ≠ 2 : 3.
- Simplify a ratio by dividing both parts by a common factor.
🟢Equivalent Ratios & Proportion
Equivalent ratios are equal in value, like equivalent fractions: 1 : 2 = 2 : 4 = 3 : 6. Multiply or divide both parts by the same number.
A proportion says two ratios are equal. If 2 pens cost ₹10, then 4 pens cost ₹20 (double the quantity, double the cost).
👀 See a worked example
Complete: 1 : 3 = 4 : ?
Multiply both parts by 4 → 12.
If 3 books cost ₹60, how much do 6 books cost?
Double the books → double the cost = ₹120.
🤖 Vidi's Key Points
- Equivalent ratios are equal (1 : 2 = 2 : 4).
- Make equivalent ratios by multiplying/dividing both parts equally.
- A proportion states that two ratios are equal.
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