Concept 4 of 7
Ratio & Proportion
Today's big idea
A ratio splits the whole into equal parts, so count all the parts before sharing.
Two to five means two parts in seven, not two in five.
How it works
👀 What's going on?
A recipe says two parts sugar to five parts flour, and you have a bag of flour rather than a recipe's worth. Ratios are about parts, not amounts, which is what makes them scale.
💡 Here's the trick
Look at the bar above. A ratio cuts the whole into equal parts and hands out groups of them. Counting the total number of parts comes before you can share anything.
🪄 How to do it
- 1.Add the numbers in the ratio to count the parts on the bar above.
- 2.Divide the total amount by that number of parts.
- 3.Multiply by each share to get each amount.
✍️ Try it
Divide 4,500 rupees between two people in the ratio 4 to 5. Then: two numbers are in the ratio 3 to 7 and differ by 24, so what are they?
There are 9 parts, so one part is 500, giving 2,000 and 2,500 rupees. In the second, the gap of 4 parts is 24, so a part is 6 and the numbers are 18 and 42.
⚠️ Watch out
You might be thinking the ratio 2 to 5 means two out of five. It means two out of seven, because the whole is every part added together, not just the larger number.
🌟 Why this matters
Mixing paint, scaling a recipe, reading a map and splitting a bill all run on parts rather than totals.
Exam tip: Write the total number of parts down first; most ratio slips come from skipping it.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“Split ₹600 between Asha and Bina in the ratio 2 : 3.”
- 1
Count parts
Total parts = 2 + 3 = 5. ⚖️
- 2
Value of one part
600 ÷ 5 = 120
- 3
Compute shares
Asha = 2 × 120 = 240; Bina = 3 × 120 = 360.
- 4
Answer ✓
Asha ₹240, Bina ₹360
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
To simplify a ratio, divide every part by their HCF. To share an amount, divide by the total number of parts.
RATIO · ROUND 1 OF 3
Simplify the ratio 15 : 25.
Quick check
✅ VERIFICATION
Sand and cement are mixed in the ratio 5 : 3. What fraction of the mixture is cement?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Speed, Distance & Time
Triangle trick: cover the unknown, read the formula.