Concept 8 of 9
The Unitary Method: Find One, Find All
Today's big idea
Find the value of one first by dividing, then multiply up to any amount.
Find what one is worth first, then scale up to however many you need.
How it works
👀 What's going on?
Five notebooks cost 60 rupees. So what would eight of them cost? You cannot get there in a single move, but two easy moves will do it.
💡 Here's the trick
Look at the chain above. Divide 60 by 5 and you find that one notebook is 12 rupees. Multiply that 12 by 8 and you find eight notebooks cost 96 rupees. Working out the value of exactly one thing first is what makes every other quantity easy.
🪄 How to do it
- 1.Divide the total by the number of items to get the value of one, as the picture above divides by 5.
- 2.Multiply that single value by whatever new quantity the question wants.
✍️ Try it
3 kg of apples cost 45 rupees, so what do 7 kg cost? Then a machine fills 6 bottles in 3 minutes, so how many does it fill in 10 minutes?
One kg of apples is 45 divided by 3 = 15 rupees, so 7 kg cost 15 x 7 = 105 rupees. One minute fills 6 divided by 3 = 2 bottles, so 10 minutes fill 2 x 10 = 20 bottles. The same two moves, on completely different things.
Compound units work the same way. For 5 km 150 m + 3 km 250 m, turn each into the smaller unit, add, then convert back. 5,150 m + 3,250 m = 8,400 m, which is 8 km 400 m.
⚠️ Watch out
You might be thinking you can jump straight from 3 kg to 7 kg, since 7 is roughly double 3. It is not exactly double, and guessing the scale is where this comes apart. Come down to one first, every time.
🌟 Why this matters
Working out the better value at a shop begins by finding the price of one. So does judging how long a journey takes, or how far a tin of paint goes.
Exam tip: Price, speed and rate word problems are nearly always this method wearing a disguise.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“4 pens cost ₹32. How much do 6 cost?”
- 1
Step 1 — find 1 unit
Divide total by quantity: ₹32 ÷ 4 = ₹8
- 2
So 1 pen = ₹8
That's the unit price.
- 3
Step 2 — multiply to scale up
₹8 × 6 = ₹48
- 4
Final cost ✓
6 pens = ₹48
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Step 1: DIVIDE to find the cost of ONE. Step 2: MULTIPLY to scale up.
SHOP SHELF · ROUND 1 OF 3
4 pencils = ₹28
Step 1 — divide to find ONE: ₹28 ÷ 4 = ?
Quick check
✅ VERIFICATION
If 4 pens cost 48 rupees, what do 9 pens cost?
⚡ Finish the activity above first to answer.
Keep going!
Up next: The Big Freeze
Above zero and below, and how far it climbs or drops.