Concept 4 of 9
Multi-Step Problems with Large Numbers
Today's big idea
Order the steps first, and each step hands its answer to the next one.
Watch for a number the question never needs; it is there only to distract.
How it works
👀 What's going on?
A factory makes 1,450 bottles a day for 24 days, then 3,200 are found cracked and thrown out. How many are left? Nobody can hold that in their head, and there is no single sum that answers it. Problems like this are won by ordering the steps before touching the numbers.
💡 Here's the trick
Look at the chain above. Each box is one small sum, and the answer from one box becomes the number going into the next. First 1,450 x 24 = 34,800 bottles made. Then 34,800 minus 3,200 leaves 31,600. Two ordinary steps, written down, instead of one impossible one. Working out the order first also shows which numbers you actually need. A long question often carries one that is never used.
🪄 How to do it
- 1.Read the final question first, then draw one box per step, as the chain above does.
- 2.Write which operation each box needs before you calculate anything.
- 3.Work the boxes in order, carrying each answer into the next.
✍️ Try it
A shop buys 18 crates of 250 tiles. It sells 3,600 tiles and breaks 150. How many tiles are left?
Box one is 18 x 250 = 4,500 tiles bought. Box two takes off the 3,600 sold, leaving 900. Box three takes off the 150 broken, leaving 750. Doing the subtractions in the other order gives the same answer here, but the multiplication has to come first, because everything else depends on it.
⚠️ Watch out
You might be thinking every number in the question must be used. In the bottle problem, if it also said the factory has 40 workers, that number does nothing. A number is only needed if a step actually asks for it, so decide the steps first and let them tell you.
🌟 Why this matters
Real questions arrive as stories, not as sums, whether it is stock in a shop or a household budget over a year. Breaking one long story into a few boxes is what makes it possible at all.
Exam tip: Write the boxes even when you can see the answer, because that is where a marker follows your reasoning.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“A factory makes 1,450 bottles a day for 24 days. 3,200 crack. How many are left?”
- 1
Read the last line first
The question asks how many are left, so the final step is a subtraction.
- 2
Box 1 — how many made
1,450 × 24 = 34,800
- 3
Box 2 — take off the cracked
Box 1’s answer feeds straight in. 34,800 − 3,200
- 4
Answer ✓
31,600 bottles left
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
THE PROBLEM
1,450 a day · 24 days · 3,200 crack
The factory also has 40 workers. How many bottles are left?
Before any arithmetic: one of these numbers is never used. Which one?
Quick check
✅ VERIFICATION
A van carries 1,250 kg per trip and makes 16 trips. If 2,400 kg is returned, how much was delivered?
⚡ Finish the activity above first to answer.
Keep going!
Up next: BODMAS
B · O · D · M · A · S, always in this order.