Concept 6 of 7
Estimating Sums & Differences
Today's big idea
Round each number to a tidy 10 or 100 first, then add or subtract for a fast 'about' answer.
296 + 405 rounds to 300 + 400 = about 700.
How it works
👀 What's going on?
A shopkeeper glances at ₹296 and ₹405 and says 'about ₹700' before touching a calculator. Estimating trades a little accuracy for a lot of speed, and often about right is all you need.
💡 Here's the trick
Look at the rounded numbers above. To estimate, round each number to the nearest 10 or 100, then add or subtract the tidy numbers. 296 rounds to 300 and 405 rounds to 400, so the total is about 700 — close to the exact 701.
🪄 How to do it
- 1.Decide what to round to: nearest 10 for small numbers, nearest 100 for hundreds, nearest 1,000 for numbers in the thousands.
- 2.Round each number, looking at the digit to the right to decide up or down.
- 3.Add or subtract the rounded numbers.
✍️ Try it
Estimate 3,880 + 2,140 to the nearest 1,000. Then estimate 6,120 − 2,970 to the nearest 1,000.
3,880 rounds to 4,000 and 2,140 rounds to 2,000, so about 6,000. And 6,120 rounds to 6,000 and 2,970 rounds to 3,000, so about 3,000.
⚠️ Watch out
Round BEFORE you add, not after. If you work out 388 + 214 = 602 and then round, you have already done the hard sum you were trying to skip.
🌟 Why this matters
Estimating checks whether a real answer is sensible and helps you shop, plan and budget without exact sums. It is the fastest maths there is.
Exam tip: If your exact answer is far from your estimate, one of them has a slip — check it.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“Estimate 388 + 214 by rounding to the nearest 100.”
- 1
Round each number
388 → 400, 214 → 200.
- 2
Add the tidy numbers
400 + 200 = 600
- 3
Answer ✓
about 600
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Peek at the digit RIGHT of the rounding place. 5 or more → up, 4 or less → down. Tap the nearer signpost.
ROUND · STEP 1 OF 3
6,742
to the nearest 100 · deciding digit = 4
Quick check
✅ VERIFICATION
Estimate 296 + 405 by rounding each number to the nearest 100.
⚡ Finish the activity above first to answer.
Keep going!
Up next: Is It Reasonable?
Estimate first, then trust it or doubt it.