Concept 7 of 7
Is It Reasonable?
Today's big idea
Estimate first, then check: an answer that is far from the estimate has a mistake in it.
480 + 320 is about 800, so an answer of 200 cannot be right.
How it works
👀 What's going on?
A calculator says 480 + 320 = 200, and something feels off. You do not need to redo the sum to know it is wrong: the two numbers are each in the hundreds, so their total cannot possibly be smaller than either one.
💡 Here's the trick
Look at the estimate above. A quick round-and-add gives roughly 500 + 300 = 800, so a real answer near 800 is reasonable and an answer of 200 is not. Estimating first tells you what range the answer should land in.
🪄 How to do it
- 1.Before trusting an answer, estimate what it should be by rounding.
- 2.Compare: is the answer close to the estimate?
- 3.If it is miles away, there is a mistake somewhere, so go back and find it.
✍️ Try it
Riya says ₹205 plus ₹189 is ₹94. Without doing the exact sum, explain why that cannot be right.
Rounding gives about 200 + 200 = 400, and adding two positive amounts must give more than either one. 94 is smaller than both, so it is not reasonable — she likely subtracted instead of adding.
⚠️ Watch out
Reasonable does not mean exact. An estimate of 400 does not prove the answer is 394; it only rules out answers that are wildly off.
🌟 Why this matters
Checking reasonableness catches the big mistakes — a misplaced digit, the wrong operation — that turn a right method into a wrong answer. It is the habit that saves marks.
Exam tip: A quick estimate in the margin is the cheapest way to catch a silly slip.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“A sum of 205 + 189 is given as 94. Is that reasonable?”
- 1
Estimate first
Round: 200 + 200 = 400.
- 2
Compare
94 is far below 400, and a total must be bigger than either number.
- 3
Answer ✓
Not reasonable — likely subtracted
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Read the story and use the clue word.
23 birds sit. 18 more fly in all. How many altogether?
Does “in all” mean add or subtract?
Quick check
✅ VERIFICATION
The sum of two numbers in the 400s is given as 90. Why is that NOT reasonable?
⚡ Finish the activity above first to answer.
Keep going!