Chapter 4 of Class 5 Maths, We the Travellers – II, continues the journey theme from Chapter 1 and applies large-number place value to actual calculation – addition and subtraction of big numbers with regrouping, estimating totals before calculating, and solving multi-step travel and distance word problems.
Key Concepts
Addition of Large Numbers with Regrouping
When adding large numbers, add column by column from the right (ones, then tens, then hundreds, and so on), carrying over (“regrouping”) to the next column whenever a column’s sum is 10 or more. For example, 4,672 + 3,859: ones (2+9=11, write 1 carry 1), tens (7+5+1=13, write 3 carry 1), hundreds (6+8+1=15, write 5 carry 1), thousands (4+3+1=8) → 8,531.
Subtraction of Large Numbers with Regrouping
Subtraction works the same way in reverse – subtract column by column from the right, and when the top digit is smaller than the bottom digit, borrow 1 from the next column to the left. For example, 6,203 − 2,458 requires borrowing across zeros, which needs careful step-by-step regrouping.
Estimating Before Calculating
Before doing an exact calculation, round the numbers involved to get a quick estimate of the answer. This helps catch mistakes – if the estimate is around 8,000 but the exact calculation gives 800, something has gone wrong in the working.
Multi-Step Word Problems
Many travel problems need more than one operation – for example, finding the total distance for a multi-leg journey (addition), then working out how much further remains to a target distance (subtraction). Reading the question carefully to identify what is being added and what is being taken away is the key skill.
Checking Answers
Addition can be checked by reversing the order of adding (or by subtracting one addend from the total to see if the other addend is recovered). Subtraction can be checked by adding the answer back to the number subtracted, which should give the original number.
Worked Examples
Example 1: Addition with Multiple Carries
A train travels 3,847 km on one route and 2,965 km on another. Find the total distance.
3,847 + 2,965: ones (7+5=12, write 2 carry 1), tens (4+6+1=11, write 1 carry 1), hundreds (8+9+1=18, write 8 carry 1), thousands (3+2+1=6) → 6,812 km.
Example 2: Subtraction with Borrowing Across Zero
A bus is meant to travel 5,004 km but has covered 2,678 km so far. How much distance remains?
5,004 − 2,678: borrowing carefully across the zeros gives 2,326 km remaining.
Example 3: Estimate then Calculate
Estimate 6,758 + 3,215 by rounding to the nearest thousand, then find the exact answer.
Estimate: 7,000 + 3,000 = 10,000. Exact: 6,758 + 3,215 = 9,973, which is close to the estimate, confirming the calculation is reasonable.
Quick Recap
- Add or subtract large numbers column by column from the right, regrouping (carrying/borrowing) as needed.
- Estimate first by rounding, so the exact answer can be checked for reasonableness.
- Multi-step word problems often need both addition and subtraction – read carefully to see which operation applies where.
- Check addition by re-adding in a different order; check subtraction by adding the answer back to the subtracted number.
- Borrowing across a zero digit needs extra care – borrow from the next non-zero column and adjust each zero in between.
Common Mistakes to Avoid
- Forgetting to carry the regrouped 1 into the next column during addition.
- Borrowing incorrectly across a zero – skipping a step instead of reducing each zero column by one in turn.
- Not lining up digits by place value when writing numbers in columns, especially with numbers of different lengths.
- Skipping the estimation step and missing an obviously wrong final answer.
- In multi-step problems, performing only one operation when the question actually requires two.
Home Practice Tips
- Use real bus, train, or car trip distances from a map app to create addition and subtraction problems together.
- Practise estimating grocery bill totals before adding the exact amounts on a receipt.
- Set up a “borrow across zero” subtraction problem, like 7,002 − 3,486, and work through it step by step out loud.
- Turn a multi-leg family trip into a word problem: add up distances for each leg, then subtract to find how much further remains to a target.
- Check every addition and subtraction answer with the reverse operation as a habit.
Frequently Asked Questions
Q1. Why is estimating before an exact calculation useful?
It gives a quick reasonableness check – if the final exact answer is very different from the rounded estimate, it signals a calculation mistake worth rechecking.
Q2. What is the trickiest part of subtracting large numbers?
Borrowing across one or more zero digits, since there is nothing to “give” directly – the borrow has to ripple back to the nearest non-zero column first.
Q3. How do you know whether a word problem needs addition or subtraction?
Look for words like “total,” “altogether,” or “in all” for addition, and “how much more,” “remaining,” or “difference” for subtraction – and always re-read the question to confirm what is being asked.
Q4. Is there more than one way to check an addition answer?
Yes – adding the numbers in reverse order should give the same total, or subtracting one number from the total should return the other original number.
Q5. Why do multi-step word problems feel harder than single-step ones?
Because they require identifying the correct order of operations and keeping track of an intermediate answer before reaching the final one, rather than a single calculation.
Full walkthrough: Chapter 4 Solutions · Extra Questions.
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