**Key Definitions:**
• Consecutive Numbers: Numbers in order with no gaps (7, 8, 9 or 42, 43, 44, 45).
• Regrouping: Trading 10 units of one place for 1 unit of the next place (10 Ones = 1 Ten; 10 Tens = 1 Hundred).
• Place Value: The value of a digit based on its position (Ones, Tens, Hundreds, Thousands).
**Important Rules:**
• Addition with Regrouping: If Ones sum ≥10, write the extra in Ones place, carry 1 to Tens.
• Subtraction with Regrouping: If top Ones < bottom Ones, borrow 1 Ten (=10 Ones) from Tens place.
• Addition−Subtraction Link: If A + B = C, then C − B = A and C − A = B (inverse operations).
**Patterns in Consecutive Numbers:**
• Sum of 2 consecutive = always odd (difference between successive sums = 2).
• Sum of 3 consecutive = middle number × 3 (difference between successive sums = 3).
• Sum of 4 consecutive = difference between successive sums = 4.
**Exam Shortcut:** Line up digits by place value before adding/subtracting. Check subtraction: 82 − 37 = 45? Verify: 37 + 45 = 82 ✓
**Don't Confuse:** Regrouping in addition (carry up) ≠ Regrouping in subtraction (borrow down). They look opposite because they are!
Q1. What are consecutive numbers?
Answer: A — Consecutive numbers must be in exact order with no skips, so 5, 6, 7, 8 is correct; 1, 3, 5, 7 skips numbers.
Q2. When you add 18 + 27, why do you regroup?
Answer: A — Regrouping happens when Ones sum to 10 or more: 8 + 7 = 15 Ones = 1 Ten + 5 Ones.
Q3. If 46 + 21 = 67, which sentence is also true?
Answer: A — Addition and subtraction are opposites: if 46 + 21 = 67, then 67 − 21 must equal 46.
Q4. What is the sum of the consecutive numbers 5 + 6 + 7 without adding them directly?
Answer: A — For 3 consecutive numbers, sum = middle number × 3, so 5 + 6 + 7 = 6 × 3 = 18.
Q5. Ravi has 1,855 km from Srinagar to a city, and 1,862 km from that city to Kanniyakumari. What is the total distance?
Answer: B — Add by place value: 1,855 + 1,862 = 3,717 km (5 + 2 = 7 Ones, 5 + 6 = 11 Tens, carry 1; 8 + 8 + 1 = 17 Hundreds).
Q6. A ship travels 2,700 km from Mumbai to Chennai, but stops at Cochin after 1,083 km. How far is left to Chennai?
Answer: A — Subtract: 2,700 − 1,083 = 1,617 km (regroup: borrow 1 Ten to make 10 Ones when needed).
Q7. When subtracting 82 − 37, if 2 Ones < 7 Ones, what do you do?
Answer: A — In subtraction, when top Ones are too small, you borrow 1 Ten (= 10 Ones) from Tens, so 2 becomes 12.
Q8. Fill in the blank: The sum of 2 consecutive numbers is always _______.
Answer: A — Two consecutive numbers are one odd and one even (like 4 + 5 = 9, or 12 + 13 = 25), and odd + even = always odd.
Q9. Mahesh spent ₹21,880 on fuel and toll, and ₹38,900 on other expenses. Which digit appears in the Thousands place of his total spending?
Answer: A — Add: 21,880 + 38,900 = 60,780; in 60,780, the Thousands place is 0, but if asking for final sum, Thousands digit is 0 (correct answer is checking: 21 + 38 = 59 thousands, +1 carry from hundreds = 60).
Q10. In the consecutive numbers 23 + 24 + 25, what is the pattern for finding the sum quickly?
Answer: A — For any 3 consecutive numbers, multiply the middle number by 3: here 24 × 3 = 72, and 23 + 24 + 25 = 72.
What are consecutive numbers?
Numbers that follow one after another without skipping, like 5, 6, 7, 8 or 29, 30, 31, 32.
When adding 28 L + 75 L, why do we regroup?
Because 8 Ones + 5 Ones = 13 Ones, and 13 Ones = 1 Ten + 3 Ones, so we write 3 in Ones place and carry 1 Ten.
In subtraction, when Ones are too small, what do you do?
Borrow 1 Ten from the Tens place (which becomes 10 Ones), then subtract.
What is the relationship between addition and subtraction?
They are opposites: if 46 + 21 = 67, then 67 − 21 = 46 and 67 − 46 = 21.
What is true about the sum of 2 consecutive numbers?
The sum is always odd, because odd + even = odd (like 3 + 4 = 7).
How do you find the sum of consecutive numbers without adding each one?
Use the pattern: for 3 consecutive numbers, the sum = middle number × 3 (like 3 + 4 + 5 = 4 × 3 = 12).
Why must digits be lined up by place value before adding or subtracting?
So Ones add with Ones, Tens with Tens, Hundreds with Hundreds—each place adds to its own place.
In the road trip example, Delhi to Mumbai is 590 km and Mumbai to Hyderabad is 1,055 km. How do you find total?
Add: 590 + 1,055 by stacking them (Ones under Ones, etc.) to get 1,645 km total.
If a ship travels 2,700 km from Mumbai to Chennai, and 1,083 km to Cochin, how much is left?
Subtract: 2,700 − 1,083 by regrouping Tens into Ones to get 1,617 km remaining.
What does the word regrouping mean in addition?
When 10 or more in one place, bundle them into 1 of the next bigger place (10 Ones become 1 Ten).
What are consecutive numbers? Give two examples. [1 mark]
Consecutive numbers follow in order without skipping. Example: 1, 2, 3 or 29, 30, 31, 32.
Add 46 + 99 by lining up place values. Show your regrouping step. [2 marks]
Stack numbers: Ones (6 + 9 = 15), write 5 and carry 1 Ten. Then Tens (4 + 9 + 1 = 14), write 14. Answer: 145.
If a fuel tank has 28 litres and you add 75 litres, how much fuel is there now? Explain your working using place value. [3 marks]
Add 28 + 75: Ones place (8 + 5 = 13), regroup to 1 Ten + 3 Ones. Tens place (2 + 7 + 1 = 10). Final answer: 103 litres.
A ship travels 2,700 km from Mumbai to Chennai but stops at Cochin after 1,083 km. Using subtraction with regrouping, find how much distance remains. Show all your steps. [5 marks]
Set up: 2,700 − 1,083. Ones: 0 < 3, so borrow 1 Ten. Tens: After borrowing, 0 − 8 needs borrowing from Hundreds. Work through each place carefully to get 1,617 km.
True or False: The sum of 2 consecutive numbers is always even. Explain with one example. [2 marks]
Two consecutive numbers are one odd and one even (like 6 + 7 = 13, which is odd, not even). Sum is always odd.
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