Problem Set 11 – Subtracting Six- and Seven-Digit NumbersClass 5 Maths · Chapter 3 Addition and Subtraction · Problem Set 11 – Maharashtra Board

Summary: Problem Set 11 – Subtracting Six- and Seven-Digit Numbers

Six- and seven-digit numbers are subtracted with the same column method as five-digit numbers.

Start from the units. When a top digit is too small, borrow 1 from the next place on the left; it gives 10 in your column.

When the next place is 0, keep going left until you find a digit to borrow from. The zeros on the way become 9.

Another method: if we add the same amount (10, 100, …) to both numbers, their difference does not change. So instead of borrowing, add 10 to the top digit and 1 to the next bottom digit.

Check every answer by adding: difference + smaller number = bigger number.

Key points to remember

• Same method as five-digit subtraction
• Line up the places from the right
• Borrow 1 from the left = 10 here
• Zeros on the way become 9 after borrowing
• Adding the same number to both keeps the difference
• Equal-addition: top digit + 10, next bottom digit + 1
• Keep borrows in your head with practice
• Check: difference + smaller = bigger

Problem Set 11 – Subtracting Six- and Seven-Digit Numbers – Notes

1. Borrowing in long numbers

• Write the numbers in columns TL, L, TTh, Th, H, T, U.
• Work from right to left. Borrow only when the top digit is smaller.
• Every time you borrow, make the lender digit 1 less.

2. Borrowing across many zeros

• In 40,05,200 − 17,36,458, the thousands need to borrow but the ten thousands and lakhs are 0.
• Go left to the 4 ten lakhs: it becomes 3, the two zeros become 9 and 9, and the thousands get 10 more.
• Answer: 22,68,742.

3. The equal-addition method

• Fact: 15 − 8 = 7 and (15 + 10) − (8 + 10) = 25 − 18 = 7. Adding the same to both numbers does not change the difference.
• When a top digit is too small, add 10 to it, and add 1 to the bottom digit in the next place on the left (that 1 is also worth 10 there).
• 813 − 467: units 3 + 10 = 13, 13 − 7 = 6, bottom tens 6 + 1 = 7. Tens 1 + 10 = 11, 11 − 7 = 4, bottom hundreds 4 + 1 = 5. Hundreds 8 − 5 = 3. Answer 346.

4. Keeping borrows in your head

• With practice you can remember the borrowed 1 without writing it.
• Say it quietly: 'sixteen take away nine is seven; the tens now have one less'.
• If you get muddled, write the borrows again.

5. Checking

• Add the answer and the smaller number: 33,72,787 + 18,67,529 = 52,40,316. ✓
• The difference must be smaller than the top number.

Formulas at a glance

Key terms

Problem Set 11 – Subtracting Six- and Seven-Digit Numbers – Flashcards

Read the question, answer it in your head, then tap the card to check. 10 cards.

Problem Set 11 – Subtracting Six- and Seven-Digit Numbers – MCQ Quiz

10 questions. Tap an option — you will see at once if it is right and why.

How to study Problem Set 11 – Subtracting Six- and Seven-Digit Numbers

⏱ About 25 minutes

1. Learn (5 min)
   Revise borrowing, then learn why adding the same amount to both numbers keeps the difference.
2. Subtract (15 min)
   Do three long subtractions (one with many zeros) and one by the equal-addition method.
3. Practise (5 min)
   Do the 4 'Try it yourself' sums, take the quiz and play 🎮 Play.