Math
Operations on Numbers - Subtraction (up to five digit numbers) by borrowing, word problems
MCQ

Introduction

Subtraction with borrowing is used when a digit in the minuend is smaller than the digit in the subtrahend at the same place value.

Visualizing the Borrow (Carry)

When you borrow 1 from a neighbor, you are actually taking 10 units of the current place value. Notice how the values change in the table below.

PlaceTThThHTU
Changes 3 (4-1)15 (5+10)1 (2-1)13 (3+10)
Top Num74523
Bottom Num- 12809
Difference61714
Table 3: Systematic borrowing in 5-digit subtraction

Borrowing Process

1. Start from Units.
2. If borrowing from a zero, move further left until you find a non-zero digit.

Examples

Example 1: 30005 - 12345
Step 1: Units 5-5 = 0.
Step 2: Tens 0-4, must borrow from Hundreds, then Thousands, then Ten-Thousands.
Final Result: 17660

Tricks and Shortcuts

For numbers ending in many zeros (like 50000), subtract 1 from both numbers to eliminate borrowing (e.g., 49999 - 12344 instead of 50000 - 12345).

Common Mistakes

Forgetting to update the neighbor's value after borrowing. Incorrectly borrowing from a zero without moving to the next place value.

Practice Questions

Easy Questions

  1. 87654 - 32143 = ?
  2. 55555 - 11111 = ?
  3. 90000 - 40000 = ?

Medium Questions

  1. 72341 - 45672 (Use borrowing).
  2. A library has 45000 books. 12850 were lent out. How many are left?
  3. Difference between 63200 and 15400.

Hard Questions

  1. Subtract the smallest 5-digit number from the largest 5-digit number.
  2. A project costs 65000. You have 48750. How much more is needed?
  3. Calculate: (45600 + 12000) - 34500.

Revision Summary

Borrowing is simply redistributing values between place holders to make subtraction possible. Always double-check by addition.

54321 - 12345 = ?
A
41976
B
41977
C
41978
D
41979
Explanation
Subtracting 12345 from 54321 gives the answer 41976.
Correct 4 Wrong 1