CBSE Class 4 Mathematics Subtraction with and without Borrowing Notes Set 03

What is subtraction?

Subtraction means taking one number away from another to find what is left or how far apart two numbers are. The larger number from which we subtract is the minuend. The number that is subtracted is the subtrahend. The answer is the difference. In 8,759 − 4,236 = 4,523, the minuend is 8,759, the subtrahend is 4,236 and the difference is 4,523.

Properties of subtraction

1. Zero property: subtracting 0 from a number gives the number itself. 25 − 0 = 25.
2. Subtracting a number from itself gives 0. 230 − 230 = 0.
3. Order cannot be changed: 76 − 55 is not equal to 55 − 76.

Subtraction without borrowing

Write the subtrahend under the minuend with matching places. Subtract column by column from the right. Subtract 4,236 from 8,759.
1. Ones: 9 − 6 = 3.
2. Tens: 5 − 3 = 2.
3. Hundreds: 7 − 2 = 5.
4. Thousands: 8 − 4 = 4.
The difference is 4,523.

Subtraction with borrowing

When the top digit in a column is smaller than the bottom digit, we borrow 1 from the next column on the left. That 1 is worth 10 of the smaller place. Subtract 3,896 from 5,642.
1. Ones: 2 is less than 6. Borrow 1 ten from 4 tens, leaving 3 tens. 12 − 6 = 6.
2. Tens: 3 is less than 9. Borrow 1 hundred from 6 hundreds, leaving 5 hundreds. 13 − 9 = 4.
3. Hundreds: 5 is less than 8. Borrow 1 thousand from 5 thousands, leaving 4 thousands. 15 − 8 = 7.
4. Thousands: 4 − 3 = 1.
The difference is 1,746.

Subtracting from a number with zeros

To find 10,000 − 2,897, borrow step by step across the zeros: 10,000 − 2,897 = 7,103. A quick way is to subtract 1 less (9,999 − 2,897 = 7,102) and then add 1 back.

Checking subtraction

Add the difference to the subtrahend. The answer should be the minuend. Check: 1,746 + 3,896 = 5,642.

Key points

1. Minuend − subtrahend = difference.
2. For whole numbers, the minuend must be greater than or equal to the subtrahend.
3. Subtraction undoes addition, so the two operations can check each other.

Worked examples

Example 1. What number is 1,097 less than 6,004? Answer: 6,004 − 1,097 = 4,907.

Example 2. The sum of two numbers is 9,051. One number is 4,872. Find the other. Answer: 9,051 − 4,872 = 4,179.

Example 3. A dairy had 7,050 litres of milk. It sent 2,868 litres to one town and 1,959 litres to another. How much is left? Answer: 2,868 + 1,959 = 4,827 litres sent, so 7,050 − 4,827 = 2,223 litres are left.

Quick Check Questions