# Subtraction

The answer of a subtraction sum is called DIFFERENCE.

How to subtract 2-digit numbers?

Steps are shown to subtract 2-digit numbers.

Subtract 189 from 638.

Line up the numbers according to place value taking care to place the bigger number on top. In the ONES column we have 8 - 9.

We cannot take away 9 from 8 so we REGROUP the next place to the left. REGROUP 78 as 6 TENS and 18 ONES. DIFFERENCE = 39

Sometimes we need to REGROUP more than once.

How to subtract 3-digit numbers?

Steps are shown to subtract 3-digit numbers.

Subtract 189 from 638. REGROUP 38 as 2 TENS 18 ONES REGROUP 62 as 5 TENS 12 ONES

We follow the same rule for subtracting 4 digits numbers or larger numbers.

How to subtract 4-digit numbers?

Steps are shown to subtract 4-digit numbers.

1. Solve: 74834 - 38915

Line up the number according to place value.

In the ONES column the number to be subtracted is greater so REGROUP as 2 TENS 14 ONES. Subtract the TENS column. REGROUP to subtract the numbers in the HUNDREDS column.

3 THOUSANDS 18 HUNDREDS REGROUP to subtract the numbers in the THOUSANDS column.

6 TEN THOUSANDS 13 THOUSANDS We can subtract from a place with a zero. Just remember to REGROUP the next place to the left.

2. Subtract: 39507 - 27386 REGROUP to subtract the TENS place

4 HUNDREDS 10 TENS

How to check the answer of a subtraction? CHECK:

Add the DIFFERENCE to the smaller number. The answer will be the smaller number.

Subtract the DIFFERENCE from the greater number. The answer will be the greater number.

In subtraction we will learn the subtraction operation of numbers having more than 4 digits with borrowing and without borrowing.

Examples:

1. Subtract 2684 from 6795.

Solution:

The numbers are arranged in column form (i) Ones are subtracted, 5 – 4 = 1

(ii) Tens are subtracted, 9 – 8 = 1

(iii) Hundreds are subtracted, 7 – 6 = 1

(iv) Thousands are subtracted, 6 – 2 = 4

Hence, difference = 4,111

2. Subtract 6732 from 9340 (with borrowing).

Solution:

The numbers are arranged in column form (i) Ones are subtracted, 0 < 2, so 1 ten is borrowed from tens.

Now 1 Ten or 10 + 0 = 10, 10 – 2 = 8

(ii) Tens are subtracted, 3Tens – 3Tens = 0

(iii)Hundreds are subtracted, 3 Hundreds < 7 Hundreds so, 1 Thousand is borrowed,

so 10 Hundreds + 3 Hundreds = 13 Hundreds,

13 Hundreds – 7 Hundreds = 6 Hundreds.

(iv) Thousands are subtracted, 8Thousands – 6Thousands = 2Thousands

Hence, difference = 2,608

3. What is the difference between 40712 and 7549? (with borrowing)

Solution:

The numbers are arranged in column form (i) 2 < 9, 1T or 10 is borrowed 10 + 2 = 12, 12 – 9 = 3

(ii) 0 < 4, 1H or 10T is borrowed 10T + 0 = 10T, Now 10T – 4T = 6T

(iii) 6H – 5H = 1H

(iv) 1 Tth is borrowed, 10Th – 7Th = 3 Th

(v) 3Tth – 0 = 3Tth

So, difference = 33,163

4. Subtract 2 3 7 4 1 2 from 6 4 9 5 2 3 (without borrowing)

Solution:

Numbers are arranged in column form (i) 3 – 2 = 1 Ones

(ii) 2 – 1 = 1 Tens

(iii) 5 – 4 = 1 Hundreds

(iv) 9 – 7 = 2 Thousands

(v) 4 – 3 = 1 Ten thousands

(vi) 6 – 2 = 4 Hundred thousands

Therefore, difference = 412111

5. Subtract (with borrowing) 6 5 6 2 9 from 3 2 3 4 7 8

Solution:

Numbers are arranged in column form (i) Ones: 8 < 9, IT or 10 is borrowed 10 + 8 = 18, 18 - 9 = 9

(ii) Tens: 6T - 2T = 4T

(iii) Hundreds: 4H < 6H, 1 th or 10H is borrowed, 10H + 4H = 14H, 14H - 6H = 8H

(iv) 2Th < 5Th, 1Tth or 10Th is borrowed 10Th + 2Th = 12Th, 12Th - 5Th = 7Th

(v) 1Tth < 6Tth,1Hth or 10Tth is borrowed 10Tth + 1Tth = 11Tth, 11Tth - 6Tth = 5Tth

(vi) 2Hth remained as it was.

So, difference = 257849

6. Find the difference between two numbers, 1 4 2 7 1 3 and 3 7 4 3 9.

Solution:

The numbers are arranged in column form.

142713 is greater than 37439, so 37439 will be subtracted from 142713. Difference = 105274

(i) Ones are subtracted

3 < 9, so 1 ten is borrowed.

Now 1T or 10 + 3 = 13, 13 - 9 = 4

(ii) Tens are subtracted, 1T < 3T, so 1H is borrowed.

Now 1H or 10T + 1 = 11,

11 - 3 = 8, answer is 11 - (3 + 1) = 7

(iii) Hundred: 6H – 4H = 2H

(iv) Thousands: 12Th – 7Th = 5Th

(v) Ten thousands: 3Th - 3Th: = 0

(vi) Hundred thousand: 1Hth – 0 = 1Hth

Therefore, 142713 - 37439 = 105274

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