Subtraction

We will learn subtraction of two-digit numbers, 3-digit numbers, 4-digit numbers, 5-digit numbers, etc. with and without regrouping. We know that to subtract numbers, we first arrange them in place value columns and then subtract the digits under ones, tens and hundreds columns.

While performing subtraction, the smaller number is always subtracted from the larger number. The smaller number is called minuend and the larger number is called subtrahend. The result is called the difference.

Now, solve the following questions given below to refresh the concepts we have learnt already.

The answer of a subtraction sum is called DIFFERENCE.

How to subtract 2-digit numbers?

Steps are shown to subtract 2-digit numbers.

Subtract 39 from 78.

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 = 3Th

(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

3. Find the difference.

For examples:

(i) 4 ten thousands - 24 thousands

4 ten thousands    →      40 thousands

-   24 thousands         →   -  24 thousands

16 thousands

(ii) 6 thousands 3 hundreds – 4 thousands 17 hundreds

6 thousands   3 hundreds    →       5 thousands + 13 hundreds

-   4 thousands 17 hundreds    →    -  5 thousands +  7 hundreds

6 hundreds

(iii) 43 lakhs – 17 lakhs 23 hundreds

43 lakhs                       →         42 lakhs + 100 hundreds

-  17 lakhs 23 hundreds    →     -  17 lakhs  +  23 hundreds

25 lakhs  + 77 hundreds

or, 25 lakhs 77 hundreds

Note: Subtraction is done only in the same grouping.

Worksheet on Subtraction:

I. Match the numbers in the two columns:

 Column A (i) 400 - 200(ii) 685 – 10(iii) 570 – 5(iv) The predecessor of 782(v) 853 – 0 Column B (a) 781(b) 853(c) 200(d) 565(e) 675

(i) → (c)

(ii) → (e)

(iii) → (d)

(iv) → (a)

(v) → (b)

II. Write any two numbers that come before the given numbers:

(i) ……………, ……………, 654

(ii) ……………, ……………, 316

(iii) ……………, ……………, 781

(iv) ……………, ……………, 999

(v) ……………, ……………, 100

(vi) ……………, ……………, 588

(i) 652, 653

(ii) 314, 315

(iii) 779, 780

(iv) 997, 998

(v) 98, 99

(vi) 586, 587

III. Fill in the blanks:

(i) 346 - 100 = ……………

(ii) 412 – 10 = ……………

(iii) 587 – 27 = ……………

(iv) 697 – 590 = ……………

(v) 962 – 15 = ……………

(vi) 740 – 80 = ……………

(i) 246

(ii) 402

(iii) 560

(iv) 107

(v) 947

(vi) 660

IV. Subtract the given numbers:

(i) 459 - 234

(ii) 762 – 430

(iii) 905 – 665

(iv) 652 – 483

(v) 790 – 548

(vi) 809 – 719

(i) 225

(ii) 332

(iii) 240

(iv) 169

(v) 242

(vi) 90

V. Subtract:

 (i)           5     7     8      -   1      0     4     ____________ (ii)           5     9     1      -   2      3     0     ____________
 (iii)           5     8     9      -   1      3     6     ____________ (iv)           4     0     0      -   3      2     2     ____________
 (v)           2     5     3      -   1      0     6     ____________ (vi)           9     0     0      -   3      7     5     ____________

V. (i) 474

(ii) 361

(iii) 453

(iv) 78

(v) 147

(vi) 525

VI. Find the difference between:

(i) 725 and 400

(ii) 153 and 965

(iii)  781 and 243

VI. (i) 325

(ii) 812

(iii) 538

VII. Arrange the following numbers in columns and subtract:

(i) 431 from 846

(ii) 261 from 642

(iii) 524 from 800

VII. (i) 415

(ii) 381

(iii) 276

VIII. Word Problem on Subtraction:

(i) What must be added to 243 to get 605?

(ii) The sum of two numbers is 924. If the greater of the two numbers is 624, find the smaller number.

(iii) Shelly has a basket full of fruits to sell. She has 326 fruits with her. She sells 180 in the morning and 75 in the evening. How many fruits are still left with her to be sold?

(iv) Neil fill 437 litres of water in the tank. His family uses 359 litres of water in a day. How much water is still left in the tank?

(i) 362

(ii) 300

(iii) 71

(iv) 78 litres

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