3rd Class Mathematics Subtraction Introduction

          Introduction

Subtraction is the difference between two quantities and this is the inverse process of addition.

The name subtraction itself means "to take away". The symbol used for subtraction is (-) called minus. In the subtraction, the quantity from which another quantity is to be subtracted is called minuend and subtracted quantity is called the subtrahend. Resulting quantity of the subtraction is called their difference. In the

S subtraction of X - Y = Z. X is minuend, Y is subtrahend and Z is difference between X and Y.

          Subtraction without Borrowing

The following steps are used for the subtraction of four digit numbers without borrowing:

 Step 1:  Write the numbers in such a way that the ones of a smaller number under the ones of bigger number and tens, hundreds, thousands of the smaller numbers under the tens, hundreds, thousands of bigger number respectively.

 Step 2: Subtract the units, tens, hundreds, thousands of smaller number from the unit, tens, hundreds and thousands of bigger number starting from right or units.

 Step 3:   The resulting numbers is the difference of the numbers. For Example.

Th           H             T              O

   7            9             8              6

- 5            6             1              2

  2            3             7              4

= 2 3 7 4

The following steps are used for the subtraction of five digit numbers (76987 - 52312) without borrowing:

Step 1: 7 – 2 = 5. Write 5 under ones column.

Step 2: 8 – 1 = 7. Write 7 under tens column.

Step 3: 9 – 3 = 6. Write 6 under hundreds column.

Step 4: 6 – 2 = 4. Write 4 under thousands column.

Step 5: 7 – 5 = 2. Write 2 under thousands column.

T              Th           Th           H             T              O

                 7              6              9              8              7

-              5              2              3              1              2

                2              4              6              7              5

There are 4095 people in a cricket stadium. The total number of females in the stadium is 1070. What is the total number of males in the stadium?

(a) 3025

(b) 3026

(c) 3027

(d) 3045

(e) None of these

Answer (a)

Explanation

Total number of males in the stadium = 4095 -1070 = 3025.

             Subtraction of Four and Five Digits Numbers with Borrowing

The following steps are used for the subtraction of four digit numbers (6748 - 5999) with borrowing:

 Step 1: 9 > 8, hence, 9 cannot be subtracted from 8. Therefore, Borrowing 1 ten from 4 tens. Thus, 4 tens become 3 tens and 8 ones become 18 ones. (1 ten = 10 ones). Their subtraction = 18 - 9= 9 ones. Write 9 under ones column.                                          

 Step 2: 9 > 3. Borrow 1 hundred from 7 hundreds, 7 hundreds become 6 hundreds and 3 tens become 13 tens. Hence, their subtraction = 13 - 9 = 4 tens.

Write 4 under tens column.                                    

 Step 3:   9 > 6. Borrow 1 thousand from 6 thousands, 6 thousands become 5 thousands and 6 hundreds become 16 hundreds. Hence, their subtraction = 16 - 9 = 7. Write 7 under hundreds column.

 Step 4: 5 – 5 = 0. Write 0 under thousands column.

The following steps are used for the subtraction of five digit numbers (97564 - 78268) with borrowing:

 Step 1: 8 > 4, 8 cannot be subtracted from 4. Borrowing 1 ten from 6 tens, 6 tens become 5 tens and 4 ones become 14 ones. Hence, their subtraction = 14 - 8 = 6 ones. Write 6 under ones column.

 Step 2: 6 > 5. Borrow 1 hundred from 5 hundreds, 5 hundreds become 4 hundreds and 5 tens become 15 tens. Hence, their subtraction = 15 - 6 = 9 tens.

Write 9 under tens column.

 Step 3: 2 < 4. Therefore, 4 – 2 = 2. Write 2 under hundreds column.

 Step 4: 8 > 7. Borrow 1 ten thousand from 9 ten thousands, 9 ten thousands become 8 ten thousands and 7 thousands become 17 thousands. Hence, their subtraction = 17 - 8 = 9. Write 9 under thousands column.

 Step 5: 8 – 7 = 1 ten thousand. Write 1 under ten thousands column.

The bank statement of the saving bank is balance of Rs 56045. Find the current balance after withdrawing Rs 29896.

(a) Rs 26252

(b) Rs 26149

(c) Rs 26272

(d) Rs 26328

(e) None of these

Answers (b)

 Explanation