**Category : **3rd Class

**Addition and Subtraction**

Addition

Addition is the combination of two or more quantities in a single quantity. This is one of the four basic arithmetic operations. Symbol for addition is +.

Addition of Four Digits Numbers without Carry Over

Following are the steps used in this type of addition.

For example: addition of 4784 and 3214.

Step 1: Add ones 4 + 4 = 8. Write 8 under ones column.

Step 2: Add tens 8 + 1 = 9. Write 9 under tens column.

Step 3: Add hundreds 7 + 2 = 9. Write 9 under hundreds column.

Step 4: Add thousands 4 + 3 = 7. Write 7 under thousands column.

Hence, addition of 4784 + 3214 = 7998.

Addition of Four Digit Numbers with Carry Over

Following are the steps used in this type of addition.

For example addition of 7569 and 5984.

Step 1: Add ones, 9 + 4 = 13 = 1 tens + 3 ones. Write 3 under ones column and carry one tens to the tens column.

Step 2: Add tens, 6 + 8 + 1 (carry over) = 15 tens = 1 hundred + 5 tens.

Write 5 under tens column and carry 1 hundred to the hundreds column.

Step 3: 1 thousand 5+9+1 (carry over) =15 hundreds.

Write 5 under hundreds column and carry 1 thousand to the thousand column

Step 4: Add thousands. 7 + 5 + 1 (carry over) = 13 thousands

Write 13 under thousands column.

Sum of 7569 and 5984 = 13553.

Adding Terms

A term with numbers and Setters can be added to those which contains the same letter but different or same numbers. The sum of the terms\[x+x=2x\].

Decimal Numbers and their Addition

A number with a decimal point is known as decimal number. The digit at left from decimal point is called whole part of the decimal number and digit at right side from the decimal point is called decimal part of the decimal number

Following are the steps used in the addition of decimal numbers.

Step 1: Arrange the decimal numbers vertically, decimal part under decimal and whole part under whole part.

Step 2: Add them starting from right of the decimal numbers»

Step 3: Carry over to the next addition.

Step 4: If carry is generated in the addition of tenths place digits then carry over to the addition of ones of the whole parts of the decimal numbers.

Step 5: Add the whole parts of the decimal numbers.

Look at the following addition:

Add ` 123. 25, ` 85.60 and ` 48.75.

= ` 257 and 60 paise

- Example

Find the digit at thousands place of resulting number of 45\[\times \]90\[\times \]100?

(a) 7 (b) 8

(c) 5 (d) All the above

(e) None of these

Ans. (c)

Explanation: Digits at ones, tens and hundreds are 0. For digits at thousands place, 45 gets multiplied by 9 which gives 5 at thousands place.

- Example

Two terms are added to form third term then the third term will be like term of:

(a) Each of the added terms

(b) Each of numerical coefficient of added terms

(c) A number

(d) All the above

(e) None of these

Ans. (a)

Explanation: Like terms are added to give like term.

Properties of Addition

Commutative Property of Addition

Sum of two numbers does not change on changing the order of the numbers. For example, sum of 4 + 5 = 9 and sum of 5 + 4 = 9. Hence, sum remains same on changing the order of the numbers.

Associative Property of Addition

Sum of the numbers does not change on changing the groups of addends. For example, sum of 4 + (5 + 6) = 15 and their sum remains same on changing the group.

Hence, (4 + 5) + 6 = 15

Additive Property for Zero

Addition of zero with a number is the number itself. This property of addition is called additive property for zero. For example, sum of 0 + 235 = 235

(a) 34 + 0 = 34 (b) 29 + 18 = 18 + 29

(c) 23 + 67 = 50 + 50 (d) All the above

(e) None of these

Ans. (a)

Explanation: On adding 0 to a number, we get the number

- Example

Consider the following statements:

Statement 1: The sum of two numbers is changed on

Statement 2: The sum of two numbers does not change on changing

Which one of the following is correct about the above statements?

(a) Statement 1 is true and 2 is false

(b) Statement 1 and 2 are false

(c) Statement 1 is false and 2 is true

(d) All the above

(e) None of these

Ans. (c)

Explanation: As per the commutative property of addition only the statement two is correct. Therefore, (c) is the correct answer.

Subtraction

Subtraction itself means ?to take away?. Quantity from which another quantity is to be subtracted is called minuend and subtracted quantity is called subtrahend.

Subtraction of Five Digit Numbers without Borrow

Following are the steps used for the subtraction of five digit numbers without borrow:

For example: 76987 ? 52312

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 ten thousands column.

= 24675 is the difference of 76987 - 52312.

Subtraction of Five Digit Numbers with borrow

Following are the steps used for the subtraction of five digit numbers with borrow:

For example: 97564 - 78268

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.

- Example

A container contains 45873 mangoes and another container contains 38765 mangoes. Find the difference of both the containers.

(a) 7108 (b) 7026

(c) 7027 (d) All the above

(e) None of these

Ans. (a)

Explanation: Difference =

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