Addition and Subtraction
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
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.
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
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.
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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