• Computaion is the process of calculating or determining something by mathematical or logical methods.
• The computation operations that we are going to study in these chapter are: Addition, Subtraction, Multiplication and Division
• Using computation operations we can find answer to different mathematical problems.

Addition

• Addition is performed by adding the digits at ones place, carrying them over and then adding the digits in the tens place and so on.

• Addition is commutative. It means that the order does not matter.

i.e, 1+2 is same as 2+1.

1+2=2+1=3

12+23+35=23+35+12= 70

• Addition is associative. It means that as long as the order remains the same grouping doesn’t matter.

For example,

2+3+4=2+3+4
(2+3) +4=2+(3+4)

5+4=2+7
9=9
LHS=RHS

• Addition has identity property. That is, the sum of any number and zero is the original number. For example, 3+0=3.

EXAMPLE 1: Add 234719 and 945735

SOLUTION:

EXAMPLE 2: Three factories in a town produced 163846, 657853 and 875436 bags of sand last year. Find the total bags of sand produced by the three factories.

SOLUTION: Total bags of sand produced by three factories= 163846+ 657853+ 875436 = 1697135 [ANS]

Subtraction

• Subtraction is the process of taking one number or amount away from another.

• Subtraction is not associative.

For example, (1-2)-3≠1-(2-3) -1-3≠1-(-1) -4≠2

• Subtraction is not commutative.

For example,

5-6≠6-5

-1≠1

EXAMPLE 1: Subtract 965634 from 675432.

SOLUTION:

EXAMPLE 2:The sum of two number is 236574. If one number is 145634, find the other number.

SOLUTION:

The number is = 236574 – 145634 =90940

Multiplication

• Multiplication is the process of adding a number to itself a certain number of times.

For example,

1. i) 5 X 4 = (5 + 5 + 5 + 5)

= 20
ii) 11 X 3 = (11+11+11) =33

• Multiplication is associative.

For example,
(1X2)X3=1X(2X3)
2X3=1X6
6=6

• Multiplication is Commutative.
  For example,
  4X2=2X4;
  8=8
  LHS=RHS

• Multiplication has identity property. The product of any number and 1 is that number.
  
  For example,
  1X3=3

• Multiplication has distributive property. The distributive property lets us multiply a sum by multiplying each addend separately and then add the products.
  
  For example,
  2X(3+4) = (2X3)+(2X4)
  2X7=6+8
  14=14
  LHS=RHS

EXAMPLE 1: Multiply the two numbers 1024 and 234.

SOLUTION:

1 0 2 4 (Multiplicand)
X2 3 4 (Multiplier)
4 0 9 6 (1024 is first multiplied by 4)

3 0 7 2 X (1024 is multiplied by 3) + 2 0 4 8 X X (1024 is multiplied by 2)
2 3 9 6 1 6 [ANS]

EXAMPLE 2: The cost of a wooden chair is Rs.1357. What is the cost of 24 chairs?

SOLUTION:
The cost of 24 chairs are = Rs. (1357X24)
= Rs.32568 [ANS]

• Division is right-distributive over addition and subtraction.
  For example,
  (6+9) ÷3 = (6÷3)+(9÷3)
  15÷3=2+3
  5=5
  LHS=RHS [PROVED]

• Division is not left-distributive over addition and subtraction.
  For example,
  60 ÷ (4+6)≠(60÷4)+(60÷6)
  60÷10≠15+10
  6≠25
  LHS≠RHS

• Division is left associative.
  For example,
  8÷4÷2 = (8÷4) ÷2
  =2÷2
  =1

EXAMPLE 1: Divide 56132 by 61

SOLUTION: 61)56132(920 -549
1232
-1220
12
Quotient= 920 Remainder=12
Check: Divisor X Quotient + Remainder= Dividend
61 920 12 56132

EXAMPLE 2: A farmer had 104832 apples in his orchard. 442 apples were packed in each carton and the remaining decayed. How many cartons were made? How many apples decayed?

Solution: No. of cartons=104832÷ 442=237

442)104832(237
-0884
1643
-1326
3172
-3094
78
Remainder=78
Thus, the total number of cartons were 237 and the 78 apples decayed.

Practice These Questions

Q1) The population of a city was 29846753 in 2010. The current population is 54723497. Find the increase in population.

Q2) Rs. 90874536 was sanctioned to construct a building. Rs. 65478734 is spent. How much money is still left?

Q3) There are 9374 bags of goods in the warehouse. Each bag weighs 103kg. Find the total weight of the bags.

Q4) The cost of a laptop is Rs.198765. Find the cost of 459 laptops.

Q5) 874563 books are going to be packed in one box. If each box has 120 books. How many boxes are packed? How many books will remain unpacked?

Q6) Solve: 873456 -567439 + 328756

Q7) Fill in the boxes:
I) II)

Q8) Find the missing number:
Dividend=9372847, Quotient= 20, Remainder= 7, Divisor=?

Q9) Find the quotient and the remainder when the smallest 10 digit number is divided by the largest 5 digit number.

Recap

• An addition is commutative, associative and has an identity property.
• Subtraction is neither commutative nor associative.
• Multiplication is commutative, distributive, associative and has an identity property.
• A division is a right distributive over addition and subtraction but not left distributive.
• A division is left associative.
• Divisor X Quotient + Remainder= Dividend