Comparison of Images
In comparison of images we compare height, thickness, numbers etc. One image can be bigger than other in size or number of image in a group may be more than that of another group. See the examples given below:
Which one of the following is true?
(a) 
(b) 
(c) 
(d) All of these
Answer (d)
Which picture given in the options is smaller than the following picture? 
(a) 
(b) 
(c) 
(d) 
Answer (c)
Which one of the following is not correct?
(a) 556 > 567
(b) 554 < 555
(c) 598 = 598
(d) 452 > 450
Answer (a)
Explanations-
First two digits from left are same in all the options except (a) 
Rules for Comparison
and
as per rule,
and
are compared as
, therefore,
Similarly
rupees>rupees.
kilometers>kilometers
Paise>Paise
seconds>seconds
If
and
are compared then as per the rule,
ofand
ofare compared as extreme left digits of the both numbers are.
In this case
Thus
Similarly for time,
hours>hours
seconds>seconds
minutes>minutes
For money,
rupees>rupees.
Paise>Paise
For distance,
Kilometers >kilometers
Meters >meters
Which one of the following is correct?
(a) 
(b) 
(c) 
(d) 
Answer (a)
Explanations
Extreme left digit of
iswhich is greater than
, extreme left digit of
.
is greater than :
(a) 
(b) 
(c) 
(d) 
Answer (a) 
Introduction
You have learnt comparison of numbers and images in the previous class. For comparing distance, time and money the same method of comparison is applied. Numbers can be compared as smaller, greater or equal. For example:
is the sign of greater than and read as
is greater than
]
Then for distance alsokilometer > kilometer
Similarly for time,
hour>hour
And for money,rupees >rupees
Note:
'>' is the sign for greater than.
'<' is the sign for less than.
'=' is the sign for equal to. 
Word Problems
In this section we will learn about some real life problems based on division.
How many bundles of
pencils can you make out of
pencils?
Explanation-
Total number of pencil divided by one bundle of pencil 
bundles.
If a mini-bus can carry
children then how many mini buses would be needed to carry 
children?
Explanation-
Total number of children is divided by capacity of one
mini- bus (28 children )
mini bus.
.
, is the number itself 
.
. 
Short Division
In this method, we breaks down a division problem into a series of easy steps.
Divide
by
.
Solution:
Step 1: To dividebyby short division method we write
as 
Step 2: Then recitetable till you come to i.e.
.
Therefore,
Or,
. The answer is
.
Divide
by
.
Step 1: To dividebyby short division method we write
as 
Step 2: Then recite 8 table till you come toi.e.
Therefore, 
Or
.The answer is
.
Division by 10
If the divisor is
then the digit at the one's place is the remainder (R) and the number ormed by the remaining digits of the dividend will be the quotient (Q.). For example.
Quotient
and Remainder
Quotient
and Remainder
Division by 100
If the divisor is 100 then the number formed by the last two digits of the dividend will be the remainder (R) and the number formed by the remaining digits of the dividend will be the quotient (Q). For example.
Quotient
and Remainder
Quotient
and Remainder
Facts about Division
. Division by Grouping Equally
Divide 24 scissors into 3 groups by dividing equally.
Division by repeated subtraction
To divide
cakes equally among
children by repeated subtraction method, follow these steps:
Step 1:
Give
cakes to first child,
are left.
Step 2:
Givecakes to second child. are left.
Step 3:
Givecakes to third child.
is left.
Division as Reverse Multiplication
Multiplication means putting together in equal groups. Division means dividing into groups. So, division is the reverse process of multiplication. 
Means 3 groups containing 5 things each.
Meansthings divided equally intogroups. 
Introduction
Division is the grouping of many articles in required number of parts. In the division, table of 2 to 20 is helpful to divide any number. In this chapter, we will learn about the division of a group of articles in required number of groups. Word Problems
In this section, we will learn about some real life problems based on multiplication. For example
A table has [4] legs. How many legs do [3] tables have?
To solve the problem multiply\[[4]\times [3]\]to get [12] as answer.
A week has [7] days. How many days will be there in [2] weeks?
Solution:
Required number of days \[=[7]\times [2]=[14]\] days.
A factory produces [15] items in a day. How many items it will produce in a week if Sunday is a holiday?
Solution:
Items produced in a day = [15]
Items produced in [6] days \[=[15]\times [6]=[90]\] items.
James scored [15] marks in an exam whereas Smith scored thrice of James. How much marks did Smith score?
Solution:
Marks scored by Smith \[=[3]\times [15]=[45]\]marks.
The cost of potato is [10] rupees per kg. What is the cost of [3] Kg of potatoes?
Solution:
Required cost = Quantity of potato\[\times \]Cost of potato
\[=[3]\times [10]=[30]\]rupees.
The cost of [1] pen is [5] rupees. What is the cost of [5] such pens?
Solution:
Required cost = Number of pens \[\times \] Cost of [1] pen
\[=[5]\times [5]=[25]\] rupees. 
Multiplication Series
Multiplication series is a table of numbers. To solve the problems based on multiplication series we require to remember tables of numbers given below.
Multiplication Table
Fill in the blank with suitable number.
Solution:
This can be found with the help of table of
. Hence, in the blank space, 20 is suitable number.
Which number should be multiplied with
to get the result
?
Solution:
is at the sixth place in the table of. Therefore,
should be multiplied withto get.
Find the next number in the series.
Solution:
In the given series each number is multiplied by
. So to find the next number multiply the previous number bythat is
.
Solution:
In the given series to find the next number multiply the previous two consecutive numbers.
and
.
is the sign of multiplication.
Multiplication of Three Numbers
It involves 3 numbers. In this type of multiplication 1st multiply any two numbers and then multiply the result with the remaining number. For example, to multiply 5, 2 and 4: first multiply
and
thus
and then
Solution:
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