Download Remedial - MoreMaths

1. Revision
Description
Recall basics of
numbers.
Reflect and Review
Teasers
Answers
To find the difference between the
largest 5-digit number and the sum
of smallest 3-digit number and
largest 4-digit number:
1) Find the largest
number formed
using the digits 3, 7,
0, 1 and 5 only once.
1) 75310
Here,
Largest 5-digit number = 99999
Smallest 3-digit number = 100
Largest 4-digit number = 9999
2) What is the smallest
5-digit number
starting with 8 and
ending with 1?
2) 80001
So, required difference
= 99999 – (100 + 9999) = 89900.
2. Operations on the Number Line
Description
Reflect
and
Review
 The numbers starting with zero See below
are called Whole Numbers.
the table

We can perform the four basic
operations on whole numbers
using a number line.
Teasers
1) Find out the value of
10 – 6 using number
line.
Answers
See below
the table
2) How many whole
numbers are there
between 27 and 45?
1
Reflect and Review
3 × 3 = 9 can be calculated using a number line in the following way:
0
1
2
3
4
5
6
7
8
9
10 11 12
Answers
1)
0
1
2
3
4
5
6
7
8
9
10 11 12
2) 18
3. Properties of Whole Numbers
Description
Reflect and Review
Closure Property
See below the
table
Associative
Property
2
Answers
234 + 506 = 740 is a whole
number, since 234 and 506
are whole numbers.
1) The cost of a
sandwich is ₹ 75.
Find the cost of 3
sandwiches.
1) ₹225

346 + 478 = 478 + 346, since
ordering doesn’t change the
sum.
111 × 999 = 999 × 111, since
ordering doesn’t change the
product.
56 + (45 + 12)
= (56 + 45) + 12
= (56 + 12) + 45,
since grouping doesn’t
change the sum.
67 × (78 × 34)
= (67 × 78) × 34
= (67 × 34) × 78,
since grouping doesn’t
change the product.
406 + 0 = 406, since zero is
additive identity.
1) 230 + ___
= 567 + 230
1) 567
See below the
table
Commutative
Property
Teasers



See below the
table

Identity Property

See below the
table

789 × 1 = 789 since 1 is
multiplicative identity.
2) 734
2) 828 × 734
= ___ × 828
1) ____ + (102 + 621)
= (542 + 621) +
____
2) 209 × (____ × 450)
= 450 × (____ ×
897)
1) 345 + ____ = 345
2) ___ × 1 = 1
1) 542;
102
2) 897;
209
1) 0
2) 1
1) 10101 × ____ =
10101
Multiplication by
0 and 1, and
Division by 1



When any whole
number is
multiplied by
zero, the
product is
always zero.
2) 0
2) 9889 × ____ = 0
3) 1

429 × 0 = 0, since on
multiplying any number by
zero, the product is always
zero.

567 ÷ 1 = 567, since on
dividing any number by one,
the quotient is the number
itself.
When any whole
number is
divided by 1, the
result is the
number itself.
See below the
table
3) 91191 ÷ _____ =
91191
0 ÷ 86 = 0, since on dividing
zero by any number (except
zero), the quotient is always
zero.
If zero is divided
by any whole
number except
0, we get zero as
the quotient.
Distributive
Property
1) 1

To evaluate: (345 × 255) +
(345 × 745):
(345 × 255) + (345 × 745)
= 345 × (255 + 745)
= 345 × 1000
= 345000.
1) 12 pens and 5
pencils are packed
in a box. Find the
total number of
items in 125 such
boxes.
1) 2125
2) 315
2) There are 25 ice
creams in a box. 18
of them are
chocolate flavored
and the rest are
butterscotch. Find
the number of
butterscotch ice
creams in 45 such
boxes.
3
Closure
Property
Commutative
Property
Associative
Property
Identity
Property
4
Addition
The whole
numbers are
closed under
addition.
Addition
Two whole
numbers can
be added in
any order.
Addition
The addition of
three whole
numbers by
grouping in any
way doesn’t
affect the sum.
Multiplication
The whole numbers
are closed under
multiplication.
Multiplication
Two whole
numbers can be
multiplied in any
order.
Subtraction
The whole numbers
are not closed under
subtraction.
Subtraction
Commutative
property is not
satisfied for
subtraction of whole
numbers.
Multiplication
The multiplication of
three whole numbers
by grouping in any way
doesn’t affect the
product.
Addition
If zero is added to any whole number,
then the sum is the number itself.
So, zero is called the additive identity
for whole numbers.
Subtraction
Associative
property is not
satisfied for
subtraction of
whole numbers.
Division
The whole
numbers are not
closed under
division.
Division
Commutative
property is not
satisfied for division
of whole numbers.
Division
Associative
property is not
satisfied for
division of whole
numbers.
Multiplication
If one is multiplied to any whole number,
then the product is the number itself.
So, one is called the multiplicative identity
for whole numbers.