Wisechamps Grade 6 Whole Numbers (Session 5)

WHOLE
NUMBERS

Quick Recap on Properties of
Whole numbers

Closure Property:

If A and B are two whole numbers, then

A + B → W

A x B → W

It is not applicable for subtraction and division of whole numbers.

Commutative Property:

A + B = B + A

A x B = B x A

Commutativity is not applicable for subtraction and division

Associativity of Addition and Multiplication:

A + (B + C) = (A + B) + C

A x (B x C) = (A x B) x C

Distributivity of Multiplication over Addition:

A x (B + C) = A x B + A x C

Identity Property of Addition and Multiplication:

W + 0 = W ( 0 is called the additive identity)

W x 1 = W ( 1 is called the multiplicative identity)

Number Line :

A number line is a picture of a graduated straight and horizontal
line in which numbers are written.

Parts of a Number line:

Operations using number line

Addition

1 + 4 =
5

Subtraction

2 - 4 = -2

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Multiplication

3 x 5 = 15

Division

14 ÷ 7 = 2

Patterns in Whole numbers

Patterns help us simplifying complicated processes like addition or multiplication without
calculations. Natural numbers can be represented using dots as:

i) Line ii) Square iii) Rectangle iv) Triangle

Example : 2 can be represented as

3 can be represented as

and so on. Every natural number can be represented in form of line with dot representation.

Square Number-

The numbers which can be arranged as square are called Square numbers. A number

multiplied by itself always gives a square number.

Example : 4 = 2 x2

9 = 3 x 3

And so on 16, 25 etc.

Rectangular Number-

The numbers which can be split into two numbers in such a way that both the numbers
are greater than 1, then the number is called Rectangular number.

Example :

8 = 2 x 4 or 4 x 2

6 = 2 x 3 or 3 x 2,

OR
OR

Triangular Number-

Numbers which can be arranged as triangles are called Triangular numbers.The
triangle formed must be right- angled and two sides must be equal.

10

Example : 6

Section-2

Multiple Choice

The following diagram is a number line. Two boys Anil & Charan start from X and go with the same speed in opposite directions. Who will reach the flag post first?

• Charan

• Anil

• Both reach at the same time

• Cannot be Determined

Explanation

We can see that from the given number line:

The distance between X and A is 250, while the Distance between X and B is 200 (450 - 250 = 200).

Thus, Distance between X and A is greater than that between X and B.

So, Anil will reach first.

Multiple Choice

Mihika makes 8 gift packs containing chocolates for Diwali. She puts 12 vanilla chocolates, 14 milk chocolates and 8 nut chocolates in each pack. With the help of which property, can you calculate the total number of chocolates in 8 packs?

• Commutative Property

• Associative Property

• Distributive Property

• None of these

Explanation

Distributivity Property:

A x (B + C) = A x B + A x C

Therefore, total number of chocolates = 8 (12 + 14+8) or

12×8+14×8+8×8 =8×(12+14+8)

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A

B

C

D

13. A vendor supplies 105 litres of milk to a hotel in the morning and 85
litres of milk in the evening. If the milk costs Rs. 20 per litre, how
much money is due to the vendor per day?

Rs. 3500

Rs. 4200

Rs. 3950

Rs. 3800

A

B

C

D

13. A vendor supplies 105 litres of milk to a hotel in the morning and 85
litres of milk in the evening. If the milk costs Rs. 20 per litre, how
much money is due to the vendor per day?

Rs. 3500

Rs. 4200

Rs. 3950

Rs. 3800

Explanation

Quantity of milk supplied in the morning = 105 L

Quantity of milk supplied in the evening = 85 L

Therefore, quantity of milk supplied in one day = 105 + 85 =

190 L

Cost of one litre milk = Rs. 20

Therefore, cost of 190 L milk= Rs. (20×190)= Rs. 3800

A

B

C

D

14. There are 222 red balls in a basket. A boy takes out 6 red balls
from it and replaces them by 12 white balls. He continues to do so, till
all red balls are replaced by white balls. Then the number of white
balls he put in the basket is __________.

333

444

345

400

A

B

C

D

14. There are 222 red balls in a basket. A boy takes out 6 red balls
from it and replaces them by 12 white balls. He continues to do so, till
all red balls are replaced by white balls. Then the number of white
balls he put in the basket is __________.

333

444

345

400

Explanation

Let n be the number of steps.

According to question, 222−6×n=0 ⇒6n=222⇒n=222/6=37

Now, number of white balls added in one step = 12

Therefore, number of white balls added in 37 steps

=12×37=444

A

B

C

D

15. The school canteen charges Rs.20 for lunch and Rs.4 for milk each
day. How much money do you spend in 5 days on these things?

120

20

24

100

A

B

C

D

15. The school canteen charges Rs.20 for lunch and Rs.4 for milk each
day. How much money do you spend in 5 days on these things?

120

20

24

100

Explanation

Cost of lunch=Rs.20

Cost of milk=Rs.4

Amount spend for one day= 20+4=Rs.24

Therefore, amount spend for 5 days=24x5=Rs.120