Wisechamps Grade 6 Whole Numbers (Session 4)

WHOLE
NUMBERS

Quick Recap on Numbers

Natural Numbers:

The numbers 1, 2, . . . . , N all are called Natural Numbers.

The negative numbers and 0 are not counted as the natural numbers
because 1 is considered as the smallest natural number.

Quick Recap on Numbers

Whole Numbers:

The numbers 0, 1, 2, . . . . . , N all are called Whole Numbers.

Zero is the smallest whole number.

Negative numbers are not whole numbers.

Rational

… -1.5, -1, -0.5, 0, 0.5, 1, 1.5 …

Integers

(... -2, -1, 0, 1, 2, …)

Whole Numbers
(0, 1, 2, 3, 4, ……)

Natural Numbers

(1, 2, 3, 4, ……)

Multiple Choice

Which of the following whole number doesn't have a predecessor as a whole number?

• 100

• 0

• 1

• 9

Explanation

The whole numbers start from 0, hence 0 does not have a predecessor.

The predecessor of 100 is 99 which is also a whole number.

The predecessor of 1 is 0 which is also a whole number.

The predecessor of 9 is 8 which is also a whole number.

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)

Dropdown

Closure Property is satisfied by whole numbers with respect to ​

Select answer

Explanation

Addition and multiplication of whole numbers satisfy closure property.

Subtraction and Division of whole numbers donot satisfy the closure property.

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

Multiple Choice

Which of the following number lines represents 8 steps more than number (-5)?

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

Multiple Choice

By using dot (..) pattern, which of the following number can be arranged in all three ways namely a line, a triangle and a rectangle.

• 10

• 9

• 11

• 8

Explanation

As we know that all numbers can be arranged as a line.

The number 10 can be shown as -

Also the number 10 can be shown in form of triangle and rectangle

Section-1

Multiple Choice

Which of the following is NOT true?

• $$(5+6)+7=5+(6+7)$$

• $$(5\times6)\times7=5\times(6\times7)$$

• 5+6 x 7 = (5+6) x (5+7)

• 5 x (6+7) = (5x6) + (5x7)

Explanation

We have (5 + 6) + 7 = 11 + 7 = 18 and 5 + (6 + 7) = 5 + 13 = 18.

Hence (5 + 6) + 7 = 5 + (6 + 7).

We have (5 × 6) × 7 = 30 × 7 = 210 and 5 × (6 × 7) = 5 × 42 = 210.

Hence (5 × 6) × 7 = 5 × (6 × 7).

We have (5 + 6) × 7 = 11 × 7 = 77 and (5 + 6) × (5 + 7) = 11 × 12 = 132.

Hence (5 + 6) × 7 ≠ (5 + 6) × (5 + 7).

We have 5 × (6 + 7) = 5 × 13 = 65 and (5 × 6) + (5 × 7) = 30 + 35 = 65.

Hence 5 × (6 + 7) = (5 × 6) + (5 × 7).

Drag and Drop

If we multiply 82 with​

Placeholder

we get 82.

Drag these tiles and drop them in the correct blank above

1

82

-82

0

Explanation

We know that 1 is the multiplicative identity, hence any number multiplied by 1 would be the number itself.

So, if we multiply 82 with 1, we will get 82 itself. So, 1 is the correct answer.

If we multiply 82 with 82, we get 82². So, 82 is not the correct answer.

If we multiply 82 with -82, we get -82². So, -82 is not the correct answer.

If we multiply 82 with 0, we get 0. So, 0 is not the correct answer.

Explanation

To form the greatest number (without repetition of digits) from the given digits, we write them in descending order and place commas after periods.

The greatest number in this case would start from 9 followed by the next greatest number i.e. 8 followed by 7 and so on.

Any other comibination of numbers would not result in the Greatest number from the given set of digits.

Drag and Drop

The three consecutive predecessors of 70010 are​​

Placeholder

Drag these tiles and drop them in the correct blank above

70009,70008,70007

70006, 70007, 70009

70011, 70012, 70013

70012, 70011, 70010

Explanation

Predecessor is obtained by subtracting 1 from the given number.

Given number is 70010

70010-1 = 70009

70009-1= 70008

70008-1=70007

Thus, the three consecutive predecessors of 70010 are 70009, 70008

and 70007

Multiple Choice

Who among Anu and Bina are correct:

Anu: 6 × 8 = 8 × 6 is an example for commutativity of whole numbers under multiplication.

Bina: 6 + 8 = 8 + 6 is an example for associativity of whole numbers under addition.

• Only Anu

• Only Bina

• Neither of them

• Both of them

Explanation

a × b = b × a is the commutative property of whole numbers under multiplication

a + b = b + a is the commutative property of addition of whole numbers.

Thus, 6 × 8 = 8 × 6 is the commutative property of multiplication and 6 + 8 = 8 + 6 is the commutative property of addition.

The Associative Property of Addition is given by

a + (b + c) = (a + b) + c

Multiple Choice

Which of the statements are correct.

Statement-I: Except zero, all whole numbers are natural numbers.

Statement-II: Zero is the only whole number.

• Statement I is true

• Statement II is true

• Both the Statements are true

• Neither of the Statements are true

Explanation

The set of whole numbers is infinite.

It has all natural numbers along with zero.

Multiple Choice

Bunny is 15 years old. He writes an equation to find his mother's age, m.

m - 15 = 35

Which operation would help him solves the equation for m?

• Add 15 to both sides

• Subtract 15 to both sides

• Multiply both sides by 15

• Divide both sides by 15

Explanation

The operation of the L.H.S of m - 15 = 35 is subtraction.

So to isolate m, the opposite operation, i.e., addition must be done.

Multiple Choice

Which of the following number line correctly represents (-7) + 4?

Multiple Choice

Which of the following number lines correctly represents (-5) - (3)?

THANK YOU