Find the value of the following: 3845 × 5 × 782 + 769 × 25 × 218

Given, 3845 × 5 × 782 + 769 × 25 × 218 . 3845 × 5 × 782 + 769 × 5 × 5 × 218 3845 × 5 × 782 + 3845 × 5 × 218 We can write 3845 = 5 × 769 . Then applying the distributive property a × b + c = a × b + a × c . Here a = 5 × 3845 ; b = 782 ; c = 218 3845 × 5 × 782 + 3845 × 5 × 218 = 3845 × 5 782 + 218 = 19225 1000 Hence, 3845 × 5 × 782 + 769 × 25 × 218 = 1 , 92 , 25 , 000 .

Match the following: ( i ) 425 × 136 = 425 × 6 + 30 + 100 Commutativity under multiplication ( i i ) 2 × 49 × 50 = 2 × 50 × 49 Commutativity under addition ( i i i ) 80 + 2005 + 20 = 80 + 20 + 2005 Distributivity of multiplication over addition

Given, 425 × 136 = 425 × 100 + 30 + 6 We know that the operation is distributive property of multiplication over addition: a × b + c = a × b + a × c . Hence, 425 × 136 = 425 × 100 + 30 + 6 shows distributive property of multiplication over addition. In i i . Given, 2 × 49 × 50 = 2 × 50 × 49 We know that this is commutative property of multiplication: a × b = b × a . Hence, 2 × 49 × 50 = 2 × 50 × 49 shows commutative property of multiplication. In i i i . Given, 80 + 2005 + 20 = 80 + 20 + 2005 We know that this is commutative property of addition : a + b = b + a . Hence, 80 + 2005 + 20 = 80 + 20 + 2005 shows commutative property of addition . Distributive property of multiplication over addition- ( i ) , Commutative property of multiplication- ( i i ) , Commutative property of addition - ( i i i ) .

Match the following columns on whole numbers: Column A Column B (a) 137 + 63 = 63 + 137 (i) Associativity of multiplication (b) ( 16 × 25 ) is a whole number (ii) Commutativity of multiplication (c) 365 × 18 = 18 × 365 (iii) Distributive law of multiplication over addition (d) ( 86 × 14 ) × 25 = 86 × ( 14 × 25 ) (iv) Commutativity of addition (e) 23 × ( 80 + 5 ) = ( 23 × 80 ) + ( 23 × 5 ) (v) Closure property for multiplication

(a) Given: 137 + 63 = 63 + 137 ⇒ 137 + 63 = 200 = 63 + 137 It follows that if a and b are any two whole numbers, then a + b = b + a , which is commutative property of whole number over addition. ∴ It follows (iv) commutativity of addition. (b) Given: ( 16 × 25 ) is a whole number. ⇒ 16 × 25 = 400 , which is also a whole number. It follows that if a and b are any two whole numbers, then a × b is also a whole number, which is closure property of whole number over multiplication. ∴ It follows (v) closure property for multiplication. (c) Given: 365 × 18 = 18 × 365 ⇒ 365 × 18 = 6570 = 18 × 365 It follows that if a and b are any two whole numbers, then a × b = b × a , which is commutative property of whole number over multiplication. ∴ it follows (ii) commutativity of multiplication. (d) Given: ( 86 × 14 ) × 25 = 86 × ( 14 × 25 ) ⇒ ( 86 × 14 ) × 25 = 1204 × 25 = 30100 and 86 × ( 14 × 25 ) = 86 × 350 = 30100 It follows that if a , b and c are whole numbers, then a × b × c = a × b × c ∴ It follows (i) associativity of multiplication. (e) Given: 23 × ( 80 + 5 ) = ( 23 × 80 ) + ( 23 × 5 ) ⇒ 23 × ( 80 + 5 ) = 23 × 85 = 1955 and ( 23 × 80 ) + ( 23 × 5 ) = 1840 + 115 = 1955 It follows that if a , b and c are whole numbers, then a × b + c = a × b + a × c ∴ It follows (iii) distributive law of multiplication over addition. Hence, the correct match is as shown below: Column A Column B (a) 137 + 63 = 63 + 137 (iv) Commutativity of addition (b) ( 16 × 25 ) is a whole number (v) Closure property for multiplication (c) 365 × 18 = 18 × 365 (ii) Commutativity of multiplication (d) ( 86 × 14 ) × 25 = 86 × ( 14 × 25 ) (i) Associativity of multiplication (e) 23 × ( 80 + 5 ) = ( 23 × 80 ) + ( 23 × 5 ) (iii) Distributive law of multiplication over addition

Match the following: (i) 425 × 136 = 425 × 6 + 30 + 100 (a) Commutativity under multiplication (ii) 2 × 49 × 50 = 2 × 50 × 49 (b) Commutativity under addition (iii) 80 + 2005 + 20 = 80 + 20 + 2005 (c) Distributivity of multiplication over addition

(i) We know that, distributivity of multiplication over addition is: a × b + c = a × b + a × c Similarly, a × b + c + d = a × b + a × c + a × d Therefore, 425 × 136 = 425 × 6 + 30 + 100 satisfies the distributivity of multiplication over addition property. (ii) We know that, commutativity under multiplication is: a × b = b × a Similarly , a × b × c = a × c × b = b × c × a Therefore , 2 × 49 × 50 = 2 × 50 × 49 satisfies commutativity under multiplication property. (iii) We know that, commutativity under addition is: a + b = b + a Similarly, a + b + c = c + b + a = c + a + b Therefore , 80 + 2005 + 20 = 80 + 20 + 2005 satisfies commutativity under addition property. Hence, the table will be as follows: (i) 425 × 136 = 425 × 6 + 30 + 100 (c) Distributivity of multiplication over addition (ii) 2 × 49 × 50 = 2 × 50 × 49 (a) Commutativity under multiplication (iii) 80 + 2005 + 20 = 80 + 20 + 2005 (b) Commutativity under addition

EASY

Earn 100

Write the distributive property of multiplication over subtraction.

Important Questions on Whole Numbers

EASY

Mathematics>Arithmetic>Whole Numbers>Properties and Operations on Whole Numbers

The multiplication of two numbers is

1.728

. If one of the numbers is

6.4

, then what is the second number?

EASY

Mathematics>Arithmetic>Whole Numbers>Properties and Operations on Whole Numbers

If the cost of $\frac{5}{3}$ parts of a pizza is Rs. $300$ , then what will be the cost of $\frac{3}{5}$ parts of the pizza?

EASY

Mathematics>Arithmetic>Whole Numbers>Properties and Operations on Whole Numbers

The sum of two numbers is

9

. The sum of their reciprocals is

\frac{1}{2}

. Find one of the numbers is :

EASY

Mathematics>Arithmetic>Whole Numbers>Properties and Operations on Whole Numbers

If the product of two whole numbers is $1$ , can we say that one or both of them will be $1$ ? Justify through examples.

EASY

Mathematics>Arithmetic>Whole Numbers>Properties and Operations on Whole Numbers

Which of the following is not true?

EASY

Mathematics>Arithmetic>Whole Numbers>Properties and Operations on Whole Numbers

For any whole numbers

a, b, c

, is it true that

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

? Give reasons.

EASY

Mathematics>Arithmetic>Whole Numbers>Properties and Operations on Whole Numbers

If the product of two whole numbers is

1,

can we say that one or both of them will be

1 ?

Justify through examples.

MEDIUM

Mathematics>Arithmetic>Whole Numbers>Properties and Operations on Whole Numbers

Find the value of the following:

$3845 \times 5 \times 782 + 769 \times 25 \times 218$

EASY

Mathematics>Arithmetic>Whole Numbers>Properties and Operations on Whole Numbers

State the property used in the following statement:
$19 \times 17 = 17 \times 19$

EASY

Mathematics>Arithmetic>Whole Numbers>Properties and Operations on Whole Numbers

If $X + Y = Z$ , where $X, Y$ and $Z$ each stand for a distinct digit from $1$ to $9$ . What is the greatest digit that $Z$ could be?

EASY

Mathematics>Arithmetic>Whole Numbers>Properties and Operations on Whole Numbers

Match the following:

$(i)$	$425 \times 136 = 425 \times (6 + 30 + 100)$	Commutativity under multiplication
$(i i)$	$2 \times 49 \times 50 = 2 \times 50 \times 49$	Commutativity under addition
$(i i i)$	$80 + 2005 + 20 = 80 + 20 + 2005$	Distributivity of multiplication over addition

MEDIUM

Mathematics>Arithmetic>Whole Numbers>Properties and Operations on Whole Numbers

If $X + Y = Z$ , where $X, Y$ and $Z$ each stand for a distinct digit from $1$ to $9$ . What is the smallest digit that $Z$ could be?

EASY

Mathematics>Arithmetic>Whole Numbers>Properties and Operations on Whole Numbers

Add $16509$ and $114$ and check by reversing the order of the addends.

EASY

Mathematics>Arithmetic>Whole Numbers>Properties and Operations on Whole Numbers

Does an identity element exist in addition of whole numbers? What is it? In which other fundamental operation does an identity element exist? What is it?

EASY

Mathematics>Arithmetic>Whole Numbers>Properties and Operations on Whole Numbers

Match the following columns on whole numbers:

Column A	Column B
(a) $137 + 63 = 63 + 137$	(i) Associativity of multiplication
(b) $(16 \times 25)$ is a whole number	(ii) Commutativity of multiplication
(c) $365 \times 18 = 18 \times 365$	(iii) Distributive law of multiplication over addition
(d) $(86 \times 14) \times 25 = 86 \times (14 \times 25)$	(iv) Commutativity of addition
(e) $23 \times (80 + 5) = (23 \times 80) + (23 \times 5)$	(v) Closure property for multiplication

EASY

Mathematics>Arithmetic>Whole Numbers>Properties and Operations on Whole Numbers

The product of two whole numbers is zero. What do you conclude?

MEDIUM

Mathematics>Arithmetic>Whole Numbers>Properties and Operations on Whole Numbers

Which is greater, the sum of first hundred whole numbers or the product of first hundred whole numbers?

MEDIUM

Mathematics>Arithmetic>Whole Numbers>Properties and Operations on Whole Numbers

A vendor supplies

32 litres

of milk to a hotel in the morning and

68 litres

of milk in the evening. If the milk costs

₹ 15 per litre

how much money is due to the vendor per day.

EASY

Mathematics>Arithmetic>Whole Numbers>Properties and Operations on Whole Numbers

Which of the following is not true ?

MEDIUM

Mathematics>Arithmetic>Whole Numbers>Properties and Operations on Whole Numbers

Match the following:

(i)	$425 \times 136 = 425 \times (6 + 30 + 100)$	(a)	Commutativity under multiplication
(ii)	$2 \times 49 \times 50 = 2 \times 50 \times 49$	(b)	Commutativity under addition
(iii)	$80 + 2005 + 20 = 80 + 20 + 2005$	(c)	Distributivity of multiplication over addition

Write the distributive property of multiplication over subtraction.

Important Questions on Whole Numbers

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