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**Brilliant’s Composite Mathematics Class 6 Solutions Chapter 3 Operations on Whole Numbers**

Welcome to NCTB Solutions. Here with this post we are going to help 6th class students for the Solutions of Brilliant’s Composite Mathematics Class 6 Math Book, Chapter 3, Operations on Whole Numbers. Here students can easily find step by step solutions of all the problems for Operations on Whole Numbers, Exercise 3.1, 3.2, 3.3 and 3.4 Also here our mathematics teacher’s are solved all the problems with easily understandable methods with proper guidance so that all the students can understand easily.

**Operations on Whole Numbers Exercise 3.1 Solution**

**Question no – (1) **

**Solution :**

**(i)** 25 + 58 = 58 + __25__ …[Commutative Property]

**(ii)** 93 + 136 = __93__ + 236 ….[Commutative Property]

**(iii)** 275 + 925 = 275 + __925__ ….[Commutative Property]

**(iv)** 1016 + 1732 = __1016__ + 1732 ….[Commutative Property]

**(v)** 56 + (137 + 963) = (56 + __137__) + 963 ….[Associative law of addition]

**(vi)** 10197 + 0 = __0__ + 10197 = 10197 ….[Additive property of zero]

**(viii)** (222944) + 956 222 + (__956__ + 944) ….[Associative property]

**Question no – (2)**

**Solution :**

No, the sum of two odd number is even number.

**Question no – (3)**

**Solution :**

No, the sum of two odd number is even number.

**Question no – (4)**

**Solution :**

Greatest number of 4 digit = 9999

Least number of 4 digit = 1000

Closure,

= 9999 + 1000

= 10999

Commutative,

= 100 + 9999

= 10999

**Question no – (5)**

**Solution :**

We know,

Greater number of 4 digit is = 9999

Least number of 5 digit is = 10000

**∴** adding = 9999 + 10000

= 19999

= 9999 + 10000

= 10000 999

= 19999 [Commutative]

**Question no – (6) **

**Solution :**

**(i) 178 + 923584;**

= 923584 + 178

= 923762

**(ii) 39784 + 5628;**

= 5028 + 39784

= 45412

**(iii) 591 + 112 + 15409;**

= 591 + (112 + 15409)

= (591 + 112) + 15409

= 16,112

**(iv) 2359 + 641 + 9000;**

= 2359 + (641 + 9000)

= (2359 + 641) + 9000

= 12000

**Question no – (7) **

**Solution :**

**(i) 653 + 747 + 856;**

= (653 + 856) + 747

= 2256

**(ii) 2983 + 1647 + 17 + 453;**

= (2983 + 17) + (1647 + 435)

= 5100

**(iii) 8265 + 1935 + 8773 + 3227;**

= (8265 + 8773) + (1935 + 3227)

= 22200

**(iv) 486 + 78+ 14 + 122 + 53.**

= (486 + 14) + (122 + 78) + 53

= 753

**Question no – (8)**

**Solution :**

= 22 + 28 + 9 + 15 + 16 = 90

= 22 + 29 + 6 + 13 + 20 = 90

= 10 + 18 + 26 + 14 + 22 = 90

= 20 + 10 + 11 + 17 + 23 = 90

= 9 + 11 + 18 + 25 + 27 = 90

= 15 + 17 + 24 + 26 + 8 = 90

= 16 + 23 + 30 + 7 + 14 + 90

Now,

22 | 29 |
6 | 13 | 20 |

28 |
10 | 12 | 19 | 21 |

9 | 11 | 18 | 25 | 27 |

15 | 17 | 24 | 26 | 8 |

16 | 23 |
30 |
7 | 14 |

**Question no – (9)**

**Solution :**

**(i) 5 * 3**

= 10 + 9

= 19

**(ii) 105 * 10**

= 210 + 30

= 240

**(iii) 219 * 25**

= 2 × 219 + 3 × 25

= 438 + 75

= 513

**(iv) 53 * 123**

= 106 + 369

= 475

**(v) 15 * 16**

= 30 + 48

= 78

**(vi) 23 * 33**

= 46 + 99

= 145

**Question no – (10) **

**Solution :**

**(i)** Zero added to a number 23 is the number 32.

= Given statement is **False**

**(ii)** The sum of two odd numbers is always an odd number.

= Given statement is **False**

**(iii)** The sum of two even numbers may be an odd number.

= Given statement is **False**

**(iv)** (15 + 17) + 19 = (17 + 15) + 19.

= Given statement is **True**

**(v)** If a, b, c are any three whole numbers, then (a + b) + c = a + (b + c).

= Given statement is **True**

**Question no – (11)**

**Solution :**

0 + 0 = 0. Is there some other whole number q such that q + q = q

No, such whole number does not exists.

**Operations on Whole Numbers Exercise 3.2 Solution**

**Question no – (1) **

**Solution :**

**(i) 59 – 45 = 14**

addition,

45 + 14

= 59

**(ii) 127 – 37 = 90**

addition,

= 90 + 37

= 127

**(iii) 453 – 356 = 97**

addition,

97 + 365

= 453

**(iv) 9652 – 1732 = 7920**

addition,

7932 + 1732

= 9652

**(v) 100000 – 99755 = 245**

addition,

= 99755 + 245

= 100000

**(vi) 3030301 – 767676 = 2262625**

addition,

2262625 + 767676

= 3030301

**Question no – (2) **

**Solution :**

**(i) (327 – *5) = 3 * 2**

= (327 – 15)

= 312

**(ii) (5376 – ** 57) = 25****

= (5376 = 2857)

= 2519

**(iii) (6000107 – ** 8978) = 506 ******

= (6000107 = 938978)

= 5061129

**(iv) (3941 – ** 78) = 18 ****

= (3941 – 2078)

= 1863

**(v) (14335 – ** 47) = 92****

= (14335 – 5147)

= 9188

**(vi) (1000000 – **** 1) = * 7042 ***

= (100000 = 29571)

= 970429

**Question no – (3)**

**Solution :**

As we know that

Greatest 4 digit number is = 9999

Smallest 5 digit number is = 10000

**∴** The difference will be,

= 10000 – 9999

= 1

**Question no – (4) **

**Solution :**

**(i)** Given, n + 5 = 8;

= n = 8 – 5

= 3

**∴** Here, ‘n’ represented = 3

**(ii)** Given, n + 3 = 19;

= n + 19 – 3

= 16

**∴** Here, ‘n’ represented = 16

**(iii)** Given, n – 5 = 14.

= n = 14 + 5

= 19

∴ Here, ‘n’ represented = 19

**Question no – (5)**

**Solution :**

As we know that,

Largest number of 5 digit = 99999

Smallest number of 6 digit = 100000

∴ The difference will be,

= 10000 – 99999

= 1

**Question no – (6)**

**Solution :**

In the given question,

Prateek deposits = Rs 25, 000

Later he withdrew = Rs 5, 425

**∴** Money left in his account,

= (25000 – 5425)

= 19575 Rs

Thus, Rs 19575 is left in his account.

**Question no – (7)**

**Solution :**

In the question we get,

The total number of men, women and children in a town is 99726.

If men is 36542 and women is 28543

**∴** Number of children,

= 99726 – (36542 + 28543)

= 99726 – 65085

= 34641

Hence, the number of children will be 34641

**Question no – (8)**

**Solution :**

In the question we get,

Amit depositing on Monday = Rs. 45000

On Tuesday he withdrew = Rs. 35450

**∴** Money left in his account,

= (45000 – 35450)

= 9550 Rs.

Thus, in the account of Amit Rs. 9550 was left.

**Question no – (9)**

**Solution :**

Given in the question,

The population of a town was = 65600.

In one year it was increased by = 24196.

However persons died or left = 7936

**∴** Population at the and of the year,

= (65600 + 24196) – 7936

= 89796 – 7936

= 81860

Hence, the population at the end of the year will be 81860

**Question no – (10)**

**Solution :**

According to the question,

Priyanka went to the market with = Rs 12560.

She spent Rs 795 on shoes, Rs 632 on shirts and Rs 939 on jean.

**∴** Money left with Priyanka,

= 12560 – (795 + 632 + 939)

= 12560 2366

= 10194 Rs.

Hence, 10194 Rs is left with Priyanka.

**Question no – (11)**

**Solution :**

From the question we get,

Number should be added to 4739 so that the sum may be 6000

**∴** Number should added,

= 6000 – 4739

= 1261

So, 1261 number should be added.

**Question no – (12)**

**Solution :**

In the given question,

A cooler is marked for = Rs 2540

the dealer allows a discount of = Rs 219

**∴** Net selling price of the colon,

= 2540 – 219

= 2321 Rs.

Thus, the net selling price of the cooler will be 2321 Rs

**Operations on Whole Numbers Exercise 3.3 Solution**

**Question no – (1) **

**Solution :**

**(i)** 129 × 0 = __0__

**(ii)** 534 × 1 = __534__

**(iii)** 643 × 199 = 199 × __643__

**(iv)** 956 × 299 = (__956__ ) × 299

**(v)** 13 × (55 +23) = __(3 × 55)__ + (13 × 23)

**(vi)** 76 × 31+ 76 × 69 = 76 × (__31 + 69__)

**(vii)** 136 × 94 = (136 × 100) 136 × (__6__)

**Question no – (2) **

**Solution :**

**(i)** 23 x 17 is a whole number

= Closure property

**(ii)** 35 × 46 = 46 × 35

= Commutative law

**(iii)** 15 × 1 = 15

= Property of unity

**(iv)** 138 × 0 = 0

= Property of zero

**(v)** (26 × 19) × 105.26 × (19 × 105)

= Associative property

**(vi)** 56 × (18 + 12) = (56 × 18) + (56 × 12)

= Distributive property of multiplication

**(vii)** 96 × (123 -11) = (96 × 123) – (96 × 11)

= Distributive property of multiplication over subtraction

**(viii)** 239 × 49 + 239 × 24 + 239 × 27 = 239 × (49 + 24 + 27)

= Distributive property

**Question no – (4) **

**Solution :**

**(i) 5 × 1956 × 20**

= (5 × 20) × 1956

= 100 × 1956

= 195600

**(ii) 389 × 60 × 15**

= 398 × (60 × 15)

= 398 × 900

= 358200

**(iii) 45 × 80 × 25**

= 45 × (25 × 80)

= 45 × 2000

= 90000

**(vi) 325 × 60 × 50 × 8**

= 325 × 8 × (60 × 50)

= 2600 × 300

= 780000

**Question no – (6)**

**Solution :**

As we know that,

Largest 4 digit number = 9999

Smallest 3 digit number = 999

**∴** The Product will be,

= 999 × 9999 = (1000 – 1) × 9999

= 9999000 – 9999

= 9989001

Hence, the product will be 9989001

**Question no – (7)**

**Solution :**

First, the Sum,

= 53 + 47

= 100

Now, the difference,

= 53 ÷ 47

= 6

**∴** The product will be,

= 100 × 6

= 600

Hence, the product will be 600

**Question no – (8)**

**Solution :**

Let, Two odd number are = 11, 13

**∴** 11

13

———————————-

33

1110

———————————-

1433 (Odd number)

Therefore, It is True.

**Question no – (9)**

**Solution :**

Let, Two even numbers, = 10, 12

= 12 × 10

= 120 (Even)

Again, two ever numbers = 2, 4

= 2 × 4

= 8 (Ever)

So, Yes product of two even number always a even number.

**Question no – (10)**

**Solution :**

If the product of two whole numbers is zero, then, at least one whole number is Zero.

**Question no – (11)**

**Solution :**

We know, that 0 × 0 = 0.

Yes, such number is,

= 1 × 1 = 1

**Question no – (12)**

**Solution :**

According to the question,

A shopkeeper bought 55 chairs and 55 tables.

Table costs Rs 1250 and a chair costs Rs 750,

**∴** The cost of all the items together,

= 55 × (1250 + 750)

= 56 × 2000

= 110000 Rs.

Hence, the cost of all the items together will be 110000 Rs.

**Question no – (13)**

**Solution :**

From the question we get,

A dealer purchased 52 colour and 48 black and white T.V sets.

Colour T.V set is = Rs 7290

Black and white set is = Rs 4125

**∴** The cost of all the set together,

= 52 × 7290 + 48 × 4125

= 379080 + 198000

= 577080 Rs.

Therefore, the cost of all the set together will be Rs. 577080

**Question no – (14)**

**Solution :**

In the question we get,

Section of class in a school total students = 35

Month by charges from each student = Rs 450.

Now,

Hence, Monthly collection will be Rs. 15750

**Question no – (15)**

**Solution :**

According to the question,

A Car moves at a uniform speed of = 67 km per hour.

How many distance it will cover in 94 hours = ?

**∴** Distance will be,

Hence, the car will cover 6298 km.

**Operations on Whole Numbers Exercise 3.4 Solution**

**Question no – (1)**

**Solution :**

We know that, a ÷ b ≠ b ÷ a

Example,

= 6 ÷ 3 = 6/3 = 2

= 3 ÷ 6 = 3/6 = 1/2

**Question no – (2)**

**Solution :**

**(i)** Given, 2371 ÷ 35

Now,

**∴** Quotient = 67

**∴** Remainder = 26

**(ii) 7419 ÷ 25**

Now,

**∴** Quotient = 269

**∴** Remainder = 19

**(iii) 46519 ÷ 127**

Now,

Quotient = 366

Remainder = 37

**(iv) 57691 ÷ 357**

Now,

**∴** Quotient = 161

**∴** Remainder = 214

**(v) 96397 ÷ 400**

Now,

**∴** Quotient = 240

**∴** Remainder = 397

**(vi) 16135 ÷ 735**

Now,

**∴** Quotient = 21

**∴** Remainder = 700

**Question no – (3) **

**Solution :**

**(i) 276 ÷ 7**

= 276 = 38 × 7 + 0

**(ii) 9275 ÷ 23**

= 9275 = 403 × 23 + 6

**(iii) 3765 ÷ 135**

= 3765 = 27 × 136 + 120

**(iv) 32796 ÷ 875**

= 32796 = 875 × 37 + 421

**(v) 4697 ÷ 746**

= 4697 = 6 × 746 + 221

**(vi) 700965 ÷ 937**

= 700965 = 748 × 937 + 89

**Question no – (4) **

**Solution :**

**(i) 3716 ÷ 1**

= 3716/1

= 3716

**(ii) 0 ÷ 271**

= 0/271

= 0

**(iii) 989 + (5760 ÷ 20)**

= 989 + 5760/20

= 989 + 288

= 1277

**(iv) (1775 ÷ 71) – 21**

= 1775/71 – 21

= 25 – 21

= 4

**(v) 32807 ÷ (648 – 29)**

= 32807 ÷ 619

= 53

**(vi) 2573 ÷ 2573 – 4563 ÷ 4563**

= 2573/2573 – 4563/4563

= 1 – 1

= 0

**Question no – (5)**

**Solution :**

Yes → n ÷ 1 = n

**Question no – (6)**

**Solution :**

According to the question,

**∴** 10 should be subtract tor perfect divided.

**Question no – (7)**

**Solution :**

In the given question we get,

Quotient = 63

Remainder = 23,

Divided = 45

**∴** Required Number,

= 63 × 45 + 23

= 2835 + 23

= 2858

Thus, the required number will be 2858

**Question no – (8)**

**Solution :**

According to the question,

**∴** The least number is to be added,

= 65 – 15

= 50

Hence, the least number will be 50

**Question no – (9)**

**Solution :**

As we know that,

Greatest number of 6 digit = 999999

Greatest number of 3 digit = 999

Now,

**∴** Quotient = 1001,

**∴** Remainder = 0

**Question no – (10)**

**Solution :**

In the question we get,

The price of 35 TV sets is 313460

Now,

Therefore, one TV will costs Rs. 8956

**Question no – (11)**

**Solution :**

In the question,

146 apples can be put in a basket.

Baskets will be required to put = 5694 apples

Now,

Thus, 39 baskets will be required.

**Question no – (13)**

**Solution :**

In the question,

least number be subtracted from = 9969

Difference is exactly divisible by = 129

Now,

Therefore, we need subject by 36

**Question no – (14)**

**Solution :**

Given in the question,

The cost of 25 refrigerators is Rs 1,63,500.

The cost of each refrigerator = ?

Now,

**∴** The cost of each refrigerator will be Rs. 6540

**Question no – (15)**

**Solution :**

In the question we get,

The product of two numbers is = 30135

One number is = 123

Other number = ?

Now,

Hence, the other number will be 245

**Question no – (16)**

**Solution :**

In the given question,

Least number must be added to = 1065

Get a number exactly divisible by = 33

Required number = ?

Now,

**∴** least number must be added,

= 33 – 9

= 24

**Question no – (17)**

**Solution :**

From the question we get,

Least number must be subtracted from = 12706

To get a number exactly divisible by = 59

Required number = ?

Now,

Thus, 21 must be subtract tor exactly divisible.

**Question no – (18)**

**Solution :**

According to the question,

The largest 3 digit number exactly divisible by = 26

We know that,

Larger 3 digit number – 999

Now,

**∴** 999 – 11 = 988 is exactly divisible by 26,

**Question no – (19)**

**Solution :**

In the question we get,

9525 trees have been equally planted in = 127 rows.

The number of trees in each row = ?

Now,

**∴** Trees in each row will be 75

**Next Chapter Solution : **