R d sharma mathematics solutions class 6 Solutions for Chapter 4 operations on whole numbers

Fill in the blanks to make each of the following a true statement: (i) 359 + 476 = 476 + …..

(ii) …. + 1952 = 1952 + 2008

(iii) 90758 + 0 = ….

(iv) 54321 + (489 + 699) = 489 + (54321 + …..)

Add each of the following and check by reversing the order of addends: (i) 5628 + 39784

(ii) 923584 + 178

(iii) 15409 + 112

(iv) 2359 + 641

Determine the sum by suitable rearrangements: (i) 953 + 407 + 647

(ii) 15409 + 178 + 591 + 322

(iii) 2359 + 10001 + 2641 + 9999

(iv) 1 + 2 + 3 + 4 + 1996 + 1997 + 1998 + 1999

(v) 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20

Which of the following statements are true and which are false:

(i) The sum of two odd numbers is an odd number.

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

(iii) The sum of two even numbers is an even number.

(iv) The sum of two even numbers is an odd number.

(v) The sum of an even number and an odd number is an odd number.

(vi) The sum of an odd number and an even number is an even number.

(vii) Every whole number is a natural number.

(viii) Every natural number is a whole number.

(ix) There is a whole number which when added to a whole number, gives that number.

(x) There is a natural number which when added to a natural number, gives that number.

(xi) Commutativity and associativity are properties of whole numbers.

(xii) Commutativity and associativity are properties of addition of whole numbers.

A magic square is an array of numbers having the same number of rows and columns and the sumof numbers in each row, column or diagonal being the same. Fill in the blank cells of the following magic squares:

Perform the following subtractions and check your results by performing corresponding additions:

(i) 57839 – 2983

(ii) 92507 – 10879

(iii) 400000 – 98798

(iv) 5050501 – 969696

(v) 200000 – 97531

(vi) 3030301 – 868686

Replace each * by the correct digit in each of the following:

What is the difference between the largest number of five digits and the smallest number of six digits?

Find the difference between the largest number of 4 digits and the smallest number of 7digits.

Rohit deposited Rs 125000 in his savings bank account. Later he withdrew Rs 35425 from it. How much money was left in his account?

The population of a town is 96209. If the number of men is 29642 and that of women is 29167,determine the number of children.

The digits of 6 and 9 of the number 36490 are interchanged. Find the difference between the original number and the new number.

The population of a town was 59000. In one year it was increased by 4536 due to new births.However, 9218 persons died or left the town during the year. What was the population at the end of the year?

Fill in the blanks to make each of the following a true statement:

(i) 785 × 0 = …..

(ii) 4567 × 1 = …..

(iii) 475 × 129 = 129 × …..

(iv) ….. × 8975 = 8975 × 1243

(v) 10 × 100 × …. = 10000

(vi) 27 × 18 = 27 × 9 + 27 × ….. + 27 × 5

(vii) 12 × 45 = 12 × 50 – 12 × …..

(viii) 78 × 89 = 78 × 100 – 78 × ….. + 78 × 5

(ix) 66 × 85 = 66 × 90 – 66 × ….. – 66

(x) 49 × 66 + 49 × 34 = 49 × (….. + …..)

Determine each of the following products by suitable rearrangements:

(i) 2 × 1497 × 50

(ii) 4 × 358 × 25

(iii) 495 × 625 × 16

(iv) 625 × 20 × 8 × 50

Using distributivity of multiplication over addition of whole numbers, find each of the following products:

(i) 736 × 103

(ii) 258 × 1008

(iii) 258 × 1008

Find each of the following products:

(i) 736 × 93

(ii) 816 × 745

(iii) 2032 × 613

Find the values of each of the following using properties:

(i) 493 × 8 + 493 × 2

(ii) 24579 × 93 + 7 × 24579

(iii) 1568 × 184 – 1568 × 84

(iv) 15625 × 15625 – 15625 × 5625

Determine the product of:

(i) the greatest number of four digits and the smallest number of three digits.

(ii) the greatest number of five digits and the greatest number of three digits.

In each of the following, fill in the blanks, so that the statement is true:

(i) (500 + 7) (300 – 1) = 299 × …..

(ii) 888 + 777 + 555 = 111 × …..

(iii) 75 × 425 = (70 + 5) (….. + 85)

(iv) 89 × (100 – 2) = 98 × (100 – …..)

(v) (15 + 5) (15 – 5) = 225 – …..

(vi) 9 × (10000 + …..) = 98766

A dealer purchased 125 colour television sets. If the cost of each set is Rs 19820, determine the cost ofall sets together.

The annual fee charged from a student of class VI in a school is Rs 8880. If there are, in all, 235students in class VI, find the total collection.

A group housing society constructed 350 flats. If the cost of construction for each flat is Rs 993570,what is the total cost of construction of all the flats.

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

What are the whole numbers which when multiplied with itself gives the same number?

In a large housing complex, there are 15 small buildings and 22 large building. Each of the large buildings has 10 floors with 2 apartments on each floor. Each of the small buildings has 12 floors with3 apartments on each floor. How many apartments are there in all.

Does there exist a whole number a such that a ÷ a = a?

Find the value of:

(i) 23457 ÷ 1

(ii) 0 ÷ 97

(iii) 476 + (840 ÷ 84)

(iv) 964 – (425 ÷ 425)

(v) (2758 ÷ 2758) – (2758 ÷ 2758)

(vi) 72450 ÷ (583 – 58)

Which of the following statements are true:

(i) 10 ÷ (5 × 2) = (10 ÷ 5) × (10 ÷ 2)

(ii) (35 – 14) ÷ 7 = 35 ÷ 7 – 14 ÷ 7

(iii) 35 – 14 ÷ 7 = 35 ÷ 7 – 14 ÷ 7

(iv) (20 – 5) ÷ 5 = 20 ÷ 5 – 5

(v) 12 × (14 ÷ 7) = (12 × 14) ÷ (12 × 7)

(vi) (20 ÷ 5) ÷ 2 = (20 ÷ 2) ÷ 5

Divide and check the quotient and remainder:

(i) 7772 ÷ 58

(ii) 6906 ÷ 35

(iii) 16135 ÷ 875

(iv) 16025 ÷ 1000

Find a number which when divided by 35 gives the quotient 20 and remainder 18.

Find the number which when divided by 58 gives a quotient 40 and remainder 31.

The product of two numbers is 504347. If one of the numbers is 1591, find the other.

On dividing 59761 by a certain number, the quotient is 189 and the remainder is 37. Find thedivisor.

On dividing 55390 by 299, the remainder is 75. Find the quotient.

Without drawing a diagram, find

(i) 10th square number

(ii) 6th triangular number

(i) Can a rectangular number also be a square number?

(ii) Can a triangular number also be a square number?

Write the first four products of two numbers with difference 4 starting from in the following order:

1, 2, 3, 4, 5, 6, ………

Identify the pattern in the products and write the next three products.

Observe the pattern in the following and fill in the blanks:

9 × 9 + 7 = 88

98 × 9 + 6 = 888

987 × 9 + 5 = 8888

9876 × 9 + 4 = ………

98765 × 9 + 3 = ………

987654 × 9 + 2 = ……….

9876543 × 9 + 1 = ……….

Observe the following pattern and extend it to three more steps:

6 × 2 – 5 = 7

7 × 3 – 12 = 9

8 × 4 – 21 = 11

9 × 5 – 32 = 13

….. × ……. – ….. = …….

….. × ……. – ….. = …….

….. × ……. – ….. = …….

Study the following pattern:

1 + 3 = 2 × 2

1 + 3 + 5 = 3 × 3

1 + 3 + 5 + 7 = 4 × 4

1 + 3 + 5 + 7 + 9 = 5 × 5

By observing the above pattern, find

(i) 1 + 3 + 5 + 7 + 9 + 11

(ii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15

(iii) 21 + 23 + 25 + ….. + 51

Study the following pattern:

1 × 1 + 2 × 2 = (2 × 3 × 5)/ 6

1 × 1 + 2 × 2 + 3 × 3 = (3 × 4 × 7) / 6

1 × 1 + 2 × 2 + 3 × 3 + 4 × 4 = (4 × 5 × 9)/ 6

By observing the above pattern, write next two steps.

Study the following pattern:

1 = (1 × 2)/ 2

1 + 2 = (2 × 3)/ 2

1 + 2 + 3 = (3 × 4)/ 2

1 + 2 + 3 + 4 = (4 × 5)/ 2

By observing the above pattern, find

(i) 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10

(ii) 50 + 51 + 52 + ……. + 100

(iii) 2 + 4 + 6 + 8 + 10 + ………. + 100