whole number

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Question 1.

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

(i) 378 + 1024 = 1024 + …….

(ii) 337 + (528 + 1164) = (337 + ……..) + 1164

(iii) (21 + 18) + ……….. = (21 + 13) + 18

(iv) 3056 + 0 = ……….. = 0 + 3056

Solution:

(i) 378 + 1024= 1024 + 378 (Commutative property of addition)

(ii) 337 + (528 + 1164) = (337 + 528) + 1164 (Associative law of addition)

(iii) (21 + 18) + 13 = (21 + 13) + 18 (Associative law of addition)

(iv) 3056 + 0 = 3056 = 0 + 3056

 

Question 2.

Add the following numbers and check by reversing the order of addends :

(i) 3189 + 53885

(ii) 33789 + 50311.

Solution:

(i) 3189 + 53885 = 57074

Check 53885 + 3189 = 57074

∴57074

(ii) 33789 + 50311 = 84100

Check 50311 + 33789 = 84100

∴ 84100

Question 3.

By suitable arrangements, find the sum of:

(i) 311,528,289

(ii) 723, 834, 66, 277

(iii) 78, 203, 435, 7197, 422.

Solution:

(i) 311, 528, 289

Sum (311 +289)+ 528

= 600+ 528= 1128

(ii) 723 + 834 + 66 + 277

= (723 + 277) + (834 + 66)

= 1000 + 900 = 1900

(iii) 78, 203, 435, 7197, 422

Sum = (78 + 422) + (203 + 7197) + 435

= 500 + 7400 + 435

= 7900 + 435 = 8335

 

Question 4.

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

(i) 375 × 57 = 57 × ……….

(ii) (33 × 16) × 25 = 33 × (…….. × 25)

(iii) 37 × 24 = 37 × 18 + 37 × …………

(iv) 7205 × 1 = …………. = 1 × 7205

(v) 366 × 0 =

(vi) …………… × 579 = 0

(vii) 473 × 108 = 473 × 100 + 473 × ………….

(viii) 684 × 97 = 684 × 100 – …………… × 3

(ix) 0 ÷= 5 =

(x) (14 – 14) ÷ 7 = ………….

Solution:

(i) 375 × 57 = 57 × 375 (Commutative property of multiplication)

(ii) 33 × 16) × 25 = 33 × (16 × 25) (Associative law of multiplication)

(iii) 37 × 24 = 37 × 18 + 37 × 6 (Distributive law of multiplication)

(iv) 7205 × 1 = 7205 = 1 × 7205

(v) 366 × 0 = 0

(vi) 0 × 579 = 0

(vii) 473 × 108 = 473 × 100 + 473 × 8

(viii) 684 × 97 = 684 × 100 – 684 × 3

(ix) 0 ÷ 5 = 0

(x) (14 – 14) ÷ 7 = 0

Question 5.

Determine the following products by suitable arrangement:

(i) 4 × 528 × 25

(ii) 625 × 239 × 16

(iii) 125 × 40 × 8 × 25

Solution:

(i) 4 × 528 × 25 = 4 × 25 × 528

= 100 × 528 = 52800

(ii) 625 × 239 × 16 = 625 × 16 × 239

= 10000 × 239 = 2390000

(iii) 125 × 40 × 8 × 25 = 125 × 8 × 40 × 25

= 1000 × 1000 = 1000000

Question 6.

Find the value of the following:

(i) 54279 × 92 + 54279 × 8

(ii) 60678 × 262 – 60678 × 162

Solution:

(i) 54279 × 92 + 54279 × 8

= 54279 (92 + 8)

= 54279 × 100 = 5427900

 

(ii) 60678 × 262 – 60678 × 162

= 60678 (262 – 162)

= 60678 × 100 = 6067800

Question 7.

Find the following products by using suitable properties:

(i) 739 × 102

(ii) 1938 × 99

(iii) 1005 × 188

Solution:

(i) 739 × 102

= 739 × (100 + 2)

= 739 × 100 + 739 × 2

= 73900 + 1478 = 75378

(ii) 1938 × 99

= 1938 × (100- 1)

= 1938 × 100 – 1938 × 1

= 193800 – 1938 = 191862

(iii) 1005 × 188

= (1000 + 5) × (100 + 88)

= 1000 × 100 + 1000 × 88 + 5 × 100 + 88 × 5

= 100000 + 88000 + 500 + 440 = 188940

Question 8.

Divide 7750 by 17 and check the result by division algorithm.

Solution:

7750 ÷ 17

On dividing 7750 by 17, we get

Quotient = 455 and Remainder = 15

Check by division algorithm:

Divident = Divisior × Quotient + Remainder

= 17 × 455 + 15 = 7750

Question 9.

Find the number which when divided by 38 gives the quotient 23 and remainder 17.

Solution:

Divisor = 38,Quotient = 23

Remainder = 17

Dividend = divisor × quotient + remainder

= 38 × 23 + 17 = 874 + 17 = 891

 

Question 10.

Which least number should be subtracted from 1000 so that the difference is exactly divisible by 35.

Solution:

On dividing 1000 by 35

we get quotient = 28 and remainder 20

So, 20 should be subtracted from 1000.

Question 11.

Which least number should be added to 1000 so that 53 divides the sum exactly.

Solution:

On dividing 1000 by 53, we get quotient = 18 and remainder = 46. To get the remainder 0, we should add 53 – 46 = 7 to 1000.

∴ 7

Question 12.

Find the largest three-digit number which is exactly divisible by 47.

Solution:

Largest three digit no. = 999

On dividing 999 by 47, we get

Quotient = 21 and Remainder =12

So on subtracting 12 from 999, we get

999 – 12 = 987

Question 13.

Find the smallest five-digit number which is exactly divisible by 254.

Solution:

Smallest 5 digit number = 10000

On dividing 10000 by 254, we get

Remainder = 94

So 254 – 94 = 160 should be added to 10000 to get the smallest 5 digit number divisible by 254.

∴ 10000 + 160 = 10160

Question 14.

A vendor supplies 72 litres of milk to a student’s hostel in the morning and 28 litres of milk in the evening every day. If the milk costs?39 per litre, how much money is due to the vendor per day?

Solution:

Supply of milk in morning = 72 litres

Supply of milk in evening = 28 litres

Cost of per litre milk = ₹ 39

Money of per day = ₹ 39 (72 l + 28 l)

= ₹ 39 × 100 = ₹ 3900

Question 15.

State whether the following statements are true (T) or false (F):

(i) If the product of two whole numbers is zero, then atleast one of them will be zero.

(ii) If the product of two whole numbers is 1, then each of them must be equal to 1.

(iii) If a and b are whole numbers such that a ≠ 0 and b ≠ 0, then ab may be zero.

Solution:

(i) True

(ii) True

(iii)False

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Question 1.

Using shorter method, find

(i) 3246 + 9999

(ii) 7501 + 99999

(iii) 5377 – 999

(iv) 25718 – 9999

(v) 123 × 999

(vi) 203 × 9999

Solution:

(i) 3246 + 9999

= (3246 – 1) + (9999 + 1) (Adding and subtracting 1)

= 3245 + 10000 = 13245

 

(ii) 7501 + 99999

= (7501 – 1) + (99999 + 1) (Adding and subtracting 1)

= 7500+ 100000 = 107500

(iii) 5377 – 999

= 5377 – (1000- 1)

= 5377 – 1000 + 1 = 4377 + 1 = 4378

(iv) 25718 – 9999

= 25718 – (10,000 – 1)

= 15718 + 1 = 15719

(v) 123 × 999

= 123 × (1000 – 1) (By subtracting 1)

= 123 × 1000 – 1 × 123 = 123000 – 123 = 122877

(vi) 203 × 9999

= 203 × (10,000 – 1) (By subtracting 1)

= 203 × 10,000 – 203 × 1 = 2030000 – 203 = 2029797

 

Question 2.

Without using a diagram, find

(i) 9th square number

(ii) 7th triangular number

Solution:

(i) 9th square number = ?

The first square number is 1 × 1 = 1

The second square number is 2 × 2 = 4

The third square number is 3 × 3 = 9

Similarly 9th square number is 9 × 9 = 81

(ii) 7th triangular number = ?

First triangular number = 1

Second triangular number = 1 + 2 = 3

Third triangular number = 1 + 2 + 3 = 6

Fourth triangular number = 1 + 2 + 3 + 4 = 10

Similarly 7th triangular number = 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28

Question 3.

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

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

Solution:

(i) Yes, 9 is a square as well as rectangular number.

(ii) Yes, 8th triangular number = 36, which is a square number.

Question 4.

Observe the following pattern and fill in the blanks:

1 × 9 + 1 = 10

12 × 9 + 2= 110

123 × 9 + 3 = 1110

1234 × 9 + 4 = ……….

12345 × 9 + 5 = …………..

Solution:

1 × 9 + 1 = 10

12 × 9 + 2= 110

123 × 9 + 3 = 1110

1234 × 9 + 4 = 11110

12345 × 9 + 5 = 111110

Question 5.

Observe the following pattern and fill in the blanks:

9 × 9 + 7 = 88

98 × 9 + 6 = 888

987 × 9 + 5 = 8888

9876 x 9 + 4 = …………

98765 × 9 + 3 = ……….

Solution:

9 × 9 + 7 = 88

98 × 9 + 6 = 888

987 × 9 + 5 = 8888

9876 × 9 + 4 = 88888

98765 × 9 + 3 = 888888

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Question 1.

Write next three consecutive whole numbers of the number 9998.

Solution:

The next three consecutive whole number of 9998 are:

9998 + 1 = 9999

9999 + 1 = 10000

10000 + 1 = 10001

∴ Numbers are = 9999, 10000, 10001

 

Question 2.

Write three consecutive whole numbers occurring just before 567890.

Solution:

The three consecutive whole numbers just before 567890 are:

567890 – 1 = 567889 – 1 = 567888 – 1

= 567887

∴ These are : 567889, 567888, 567887

Question 3.

Find the product of the successor and the predecessor of the smallest number of 3-digits.

Solution:

Smallest number of 3-digits = 100

Successor = 100 + 1

Predecessor =100 – 1

∴ Product = 100 + 1 × 100 – 1

= 101 × 99 = 9999

Question 4.

Find the number of whole numbers between the smallest and the greatest numbers of 2-digits.

Solution:

Smallest number of 2-digits = 10

Greatest number of 2-digits = 99

Numbers between 10 and 99

11, 12, …………, 98

= 98 – 10 = 88

Question 5.

Find the following sum by suitable arrangements:

(i) 678 + 1319 + 322 + 5681

(ii) 777 + 546 + 1463 + 223 + 537

Solution:

(i) 678 + 1319 + 322 + 5681

= (678 + 322) + (5681 + 1319)

= 1000 + 7000 = 8000

(ii) 777 + 546 + 1463 + 223 + 537

= (777 + 223) + (1463 + 537) + 546

= 1000 + 2000 + 546 = 3546

 

Question 6.

Determine the following products by suitable arrangements:

(i) 625 × 437 × 16

(ii) 309 × 25 × 7 × 8

Solution:

(i) 625 × 437 × 16

= 437 × (625 × 16)

= 437 × 10000 = 4370000

(ii) 309 × 25 × 7 × 8

= (309 × 7) × (25 × 8)

= 2163 × 200 = 432600

Question 7.

Find the value of the following by using suitable properties:

(i) 236 × 414 + 236 × 563 + 236 × 23

(ii) 370 × 1587 – 37 × 10 × 587

Solution:

(i) 236 × 414 + 236 × 563 + 236 × 23

= 236 × (414 + 563 + 23)

= 236 × (1000) = 236000

(ii) 370 × 1587 – 37 × 10 × 587

= 37 × 10(1587 – 587)

= 370 × 1000 = 370000

Question 8.

Divide 6528 by 29 and check the result by division algorithm.

Solution:

6528 ÷ 29

∴ Quotient = 225

and Remainder = 3

Question 9.

Find the greatest 4-digit number which is exactly divisible by 357.

Solution:

Largest 4 digit number is 9999

Dividing 9999 by 357, we get

Remainder = 3

Subtracting 3 from 9999, 9999 – 3 = 9996,

we get the required number divisible by 357.

So 9996

Question 10.

Find the smallest 5-digit number which is exactly divisible by 279.

Solution:

Smallest 5-digit number is 10000

Dividing it by 279, we get remainder = 235

To make the smallest 5-digit number exactly divisible by 279, we have to add 279 – 235 = 44 in 10000

∴ 10000 + 44 = 10044.