{"id":2145,"date":"2020-12-05T15:57:23","date_gmt":"2020-12-05T15:57:23","guid":{"rendered":"https:\/\/themindpalace.in\/?p=2145"},"modified":"2021-08-26T05:34:16","modified_gmt":"2021-08-26T05:34:16","slug":"whole-number","status":"publish","type":"post","link":"https:\/\/themindpalace.in\/index.php\/2020\/12\/05\/whole-number\/","title":{"rendered":"Whole Number"},"content":{"rendered":"\n

Summary of whole numbers<\/a><\/p>\n\n\n\n

Solved exercise of whole numbers<\/a><\/p>\n\n\n\n

<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

<\/p>\n\n\n\n

Summary<\/h1>\n\n\n\n

The whole numbers are the part of the number system in which it includes all the positive integers from 0 to infinity. These numbers exist in the number line.<\/p>\n\n\n\n

Example: 0, 11, 25, 36, 999, 1200, etc.<\/span><\/strong><\/p>\n\n\n\n

What is predecessor and Successor<\/strong><\/span><\/p>\n\n\n\n

Predecessor: <\/strong> The number which comes before the particular  number<\/p>\n\n\n\n

Example: 5 ,6,7<\/strong><\/p>\n\n\n\n

6 is the predecessor of 7<\/strong><\/span>.<\/p>\n\n\n\n

Successor<\/strong>: The number which comes after a particular number<\/p>\n\n\n\n

Example: 5,6,7<\/strong><\/p>\n\n\n\n

7 is the successor of 6<\/strong><\/span>.<\/p>\n\n\n\n

Addition on the number line:<\/span><\/strong>Is to add a positive number that we move the point to the right of the number line. Similarly to add a negative number implies that we move the point to the left of the number line.<\/p>\n\n\n\n

Example<\/strong><\/p>\n\n\n\n

\"\"<\/figure><\/div>\n\n\n\n

Subtraction on the number line<\/span><\/strong>:Subtraction on the number line is the subtraction of two whole numbers can also be shown on number line.<\/p>\n\n\n\n

Example:<\/strong><\/p>\n\n\n\n

\"\"<\/figure><\/div>\n\n\n\n

Multiplication on the number line<\/span><\/strong>:Multiplication of whole number on the number line.<\/p>\n\n\n\n

Example<\/strong><\/p>\n\n\n\n

\"\"<\/figure><\/div>\n\n\n\n

Properties of whole numbers<\/span><\/strong><\/p>\n\n\n\n

1. Closure property<\/strong>:<\/span> Whole numbers are closed under addition and also under multiplication<\/p>\n\n\n\n

 The collection of whole number is closed under addition this property is known as closure property for addition of whole number.<\/p>\n\n\n\n

Commutativity of addition and multiplication<\/span><\/strong><\/p>\n\n\n\n

Addition is commutation for whole numbers.  This property is known as Commutativity for addition.<\/p>\n\n\n\n

Ex:4+6 and 6+4<\/strong><\/p>\n\n\n\n

Associativity of addition and multiplication<\/strong>:- <\/span>It states that when three or more numbers are added or multiplies the sum is the same regardless of the grouping of the addends .<\/strong><\/p>\n\n\n\n

Example: (2+3)+4=5+4=9<\/strong><\/p>\n\n\n\n

Distributivity of multiplication over addition:<\/span> <\/strong>Can be used when you multiply a number by a sum.<\/p>\n\n\n\n

Example: 3(10+2)=3(12)=36<\/strong><\/p>\n\n\n\n

\n\n\n\n

Exercise 2.1<\/span><\/strong><\/h1>\n\n\n\n

1. Write the next three natural numbers after 10999.<\/span><\/strong><\/p>\n\n\n\n

Ans:The next three natural numbers after 10999 are 11000, 11001 and 11002<\/span><\/p>\n\n\n\n

2. Write the three whole numbers occurring just before 10001.<\/span><\/strong><\/p>\n\n\n\n

Ans:The three whole numbers occurring just before 10001 are 10000, 9999 and 9998<\/span><\/p>\n\n\n\n

3. Which is the smallest whole number?<\/span><\/strong><\/p>\n\n\n\n

Ans:The smallest whole number is 0<\/span><\/p>\n\n\n\n

4. How many whole numbers are there between 32 and 53?<\/span><\/strong><\/p>\n\n\n\n

Ans:The whole numbers between 32 and 53 are<\/span><\/p>\n\n\n\n

(33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52)<\/span><\/p>\n\n\n\n

Hence, there are 20 whole numbers between 32 and 53<\/span><\/p>\n\n\n\n

\n\n\n\n

5. Write the successor of: (a) 2440701 (b) 100199 (c) 1099999 (d) 2345670<\/span><\/strong><\/p>\n\n\n\n

The successors are<\/p>\n\n\n\n

(a) 2440701 + 1 = 2440702<\/span><\/p>\n\n\n\n

(b) 100199 + 1 = 100200<\/span><\/p>\n\n\n\n

(c) 1099999 + 1 = 1100000<\/span><\/p>\n\n\n\n

(d) 2345670 + 1 = 2345671<\/span><\/p>\n\n\n\n

\n\n\n\n

6. Write the predecessor of: (a) 94 (b) 10000 (c) 208090 (d) 7654321<\/span><\/strong><\/p>\n\n\n\n

The predecessors are<\/p>\n\n\n\n

(a) 94 \u2013 1 = 93<\/span><\/p>\n\n\n\n

(b) 10000 \u2013 1 = 9999<\/span><\/p>\n\n\n\n

(c) 208090 \u2013 1 = 208089<\/span><\/p>\n\n\n\n

(d) 7654321 \u2013 1 = 7654320<\/span><\/p>\n\n\n\n

\n\n\n\n

7. In each of the following pairs of numbers, state which whole number is on the left of the other number on the number line. Also write them with the appropriate sign (>, <) between them.<\/span><\/strong><\/p>\n\n\n\n

(a) 530, 503 (b) 370, 307 (c) 98765, 56789 (d) 9830415, 10023001<\/strong><\/p>\n\n\n\n

(a) Since, 530 > 503<\/span><\/p>\n\n\n\n

Hence, 503 is on the left side of 530 on the number line<\/p>\n\n\n\n

(b) Since, 370 > 307<\/span><\/p>\n\n\n\n

Hence, 307 is on the left side of 370 on the number line<\/p>\n\n\n\n

(c) Since, 98765 > 56789<\/span><\/p>\n\n\n\n

Hence, 56789 is on the left side of 98765 on the number line<\/p>\n\n\n\n

(d) Since, 9830415 < 10023001<\/span><\/p>\n\n\n\n

Hence, 9830415 is on the left side of 10023001 on the number line.<\/p>\n\n\n\n

\n\n\n\n

8. Which of the following statements are true (T) and which are false (F)?<\/span><\/strong><\/p>\n\n\n\n

(a) Zero is the smallest natural number.<\/span><\/strong><\/p>\n\n\n\n

Ans:<\/span>False 0 is not a natural number<\/span><\/p>\n\n\n\n

(b) 400 is the predecessor of 399.<\/span><\/strong><\/p>\n\n\n\n

Ans:False The predecessor of 399 is 398 Since, (399 \u2013 1 = 398)<\/span><\/p>\n\n\n\n

(c) Zero is the smallest whole number.<\/span><\/strong><\/p>\n\n\n\n

Ans:True Zero is the smallest whole number<\/span><\/p>\n\n\n\n

(d) 600 is the successor of 599.<\/span><\/strong><\/p>\n\n\n\n

Ans:True Since (599 + 1 = 600)<\/span><\/p>\n\n\n\n

(e) All natural numbers are whole numbers.<\/span><\/strong><\/p>\n\n\n\n

Ans:True All natural numbers are whole numbers<\/span><\/p>\n\n\n\n

(f) All whole numbers are natural numbers.<\/span><\/strong><\/p>\n\n\n\n

Ans:False 0 is a whole number but is not a natural number<\/span><\/p>\n\n\n\n

g) The predecessor of a two digit number is never a single digit number.<\/strong><\/span><\/p>\n\n\n\n

Ans:False Example the predecessor of 10 is 9<\/span><\/p>\n\n\n\n

(h) 1 is the smallest whole number.<\/span><\/strong><\/p>\n\n\n\n

Ans:False 0 is the smallest whole number<\/span><\/p>\n\n\n\n

(i) The natural number 1 has no predecessor.<\/span><\/strong><\/p>\n\n\n\n

Ans:True The predecessor of 1 is 0 but is not a natural number<\/span><\/p>\n\n\n\n

(j) The whole number 1 has no predecessor.<\/span><\/strong><\/p>\n\n\n\n

Ans:False 0 is the predecessor of 1 and is a whole number<\/span><\/p>\n\n\n\n

(k) The whole number 13 lies between 11 and 12.<\/span><\/strong><\/p>\n\n\n\n

Ans:False 13 does not lie between 11 and 12<\/span><\/p>\n\n\n\n

(l) The whole number 0 has no predecessor.<\/span><\/strong><\/p>\n\n\n\n

Ans:True The predecessor of 0 is -1 and is not a whole number<\/span><\/p>\n\n\n\n

(m) The successor of a two digit number is always a two digit number.<\/span><\/strong><\/p>\n\n\n\n

Ans:False As the successor of 99 is 100<\/span><\/p>\n\n\n\n

\n\n\n\n

Exercise 2.2<\/span><\/strong><\/p>\n\n\n\n

1. Find the sum by suitable rearrangement:<\/span><\/strong><\/p>\n\n\n\n

(a) 837 + 208 + 363<\/strong><\/p>\n\n\n\n

(a) Given 837 + 208 + 363<\/p>\n\n\n\n

= (837 + 363) + 208<\/p>\n\n\n\n

= 1200 + 208<\/p>\n\n\n\n

= 1408<\/span><\/strong><\/p>\n\n\n\n

(b) 1962 + 453 + 1538 + 647<\/strong><\/p>\n\n\n\n

Given 1962 + 453 + 1538 + 647<\/strong><\/p>\n\n\n\n

= (1962 + 1538) + (453 + 647)<\/p>\n\n\n\n

= 3500 + 1100<\/p>\n\n\n\n

= 4600<\/span><\/p>\n\n\n\n

\n\n\n\n

2. Find the product by suitable rearrangement<\/span><\/strong><\/p>\n\n\n\n

(a) 2 \u00d7 1768 \u00d7 50<\/strong><\/p>\n\n\n\n

Given 2 \u00d7 <\/strong>1768 \u00d7 <\/strong>50<\/p>\n\n\n\n

= 2 \u00d7 50 \u00d7 1768<\/p>\n\n\n\n

= 100 \u00d7 1768<\/p>\n\n\n\n

= 176800<\/span><\/p>\n\n\n\n

\n\n\n\n

(b) 4 \u00d7 166 \u00d7 25<\/strong><\/p>\n\n\n\n

(b) Given 4 \u00d7 166 \u00d7 25<\/p>\n\n\n\n

= 4 \u00d7 25 \u00d7 166<\/p>\n\n\n\n

= 100 \u00d7 166<\/p>\n\n\n\n

= 16600<\/span><\/p>\n\n\n\n

\n\n\n\n

(c) 8 \u00d7 291 \u00d7 125<\/strong><\/p>\n\n\n\n

Given 8 \u00d7 291 \u00d7 125<\/p>\n\n\n\n

= 8 \u00d7 125 \u00d7 291<\/p>\n\n\n\n

= 1000 \u00d7 291<\/p>\n\n\n\n

= 291000<\/span><\/p>\n\n\n\n

\n\n\n\n

(d) 625 \u00d7 279 \u00d7 16<\/strong><\/p>\n\n\n\n

Given 625 \u00d7 279 \u00d7 16<\/p>\n\n\n\n

= 625 \u00d7 16 \u00d7 279<\/p>\n\n\n\n

= 10000 \u00d7 279<\/p>\n\n\n\n

= 2790000<\/span><\/p>\n\n\n\n

\n\n\n\n

(e) 285 \u00d7 5 \u00d7 60<\/strong><\/p>\n\n\n\n

Given 285 \u00d7 5 \u00d7 60<\/p>\n\n\n\n

= 285 \u00d7 300<\/p>\n\n\n\n

= 85500<\/span><\/p>\n\n\n\n

\n\n\n\n

(f) 125 \u00d7 40 \u00d7 8 \u00d7 25<\/strong><\/p>\n\n\n\n

Given 125 \u00d7 40 \u00d7 8 \u00d7 25<\/p>\n\n\n\n

= 125 \u00d7 8 \u00d7 40 \u00d7 25<\/p>\n\n\n\n

= 1000 \u00d7 1000<\/p>\n\n\n\n

= 1000000<\/span><\/p>\n\n\n\n

\n\n\n\n

3. Find the value of the following:<\/span><\/strong><\/p>\n\n\n\n

(a) 297 \u00d7 17 + 297 \u00d7 3<\/strong><\/p>\n\n\n\n

Given 297 \u00d7 17 + 297 \u00d7 3<\/p>\n\n\n\n

= <\/strong>297 \u00d7 (17 + 3)<\/p>\n\n\n\n

= 297 \u00d7 20<\/p>\n\n\n\n

= 5940<\/p>\n\n\n\n

\n\n\n\n

(b) 54279 \u00d7 92 + 8 \u00d7 54279<\/strong><\/p>\n\n\n\n

Given 54279 \u00d7 92 + 8 \u00d7 54279<\/p>\n\n\n\n

= 54279 \u00d7 92 + 54279 \u00d7 8<\/p>\n\n\n\n

= 54279 \u00d7 (92 + 8)<\/p>\n\n\n\n

= 54279 \u00d7 100<\/p>\n\n\n\n

= 5427900<\/p>\n\n\n\n

\n\n\n\n

(c) 81265 \u00d7 169 \u2013 81265 \u00d7 69<\/strong><\/p>\n\n\n\n

Given 81265 \u00d7 169 \u2013 81265 \u00d7 69<\/p>\n\n\n\n

= <\/strong>81265 \u00d7 (169 \u2013 69)<\/p>\n\n\n\n

= 81265 \u00d7 100<\/p>\n\n\n\n

= 8126500<\/p>\n\n\n\n

\n\n\n\n

(d) 3845 \u00d7 5 \u00d7 782 + 769 \u00d7 25 \u00d7 218<\/strong><\/p>\n\n\n\n

Given 3845 \u00d7 5 \u00d7 782 + 769 \u00d7 25 \u00d7 218<\/p>\n\n\n\n

= 3845 \u00d7 5 \u00d7 782 + 769 \u00d7 5 \u00d7 5 \u00d7 218<\/p>\n\n\n\n

= 3845 \u00d7 5 \u00d7 782 + 3845 \u00d7 5 \u00d7 218<\/p>\n\n\n\n

= 3845 \u00d7 5 \u00d7 (782 + 218)<\/p>\n\n\n\n

= 19225 \u00d7 1000<\/p>\n\n\n\n

= 19225000<\/p>\n\n\n\n

\n\n\n\n

4. Find the product using suitable properties.<\/strong><\/p>\n\n\n\n

(a) 738 \u00d7 103<\/strong><\/p>\n\n\n\n

(a) Given 738 \u00d7 103<\/p>\n\n\n\n

= 738 \u00d7 (100 + 3)<\/p>\n\n\n\n

= 738 \u00d7 100 + 738 \u00d7 3 (using distributive property)<\/p>\n\n\n\n

= 73800 + 2214<\/p>\n\n\n\n

= 76014<\/p>\n\n\n\n

\n\n\n\n

(b) 854 \u00d7 102<\/strong><\/p>\n\n\n\n

Given 854 \u00d7 102<\/p>\n\n\n\n

= 854 \u00d7 (100 + 2)<\/p>\n\n\n\n

= 854 \u00d7 100 + 854 \u00d7 2 (using distributive property)<\/p>\n\n\n\n

= 85400 + 1708<\/p>\n\n\n\n

= 87108<\/p>\n\n\n\n

\n\n\n\n

(c) 258 \u00d7 1008<\/strong><\/p>\n\n\n\n

Given 258 \u00d7 1008<\/p>\n\n\n\n

= 258 \u00d7 (1000 + 8)<\/p>\n\n\n\n

= 258 \u00d7 1000 + 258 \u00d7 8 (using distributive property)<\/p>\n\n\n\n

= 258000 + 2064<\/p>\n\n\n\n

= 260064<\/p>\n\n\n\n

\n\n\n\n

(d) 1005 \u00d7 168<\/strong><\/p>\n\n\n\n

Given 1005 \u00d7 168<\/p>\n\n\n\n

= (1000 + 5) \u00d7 168<\/p>\n\n\n\n

= 1000 \u00d7 168 + 5 \u00d7 168 (using distributive property)<\/p>\n\n\n\n

= 168000 + 840<\/p>\n\n\n\n

= 168840<\/p>\n\n\n\n

\n\n\n\n

5. A taxi driver filled his car petrol tank with 40 litres of petrol on Monday. The next day, he filled the tank with 50 litres of petrol. If the petrol costs \u20b9 44 per litre, how much did he spend in all on petrol?<\/strong><\/p>\n\n\n\n

Petrol quantity filled on Monday = 40 litres<\/p>\n\n\n\n

Petrol quantity filled on Tuesday = 50 litres<\/p>\n\n\n\n

Total petrol quantity filled = (40 + 50) litre<\/p>\n\n\n\n

Cost of petrol per litre = \u20b9 44<\/p>\n\n\n\n

Total money spent = 44 \u00d7 (40 + 50)<\/p>\n\n\n\n

= 44 \u00d7 90<\/p>\n\n\n\n

= \u20b9 3960<\/span><\/strong><\/p>\n\n\n\n

\n\n\n\n

6. 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 \u20b9 45 per litre, how much money is due to the vendor per day?<\/strong><\/p>\n\n\n\n

Milk quantity supplied in the morning = 32 litres<\/p>\n\n\n\n

Milk quantity supplied in the evening = 68 litres<\/p>\n\n\n\n

Cost of milk per litre = \u20b9 45<\/p>\n\n\n\n

Total cost of milk per day = 45 \u00d7 (32 + 68)<\/p>\n\n\n\n

= 45 \u00d7 100<\/p>\n\n\n\n

= \u20b9 4500<\/p>\n\n\n\n

Hence, the money is due to the vendor per day is \u20b9 4500<\/strong><\/span><\/p>\n\n\n\n

\n\n\n\n

7. Match the following:<\/span><\/strong><\/p>\n\n\n\n

425 \u00d7 136 = 425 \u00d7 (6 + 30 + 100)<\/strong><\/td> Distributivity of multiplication over addition.<\/strong>  <\/td><\/tr>
 2 \u00d7 49 \u00d7 50 = 2 \u00d7 50 \u00d7 49<\/strong><\/td>Commutativity under multiplication  <\/td><\/tr>
80 + 2005 + 20 = 80 + 20 + 2005<\/strong><\/td>Commutativity under addition  <\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
\n\n\n\n

Exercise 2.3<\/strong><\/span><\/p>\n\n\n\n

Which of the following will not represent zero?<\/strong><\/p>\n\n\n\n

(a) 1 + 0<\/strong><\/p>\n\n\n\n

Ans: 1 + 0 = 1 Hence, it does not represent zero<\/p>\n\n\n\n

<\/p>\n\n\n\n

\n\n\n\n

(b) 0 \u00d7 0<\/strong><\/p>\n\n\n\n

Ans: 0 \u00d7 0 = 0 Hence, it represents zero<\/p>\n\n\n\n

\n\n\n\n

(c) 0 \/ 2<\/strong><\/p>\n\n\n\n

\n\n\n\n

Ans:0 \/ 2 = 0<\/p>\n\n\n\n

Hence, it represents zero<\/p>\n\n\n\n

\n\n\n\n

(d) (10 \u2013 10) \/ 2<\/strong><\/p>\n\n\n\n

Ans:(10 \u2013 10) \/ 2 = 0 \/ 2 = 0 Hence, it represents zero<\/span><\/p>\n\n\n\n

\n\n\n\n

2. If the product of two whole numbers is zero, can we say that one or both of them will be zero? Justify through examples.<\/strong><\/p>\n\n\n\n

If product of two whole numbers is zero, definitely one of them is zero<\/p>\n\n\n\n

Example: 0 \u00d7 3 = 0 and 15 \u00d7 0 = 0<\/p>\n\n\n\n

If product of two whole numbers is zero, both of them may be zero<\/p>\n\n\n\n

Example: 0 \u00d7 0 = 0<\/p>\n\n\n\n

Yes, if the product of two whole numbers is zero, then both of them will be zero<\/span><\/p>\n\n\n\n

\n\n\n\n

3. If the product of two whole numbers is 1, can we say that one or both of them will be 1? Justify through examples<\/strong><\/p>\n\n\n\n

If the product of two whole numbers is 1, both the numbers should be equal to 1<\/p>\n\n\n\n

Example: 1 \u00d7 1 = 1<\/p>\n\n\n\n

But 1 \u00d7 5 = 5<\/p>\n\n\n\n

Hence, its clear that the product of two whole numbers will be 1, only in situation when both numbers to be multiplied are 1<\/span><\/p>\n\n\n\n

\n\n\n\n

4. Find using distributive property:<\/span><\/strong><\/p>\n\n\n\n

(a) 728 \u00d7 101<\/strong><\/p>\n\n\n\n

Given 728 \u00d7 101<\/p>\n\n\n\n

= <\/strong>728 \u00d7 (100 + 1)<\/p>\n\n\n\n

= 728 \u00d7 100 + 728 \u00d7 1<\/p>\n\n\n\n

= 72800 + 728<\/p>\n\n\n\n

= 73528<\/span><\/strong><\/p>\n\n\n\n

\n\n\n\n

(b) 5437 \u00d7 1001<\/strong><\/p>\n\n\n\n

Given 5437 \u00d7 1001<\/p>\n\n\n\n

= 5437 \u00d7 (1000 + 1)<\/p>\n\n\n\n

= 5437 \u00d7 1000 + 5437 \u00d7 1<\/p>\n\n\n\n

= 5437000 + 5437<\/p>\n\n\n\n

= 5442437<\/span><\/strong><\/p>\n\n\n\n

\n\n\n\n

(c) 824 \u00d7 25<\/strong><\/p>\n\n\n\n

Given 824 \u00d7 25<\/p>\n\n\n\n

= (800 + 24) \u00d7 25<\/p>\n\n\n\n

= (800 + 25 \u2013 1) \u00d7 25<\/p>\n\n\n\n

= 800 \u00d7 25 + 25 \u00d7 25 \u2013 1 \u00d7 25<\/p>\n\n\n\n

= 20000 + 625 \u2013 25<\/p>\n\n\n\n

= 20000 + 600<\/p>\n\n\n\n

= 20600<\/span><\/strong><\/p>\n\n\n\n

\n\n\n\n

(d) 4275 \u00d7 125<\/strong><\/p>\n\n\n\n

Given 4275 \u00d7 125<\/p>\n\n\n\n

= (4000 + 200 + 100 \u2013 25) \u00d7 125<\/p>\n\n\n\n

= (4000 \u00d7 125 + 200 \u00d7 125 + 100 \u00d7 125 \u2013 25 \u00d7 125)<\/p>\n\n\n\n

= 500000 + 25000 + 12500 \u2013 3125<\/p>\n\n\n\n

= 534375<\/span><\/p>\n\n\n\n

\n\n\n\n

(e) 504 \u00d7 35<\/strong><\/p>\n\n\n\n

Given 504 \u00d7 35<\/p>\n\n\n\n

= (500 + 4) \u00d7 35<\/p>\n\n\n\n

= 500 \u00d7 35 + 4 \u00d7 35<\/p>\n\n\n\n

= 17500 + 140<\/p>\n\n\n\n

= 17640<\/span><\/strong><\/p>\n\n\n\n

\n\n\n\n

<\/p>\n\n\n\n

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